Answer:
100 in²
Step-by-step explanation:
4 triangles, each of them has area = 10*5/2
so total area = (10*5/2)*4
= (10*5*2)
= 100 in²
Answered by GAUTHMATH
The lateral surface area of the pyramid is 100 in²
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
The pyramid has four triangular faces and one rectangular base we need to calculate the lateral surface area so we will calculate the area of the four triangles and sum up all the triangles.
4 triangles, each of them has an area = 10 x ( 5/2 )
So total area = (10 x 5/2) x 4
Total area = (10 x 5 x 2)
Total area = 100 in²
Therefore the lateral surface area of the pyramid is 100 in²
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The automatic opening device of a military cargo parachute has been designed to open when the parachute is 185 m above the ground. Suppose opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m. Equipment damage will occur if the parachute opens at an altitude of less than 100 m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes
Answer:
0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.
Step-by-step explanation:
For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.
To find the probability of damage on a parachute, the normal distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Probability of a parachute having damage.
The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that [tex]\mu = 185, \sigma = 32[/tex]
Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of Z when X = 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 185}{32}[/tex]
[tex]Z = -2.66[/tex]
[tex]Z = -2.66[/tex] has a p-value of 0.0039.
What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?
0.0039 probability of a parachute having damage, which means that [tex]p = 0.0039[/tex]
5 parachutes, which means that [tex]n = 5[/tex]
This probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193[/tex]
0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.
Which equation is in standard form?
a. X +3= -5y
b. 5-y=x
c. y =3x + 6
d. -8x+ 3y = 12
选项 (d)
option (d)
!!!!!!!!!
Power Function:
Consider the following graphs (1 and 2), and answer the questions FOR EACH GRAPH:
A) In what interval of the graph is it increasing, decreasing and constant? This answer must be justified by means of the definition
B) What is the domain and range?
C) Is it an odd or even function? This answer must be justified by means of the definition
Graph 1
Part (a)
The function is increasing when x > 0. The function is decreasing when x < 0.
The function is never constant
An increasing portion is when the graph goes uphill when moving left to right. A decreasing portion goes in the opposite direction: it goes downhill when moving left to right.
The reason why the function is never constant is because there aren't any flat horizontal sections. Such sections are when x changes but y does not. No such sections occur.
------------------------
Graph 1
Part (b)
Domain = set of all real numbers
Range = set of y values such that [tex]y \ge 0[/tex]
The domain is the set of all real numbers because we can plug in any value for x without any restriction. There are no division by zero errors to worry about, or square roots of negative numbers to worry about either.
The range is the set of nonnegative numbers as the graph indicates. The lowest y gets is y = 0.
------------------------
Graph 1
Part (c)
The function is even
The function f(x) = 1.6x^12 is an even function due to the even number exponent. For any polynomial, as long as the exponents are all even, then the function itself is even. If all the exponents were odd, then the function would be odd. This applies to polynomials only. A power function is a specific type of polynomial.
Note in the graph, we have y axis symmetry. The mirror line is vertical and placed along the y axis. This is a visual trait of any even function.
We could use algebra to show that f(-x) = f(x) like so
f(x) = 1.6x^12
f(-x) = 1.6(-x)^12
f(-x) = 1.6x^12
The third step is possible because (-x)^12 = x^12 for all real numbers x. It's similar to how (-x)^2 = x^2. You could think of it like (-1)^2 = (1)^2
============================================================
Graph 2
Part (a)
The function is decreasing when x < 0 and when x > 0
The function is never increasing
The function is never constant
In other words, the function is decreasing over the entire domain (see part b). The only time it's not decreasing is when x = 0.
The function is decreasing because the curve is going downhill when moving to the right. You can think of it like a roller coaster of sorts.
At no point of this curve goes uphill when moving to the right. Therefore, it is never increasing. The same idea applies to flat horizontal sections, so there are no constant intervals either.
------------------------
Graph 2
Part (b)
Domain: x is any real number but [tex]x \ne 0[/tex]
Range: y is any real number but [tex]y \ne 0[/tex]
Explanation: If we tried plugging x = 0 into the function, we get a division by zero error. This doesn't happen with any other number. Therefore, the set of allowed inputs is any number but 0.
The range is a similar story. There's no way to get y = 0 as an output.
If we plugged y = 0 into the equation, then we'd get this
y = 17x^(-3)
0 = 17/(x^3)
There's no way to have the right hand side turn into 0. The numerator is 17 and won't change. Only the denominator changes. We can't have the denominator be 0.
------------------------
Graph 2
Part (c)
The function is odd
We can prove this by showing that f(-x) = -f(x)
f(x) = 17x^(-3)
f(-x) = 17(-x)^(-3)
f(-x) = 17* ( -(x)^(-3) )
f(-x) = -17x^(-3)
f(-x) = -f(x)
This is true for nearly all real numbers x, except we can't have x = 0.
Graphic 1:
(A) If f(x) = 1.6x ¹², then f '(x) = 19.2x ¹¹. Both f '(x) and x have the same sign, which means
• for -∞ < x < 0, we have f '(x) < 0, so that f(x) is decreasing on this interval
• for 0 < x < ∞, we have f '(x) > 0, so f(x) is increasing on this interval
f(x) is not constant anywhere on its domain.
(B) Speaking of domain, since f(x) is a polynomial (albeit only one term), it has
• a domain of all real numbers
• a range of {y ∈ ℝ : y = f(x) and y ≥ 0} (in other words, all real numbers y such that y = 1.6x ¹² and y is non-negative)
(C) This function is even, since
f(-x) = 1.6 (-x)¹² = (-1)¹² × 1.6x ¹² = 1.6x ¹² = f(x)
Graphic 2:
(A) Now if f(x) = 17/x ³, then f '(x) = -51/x ⁴. Because x ⁴ ≥ 0 for all x, this means f '(x) < 0 everywhere, except at x = 0. So f(x) is decreasing for (-∞ < x < 0) U (0 < x < ∞).
(B) f(x) has
• a domain of {x ∈ ℝ : x ≠ 0} (or all non-zero real numbers)
• a range of {y ∈ ℝ : y = f(x) and y ≠ 0} (also all non-zero reals)
(C) This function is odd:
f(-x) = 17/(-x)³ = 1/(-1)³ × 17/x ³ = -17/x ³ = -f(x)
What is the distance between the following points?
WILL GIVE BRAINLIEST
Answer:
D.√85
Step-by-step explanation:
We can find the distance between two points using the distance between two points formula
Distance between two points formula:
d = √(x2 - x1)² + (y2 - y1)²
Where the x and y values are derived from the given points
We are given the two points (-2,7) and (7,9)
Using these points let's define the variables ( variables are x1, x2, y1, and y2)
Remember points are written as follows (x,y)
The x value of the first point is -2 so x1 = -2
The x value of the second point is 7 so x2 = 7
The y value of the first point is 7 so y1 = 7
The y value of the second point is 9 so y2 = 9
Now that we have defined each variable let's find the distance between the two points
We can do this by substituting the values into the formula
Formula: d = √(x2 - x1)² + (y2 - y1)²
Variables: x1 = -2, x2 = 7, y1 = 7, y2 = 9
Substitute values in formula
d = √(7 - (-2))² + (9 - 7)²
Evaluation:
The two negative signs cancel out on 7-(-2) and it changes to +7
d = √ (7+2)² + (9-7)²
Add 7+2 and subtract 9 and 7
d = √ (9)² + (2)²
Simplify exponents 9² = 81 and 2² = 4
We then have d = √ 81 + 4
Finally we add 81 and 4
We get that the distance between the two points is √85
I need help on this plzzz I and not the best at math
Answer:
See attachment for graph
Step-by-step explanation:
Given
[tex]f(x) = \left[\begin{array}{cc}-1&x<-1\\0&-1\le x \le -1\\1&x>1\end{array}\right[/tex]
Required
The graph of the step function
Before plotting the graph, it should be noted that:
[tex]\le[/tex] and [tex]\ge[/tex] use closed circle at its end
[tex]<[/tex] and [tex]>[/tex] use open circle at its end
So, we have:
[tex]f(x) = -1,\ \ \ \ x < -1[/tex]
The line stops at -1 with an open circle
[tex]f(x) = 0,\ \ \ \ -1 \le x \le 1[/tex]
The line starts at - 1 and stops at -1 with a closed circle at both ends
[tex]f(x) = 1,\ \ \ \ x > 1[/tex]
The line starts at 1 with an open circle
The options are not complete, so I will plot the graph myself.
See attachment for graph
11 10 Find the area of the shaded region. Round your answer to the nearest tenth.
if x and y are linear pair of angel then x +y=
Answer: x + y = 180²
Step-by-step explanation:
A linear pair is a pair of adjacent, supplementary angles.
Adjacent means next to each other.
Supplementary means that the measures of the two angles add up to equal 180 degrees.
Therefore, by definition, if x and y are linear pairs of angles, then x + y = 180.
5. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true negative numbers will _____________________ . (5 points)
Answer:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase
Step-by-step explanation:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase.
Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. If 390 tickets were sold for a total of $2190.00, how many student tickets were sold
Answer: Therefore 100 student tickets were sold
Step-by-step explanation:
Let the number of student tickets be x
So adult tickets = 390 - x
ATQ
4.5(x) + 6(390-x) = 2190
4.5x + 2340 - 6x = 2190
-1.5x + 2340 = 2190
-1.5x = 2190-2340
-1.5x = -150
x = -150/-1.5
x = 100
Therefore 100 student tickets were sold
please click thanks and mark brainliest if you like :)
The length L of the base of a rectangle is 5 less than twice its height H. Write the algebraic expression to model the area of the rectangle.
Answer:
Area of rectangle = 2H² - 5H
Step-by-step explanation:
Let the length be L.Let the height be H.Translating the word problem into an algebraic expression, we have;
Length =2H - 5
To write the algebraic expression to model the area of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = L * H
Where;
L is the Length.H is the Height.Substituting the values into the formula, we have;
Area of rectangle = (2H - 5)*H
Area of rectangle = 2H² - 5H
a number has 7 at the tens place .there is zero in the thousand place. the number 5 is at the hundreds place .there is number 1at the ten thousand place..what is the number?
how many ways can this be done. if a committee of 5 people from 7 men and 8 women?
Answer:
3003 ways
Step-by-step explanation:
(7+8)C5
= 15C5
= 15!/(5!10!)
= 3003
Write the point-slope form of an equation of the line through the points (-1, 4) and (-2, 2).
Answer:
Point-slope form: y-4=2(x+1)
Slope intercept form: y=2x+6
I hope this helps!
Answer:
[tex]y-4=2(x+1)[/tex]
Step-by-step explanation:
Point-slope form is equal to
[tex]y-y_1=m(x-x_1)[/tex]
where y and y1 are the known y coordinates of two points on the line, and x and x1 are the known x coordinates of two points on the line. All we need now is m, which is the slope:
[tex]4-2=m(-1-(-2))[/tex]
We can simplify negative one minus negative two as positive 1.
[tex]4-2=m(1)[/tex]
4 minus 2 is 2, so m times 1 is 2. That means m is 2.
Now, we have the slope, so we can convert to point-slope form using one of the two points. Let's use (-1, 4). We can plug those values in for x1 and y1:
[tex]y-4=2(x+1)[/tex]
HELP WILL GIVE BRAINLYIST
Answer:
The parent cubic function has been vertically stretched by a factor of 4.
Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]
Answer: Option B
OAmalOHopeO
[tex]2i+3x=4-ix[/tex]
Show work.
No wrong answers or you will be reported. I will mark Brainliest! Thank you!
Answer:
Step-by-step explanation:
I am assuming i is the imaginary number:
Factor:
(3 + i)x - (4-2i) = 0.
In order for this to equal 0, x must be equal to 1-i.
I don't want to be reported to so take my word for it.
Also I plugged it into wolfram alpha so if it is wrong, blame the most powerful math equation solver available on the internet.
Using BTS he properties, find the unit's digit of the cube of each of the following numbers
what are the factor of pair of number?
a.45 and 60
b.45 and 70
c.40 and 80
d.30 and 50
PLEASE gelp me with this, gelp me please oh please gelp me!
Answer:
V = 2143.57 cm^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
The diameter is 16 so the radius is 1/2 of the diameter or 8
V = 4/3 ( 3.14) (8)^3
V =2143.57333
Rounding to the nearest hundredth
V = 2143.57 cm^3
Answer:
2143.57 cm^3
Step-by-step explanation:
V = 4/3 * 3.14 * r^3
r = 1/2 * 16 = 8
So V = 4/3 * 3.14 * 8^3
= 2143.57 cm^3.
please help me with geometry
Answer:
x = 7
Explaination:
ABC = 40°
and BD bisects the angle so ABD = 20°
so 3x-1=20
solving for x gets us
x = 7
If a ∥ b and b ⊥ y, then _____
Answer:
a ⊥ y
Step-by-step explanation:
since b is parallel to a & perpendicular to y , line y will eventually cut across line a at a 90 degree angle as well
Answer:
a ⊥ y
Step-by-step explanation:
Look at the image given below.
Find the missing segment in the image below
Answer:
x = 42
Step-by-step explanation:
24+8 = 32
[tex]\frac{x}{24}[/tex] = [tex]\frac{x+14}{32}[/tex]
32x = 24(x+14)
32x = 24x+336
8x = 336
x = 42
The measurements of a circular object are given in the ratio table.
a. Find the missing dimensions of other circular objects by completing the ratio table.
b. Graph the pairs of values.
Answer:
answer hajandtb Tj.yfs5bsyb
OLVE
(a) 3^2x+1=9^
2x-1
Answer:
x=2
Step-by-step explanation:
you first have to make the bases the same
3^2x+1=9^2x-1
3^2x+1=3^2(2x-1) if you make the bases the same you will use 3^2 because it's equal to 9
3^2x+1=3^4x-2
2x+1=4x-2
2x-4x=-2-1
-2x/-2=-4/-2
x=2
I hope this helps
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2
= 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance σ2 = 83.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Use the traditional method. Assume that a simple random sample is selected from a normally distributed population.
a. Check requirements.
b. Establish H0 and H1 and note the level of significance.
c. Find the sample test statistic.
d. Find Critical Value.
e. Conclude the test and interpret results.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
The hypothesis :
H0 : σ²= 47.1
H1 : σ² > 47.1
α = 5% = 0.05
Population variance, σ² = 47.1
Sample variance, s² = 83.2
Sample size, n = 15
The test statistic = (n-1)*s²/σ²
Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1
Test statistic = T = [(14 * 83.2)] * 47.1
Test statistic = 1164.8 / 47.1
Test statistic = 24.73
The degree of freedom, df = n - 1 ; 10 = 9
Critical value (0.05, 9) = 16.92 (Chisquare distribution table)
Reject H0 ; If Test statistic > Critical value
Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.
For each of the following angles, assume that the terminal ray of the angle opens up in the counter-clockwise direction. A circle with a radius 7 cm long is centered at Angle A's vertex, and Angle A subtends an arc length of 9.8 cm along this circle. The subtended arc is how many times as long as the circle's radius
9514 1404 393
Answer:
1.4
Step-by-step explanation:
We want to find the multiplier n such that ...
arc length = n × radius
n = arc length / radius = (9.8 cm)/(7 cm)
n = 1.4
The subtended arc is 1.4 times as long as the circle's radius.
Một cuộc điều tra tại một đô thị cho kết quả: 20% dân số dùng một loại sản phẩm A, 50% dân số
dùng một loại sản phẩm B, 15% dân số dùng cả hai loại A và B. Chọn ngẫu nhiên một người dân
trong đô thị đó, tìm xác suất để:
a. Người đó dùng sản phẩm A hoặc B.
b. Người đó không dùng sản phẩm A cũng không dùng sản phẩm B.
c. Người đó chỉ dùng đúng một trong hai loại sản phẩm A hoặc B.
d. Người đó chỉ dùng duy nhất sản phẩm A.
Put 1.09, 1.0, 1.9, 1.19, 1.1 on a number line in order?
Answer:
1.0, 1.09, 1.1, 1.19, 1.9
Step-by-step explanation:
Basic ordering of decimals
Jordan buys sandals and sunglasses for a trip to the beach. The sunglasses cost $6. The sandals cost 3 times as much as the sunglasses. How much do the sandals cost?
Answer:
18 dollars
Step-by-step explanation:
sunglasses = 6 dollars
sandals = 3 * sunglasses
= 3 * 6 dollars
= 18 dollars
The weight of an object above the surface of the Earth varies inversely with the square of the
distance from the center of the Earth. If a body weighs 50 pounds when it is 3,960 miles from
Earth's center, what would it weigh if it were 4,015 miles from Earth's center?
Answer:
weight =48.71228786pounds
Step-by-step explanation:
[tex]w = \frac{k}{ {d}^{2} } \\ 50 = \frac{k}{ {3960}^{2} } \\ \\ k = 50 \times {3960}^{2} \\ k = 50 \times 15681600 \\ k = 784080000 \\ \\ w = \frac{784080000}{ {d}^{2} } \\ w = \frac{784080000}{16120225} \\ \\ w = 48.71228786 \\ w = 48.7pounds[/tex]
If a body weighs 50 pounds when it is 3,960 miles from Earth's center, it would weigh approximately 48.547 pounds if it were 4,015 miles from Earth's center, according to the inverse square law formula.
We know the inverse square law formula:
W₁ / W₂ = D²₂ / D²₁
Where W₁ is the weight of the body at the initial distance D₁, and W₂ is the weight at the final distance D₂.
So we have,
W₁ = 50
D₁ = 3,960
D₂ = 4015
We know that the body weighs 50 pounds when it is 3,960 miles from Earth's center,
So we can plug in those values as follows:
50 / W₂ = (4,015)²/ (3,960)²
To solve for W₂, we can cross-multiply and simplify as follows:
W₂ = 50 x (3,960)² / (4,015)²
W₂ = 50 x 15,681,600 / 16,120,225
W₂ = 48.547 pounds (rounded to three decimal places)
Therefore, if the body were 4,015 miles from Earth's center, it would weigh approximately 48.547 pounds.
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I need help in understanding and solving quadratic equations using the quadratic formula
x^2+8x+1=0
Answer:
Exact Form: -4⊥√15
Decimal Form:
0.12701665
7.87298334
…
I really need the help please and thank you
Asnwer: C
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