Answer:
384 cm
Step-by-step explanation:
hope this helps ! good luck on ur assignment! <3
solve for x; (a+bx)/(a+b)=(c+dx)/(c+d) if cb=ad
Answer:
To solve for x, we can start by cross-multiplying the equation to eliminate the denominators:
(a+bx)(c+d) = (c+dx)(a+b)
Expanding the terms on both sides:
ac + adx + bc + bdx^2 = ac + abx + cdx + bd
Simplifying and rearranging the terms:
adx + bdx^2 - abx - cdx = bd - ac
dx(ad - ab - c) = bd - ac
Now, since we know that cb=ad, we can substitute ad=cb into the equation:
dx(cb - ab - c) = bd - ac
dx(cb - ab - c) = b(cd - ac)
x = b(cd - ac)/(d(cb - ab - c))
Therefore, the solution for x is:
x = b(cd - ac)/(d(cb - ab - c))
Question What is the value of the expression? (9 1/2 − 3 7/8)+(4 4/5 − 1 1/2) Enter your answer as a mixed number in simplest form by filling in the boxes. $$
Answer:
To add mixed numbers, we need to add the whole numbers separately and fractions separately.
Starting with the whole numbers, we have:
9 1/2 − 3 7/8 + 4 4/5 − 1 1/2
= (9 + 4) − (3 + 1) + (4/5 − 1/2) + (1/8 − 7/8) (grouping the terms)
= 10 − 4 + (8/10 − 5/10) + (−6/8) (converting fractions to have a common denominator)
= 6 + 3/10 − 3/4 (simplifying fractions and adding whole numbers)
= 5 7/20 (expressing the result as a mixed number in simplest form)
Therefore, the value of the expression is 5 7/20.
Any help please? i cant seem to understand it
The no of people take more than 19 mins are above 50%
1. Break it down: Divide the topic into smaller subtopics or concepts. This can make it easier to understand and digest each piece of information.
2. Research: Look up definitions, explanations, or examples related to the terms or concepts you're trying to understand. This can help clarify any confusion or uncertainty.
3. Take notes: Write down important information, key points, or definitions as you research. This can help you remember and better understand the material.
4. Ask questions: If you're still unsure about certain aspects, don't hesitate to ask for help or clarification from a teacher, tutor, or friend.
5. Practice: Apply what you've learned to related problems or questions. Practicing can help reinforce your understanding
for such more questions on uncertainty.
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A dilation centered at the origin maps the point (4,6) to the point (5/2,15/4). What is the scale factor of the dilation
We may be confident that this is the correct scale factor because both equation equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
What is equation?An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.
Let (x,y) be a point on the plane and k be the dilation scale factor centred at the origin. The image of (x,y) under dilation is thus given by (kx, ky).
The dilation is given as (4,6) to (5/2,15/4). That is to say:
[tex]k(4) = 5/2 \sk(6) = 15/4\\k = 5/8 \sk = 5/8[/tex]
We may be confident that this is the correct scale factor because both equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.
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Answer the question below
The volume of the solid is (64/3)√3 cubic units, which is answer choice B.
Describe Circle?A circle is a geometric shape in a two-dimensional plane, consisting of all the points that are at a fixed distance, called the radius, from a given point, called the center. The distance around the circle is called the circumference. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. The formula for the area of a circle is A = πr^2, where r is the radius of the circle. Circles have many real-world applications, such as in the design of wheels, gears, and other rotating objects. They are also important in mathematics and science, as they provide a simple and elegant way to study and understand the properties of curves and curved surfaces.
We can approach this problem by considering a vertical slice of the solid taken perpendicular to the y-axis. This slice will be an equilateral triangle with a side length that depends on the y-coordinate.
At y = 0, the circle x² + y² = 16 intersects the x-axis at x = ±4. This means that the equilateral triangle at y = 0 has side length 2√3 times the distance from the origin to the x-axis, which is 4√3. Therefore, the area of this triangle is:
A(0) = (√3/4) (4√3)² = 12√3
At a general y-coordinate y > 0, the equilateral triangle will have side length equal to the distance between the points where the circle intersects the line y = k, where k is the y-coordinate. This distance can be found using the Pythagorean theorem:
d = √(16 - k²) - √k² = √(16 - 2k²)
The area of the equilateral triangle at y is then:
A(y) = (√3/4) d² = (√3/4) (16 - 2k²)
To find the volume of the solid, we can integrate the cross-sectional areas with respect to y from 0 to 4, using the formula for the area of an equilateral triangle:
V = ∫(0 to 4) A(y) dy = ∫(0 to 4) (√3/4) (16 - 2k²) dy
= (√3/4) (16y - (2/3) y³)|0 to 4
= (√3/4) [(64 - (2/3)(64)) - (0 - 0)]
= (64/3)√3
Therefore, the volume of the solid is (64/3)√3 cubic units, which is answer choice B.
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if x = 3/4y and y = 8 what is 3x-4
Please help me with my trig hw
Yellow Sticker Company’s variable expenses are 40% of sales. The company has monthly fixed expenses of $15,000 and sells each unit for $0.50. The monthly target operating income is $8,250.
a. What is the monthly margin of safety in dollars if Yellow Sticker Company achieves its operating income goal?
If Yellow Sticker Business meets its operating income goal, the quarterly safety margin in dollars will be $4,583.33.
Which financial objectives are sound?Budgeting, debt reduction, and setting up an emergency fund are important short-term objectives. Key insurance policies should be included in medium-term goals, whilst retirement should be the primary emphasis of long-term objectives.
Next, we deduct our break-even sales from actual sales at the goal operating income level to determine the margin of safety:
Real sales are determined by dividing target operating income by total fixed costs and contribution margin ratio.
Real sales equal $8,250 plus $15,000 / 0.60.
Real sales were $29,583.33
Safety margin = Real sales Breakeven sales
Margin of safety is calculated as $29,583.33 - ($0.50 x 50,000 units).
$25,000 - 29,583.33 is the margin of safety.
$4,583.33 is the safety margin.
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Ava is going on holiday with Fly Away airlines. The maximum weight her suitcase can be is 2020 kg.
When empty her suitcase weighs 33 kg.
The clothes she plans on taking have a combined weight of 55 kg.
Her electrical accessories have a combined weight of 44 kg.
She is also taking 55 hardback books, which each weigh 720720 g.
Finally, the toiletries she is taking have a combined weight of 46004600 g.
How much over the maximum weight will Ava's suitcase be? Give your answer in grams.
As a result, Ava's luggage will weigh 123622200 grams more than the permitted maximum.
What exactly is weight?Weight is the force of gravity that pulls objects toward the core of the Earth. The resulting force that pulls a substance toward Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Earth as well as a mass.
First, we need to convert all the weights to grams, since the weight limit is given in kilograms and the weights of clothes, electrical accessories, and toiletries are given in grams.
Maximum weight limit = 2020 kg = 2020000 g
Weight of empty suitcase = 33 kg = 33000 g
Weight of clothes = 55 kg = 55000 g
Weight of electrical accessories = 44 kg = 44000 g
Weight of 55 hardback books = 55 x 720720 g = 39639600 g
Weight of toiletries = 46004600 g
Total weight of suitcase and contents = 33000 + 55000 + 44000 + 39639600 + 46004600 = 125642200 g
Amount over maximum weight limit = total weight - maximum weight limit = 125642200 - 2020000 = 123622200 g
Therefore, Ava's suitcase will be over the maximum weight limit by 123622200 grams.
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DIRECTIONS: Use this information to answer Parts A, B, and C.
Each small square on this scale weighs 1 unit. Each larger square weighs 10 units. The weight of the triangle x is unknown. The scale is balanced. Look at the image.
A balanced scale. On one side there are four small squares and three large squares each labeled ten. On the other side there are two small squares, two large squares each labeled ten, and a triangle labeled x.
Question 1
Part A
Write an equation to represent relationship of the weights shown on the scale.
Enter the correct answer in the box.
An equation to represent relationship of the weights shown on the scale include the following: 22 + x = 34.
How to write an equation to represent relationship of the weights?Based on the information provided about the weights on this balanced scale, we can logically deduce the following parameters;
Each small square = 1 unit.
Each larger square = 10 units.
The variable x represent the weight of the triangle.
Since there are four small squares and three large squares each labeled ten on one side of this balanced scale, we have:
Total weight = 4(1) + 3(10)
Total weight = 34 units.
Similarly, there are two small squares, two large squares, and a triangle labeled x on the other side of this balanced scale, we have:
Total weight = 2(1) + 2(10) + x
Total weight = 22 + x
By equating the two equations, we have:
22 + x = 34
x = 34 - 22
x = 12
In conclusion, there are 34 units on each side of this balanced scale.
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Find a fraction that is equivalent to 5/7 and its denominator is 9 less than twice its numerator.
5/7=
The fraction that is equivalent to 5/7 is 15/21
How to determine the fraction?It is important to note that fractions are simply described as part of a whole number or element.
Also, equivalent expressions are defined as expressions that have the same solution but differ in the mode of arrangement of the values.
From the information given, we have;
The numerator be x
The denominator is 9 less than twice the numerator
This is represented as;
x/2x - 9 = 5/7
Cross multiply the values, we have;
7(x) = 5(2x - 9)
expand the bracket
7x = 10x - 45
collect the like terms, we have;
7x - 10x = -45
-3x = -45
Make 'x' the subject
x = 15
Then, the fraction = 15/21
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can you solve this quesiton?
f'(x)=?
The derivative of f(x) is (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x)).
What is a derivative?
A derivative is a mathematical concept used in calculus to determine the rate at which a function changes with respect to its input variable. It measures the instantaneous rate of change of the function at a specific point, and is calculated as the limit of the rate of change as the input variable approaches zero. The derivative is represented by the notation f'(x) or dy/dx, and can be used to find important information about the function, such as its slope, maxima and minima, and points of inflection.
What are expression?
In mathematics, an expression is a combination of numbers, symbols, and/or variables that are combined in some way using mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.
According to given information:To find the derivative of f(x) = √[9x - sin²(2x)], we can use the chain rule and the power rule of differentiation:
f(x) = √[9x - sin²(2x)]
f'(x) = (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x))
Using the chain rule, we first take the derivative of the expression inside the square root, which is 9x - sin²(2x), and then multiply it by the derivative of the expression inside the square root. The derivative of the expression inside the square root is:
(1/2)(9x - sin²(2x))^(-1/2) * (d/dx)(9x - sin²(2x))
Using the chain rule and the power rule of differentiation, we can find the derivative of 9x - sin²(2x) as:
d/dx (9x - sin²(2x)) = 9 - 4sin(2x)cos(2x)
Substituting this into the expression for f'(x), we get:
f'(x) = (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x))
So, the derivative of f(x) is (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x)).
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The derivative of f(x) is: f'(x) = (9 - 4sin(2x)cos(2x)) / [2√(9x - sin²(2x))].
What is differentiation?Differentiation is a mathematical concept used to calculate the rate at which one quantity changes with respect to another. In calculus, it refers to the process of finding the derivative of a function, which gives the slope of the tangent line at any point on the function.
In the given question,
To find the derivative of f(x), we can use the chain rule and the power rule of differentiation.
f(x) = √[9x - sin²(2x)]
Let's first simplify the expression under the square root:
g(x) = 9x - sin²(2x)
Taking the derivative of g(x) gives:
g'(x) = 9 - 2sin(2x) * cos(2x) * 2
g'(x) = 9 - 4sin(2x)cos(2x)
Now we can use the chain rule to find f'(x):
f'(x) = [1/2(9x - sin²(2x))^(-1/2)] * g'(x)
f'(x) = [1/2√(9x - sin²(2x))] * [9 - 4sin(2x)cos(2x)]
Therefore, the derivative of f(x) is:
f'(x) = (9 - 4sin(2x)cos(2x)) / [2√(9x - sin²(2x))]
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What is the least amount of wrapping paper needed to wrap a gift box that measures 8 inches by 8 inches by 10 inches.
The first thing we must do for this case is to find the surface area of the rectangular prism.
We have then:
[tex]A = 2 \times (l \times h) + 2 \times (h \times w) + 2 \times (w \times l)[/tex]
Where,
w: width
l: long
h: height
Substituting values we have:
[tex]A = 2 \times (10 \times 8) + 2 \times (8 \times 8) + 2 \times (8 \times 10)[/tex]
[tex]A = 448 \ in ^ 2[/tex]
Answer:
the least amount of wrapping paper needed to wrap the gift box answer is:
A = 448 in²
Use the simple interest formula to determine the missing value.
P= $1275, R= ?, T= four years, I= $112.20.
R= —-%
Do not round into the final answer, then round to one decimal place as needed
Step-by-step explanation:
2.2 percentage answer you silly
What ordered pair contains the y-intercept of y= -2x^ -4x -5
(-1,3)
(0,-5)
(-5,0)
(0,-2)
Answer:
To find the y-intercept, we can set x = 0 in the equation y= -2x^2 -4x -5, which gives us:
y = -2(0)^2 - 4(0) - 5 = -5
So the y-intercept is (0, -5). Therefore, the correct answer is (0,-5).
In the diagram, point B is a point of tangency. Find
the radius r of OC.
The radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC
How to evaluate for the radius using Pythagoras ruleSince the line AB is tangent to the circle at point B, then the triangle ABC is a right triangle and the Pythagoras rule can be applied as follows:
(50 + r)² = r² + 80²
r² = (50 + r)² - 80²
r² = (50 + r - 80)(50 + r + 80) {difference of two square}
r² = (r - 30)(r + 130)
r² = r² + 130r - 30r - 3900 {expansion of brackets}
r² - r² + 130r - 30r = 3900 {collect like terms}
100r = 3900
r = 3900/100 {divide through by 100}
r = 39
Therefore, the radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC.
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Which is an intercept of the function y = log base of 3 x?
The x-intercept of the function y = log base 3 x is (1, 0)
What is logarithm ?
A logarithm is a mathematical function that is used to solve equations involving exponential expressions. It is the inverse operation of exponentiation.
The logarithm of a number y to a given base b is the power or exponent to which the base must be raised to yield the number y. In other words, if we have the equation [tex]b^x = y[/tex], then the logarithm of y to the base b is x, which we can write as log base b y = x.
For example, if we take the base 2 and the number 8, the logarithm of 8 to base 2 is 3, because [tex]2^3 = 8[/tex]. This is written as log base 2 8 = 3.
According to the question:
The intercept of the function y = log base 3 x is the point where the graph of the function intersects either the x-axis or the y-axis. To find the intercepts, we set one of the variables to zero and solve for the other variable.
To find the y-intercept, we set x = 0 and evaluate the function:
y = log base 3 0
However, it is not possible to take the logarithm of 0 in any base, since 0 is not a positive number. Therefore, the function does not have a y-intercept.
To find the x-intercept, we set y = 0 and solve for x:
0 = log base 3 x
This equation can be rewritten in exponential form as:
[tex]3^0 = x[/tex]
Since any number raised to the 0th power is 1, we have:
1 = x
Therefore, the x-intercept of the function y = log base 3 x is (1, 0).
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Please helpppp I need helppp please
The value of x in the rectangle is 36.
How to find the angle of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
All angles measure 90∘ in a rectangle. The sum of angles in a rectangle is 360 degrees.
Therefore, let's find the value of x in the angles.
Hence,
∠2 = x + 30
∠5 = 2x - 48
Therefore,
∠2 + ∠5 = 90°
x + 30 + 2x - 48 = 90
3x - 18 = 90
3x = 90 + 18
3x = 108
divide both sides by 3
x = 108 / 3
x = 36
Therefore,
x = 36
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HELPPP ASAP IM AWARDING 80 POINTS!!!!
A cylindrical candle has a radius of 4 cm and a height of 10.4 cm.
What is the exact surface area of this candle?
32.0π cm²
83.2π cm²
91.2π cm²
115.2π cm²
Answer:
D) 115.2π cm².
Step-by-step explanation:
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder.
In this case, r = 4 cm and h = 10.4 cm. Substituting these values in the formula, we get:
Surface Area = 2π(4)² + 2π(4)(10.4)
Surface Area = 2π(16) + 2π(41.6)
Surface Area = 32π + 83.2π
Surface Area = 115.2π
Therefore, the exact surface area of the candle is 115.2π cm².
The answer is (D) 115.2π cm².
Answer: The answer is D, 115.2π cm²
Step-by-step explanation: When we use the formula of 2πrh+2πr2=2·π·4·10.4+2·π·42 to get the surface area, which equals 361.91
We can divide this by pi to get 115.2π cm²
Hope this helped!
I need to know how to solve this problem and the answer of it.
Answer:
P = 8g⁵ - 15g + 14
Step-by-step explanation:
This question has expressions to represent the side lengths of a triangle.
The side lengths are:
-8g⁵ - 7g
10g⁵ - 8g
6g⁵ + 14
They ask for a simplified expression for the perimeter. The purpose of this question is to combine like terms.
P = s₁ + s₂ + s₃ where s is a side length of the triangle.
P = (-8g⁵ - 7g) + (10g⁵ - 8g) + (6g⁵ + 14)
P = 8g⁵ - 15g + 14
The graph shows g(x) = x2 − 9x + 20. graph of parabola falling from the left, passing through 3 comma 2 to about 4 and one half comma negative one fourth, and rising to the right, passing through 6 comma 2 What are the x-intercepts of g(x)? (4.5, 0) and (5, 0) (0, 4.5) and (0, 5) (0, 5) and (0, 4) (5, 0) and (4, 0)
Parabola intersects x-axis at two points: (-5,0) and (-4,0)
What does a parabola actually mean?
Each point on a parabola with a U-shape is equally spaced from both the focus, a fixed point, and the directrix, a fixed line. As the topic of conic sections depends heavily on the parabola, all of the parabola-related concepts are covered here.
The x-intercepts of a parabola are where the parabola intersects the x-axis on its graph. There are a number of ways to find the x-intercepts of a parabola, and each one is usually specific to each situation.
In the case, when you are given the graph, the easiest way to find x-intercepts is to identify points at which parabola intersects the x-axis.
From your graph, parabola intersects x-axis at two points: (-5,0) and (-4,0)
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The graph shows the velocity versus time for 4 different cars on a race track. If all four cars have the same mass, which one experiences the largest net force?
Answer:
Step-by-step explanation: 1
An air tank of 500 mL is 80% oxygen and 20% nitrogen. What is the amount of oxygen in milliliters in a 200 ml air tank that contains the same ratio?
Hence, 160 mL of oxygen is contained inside a 200 mL air tank using the same ratio as a 500 mL air tank.
How is ratio calculated?Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were trying to compare one piece of data (A) to some other data point (B). We are multiplying information A by data B, as this suggests. In the event that A and B are both 5, for example, your ratio would've been 5/10.
80% of 500 mL of oxygen if indeed the air tank contains 80% oxygen & 20% nitrogen, which is:
0.80 x 500 mL = 400 mL
This means that the air tank contains 400 mL of oxygen and 100 mL of nitrogen.
To find the amount of oxygen in a 200 mL air tank that contains the same ratio, we need to use proportions:
If 500 mL contains 400 mL of oxygen, then 1 mL contains 400/500 = 0.8 mL of oxygen.
Therefore, if 200 mL contains the same ratio of oxygen, it will contain:
0.8 mL x 200 mL = 160 mL
So, the amount of oxygen in a 200 mL air tank with the same ratio as the 500 mL air tank is 160 mL.
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solve equation
log 4x=2
Answer: x=25
Step-by-step explanation:
log 10 4x = 2
10^2 = 4x
100 = 4x
25 = x
the diameter of a spherical balloon is 21.6 centimeters
The parameter for determining the diameter of an object depends on the specific object being measured. Here are some examples of parameters that can be used to determine diameter the answer is 5276.7 cm3. Thus, option D is correct.
What are the parameter for determining the diameter?The formula for the volume of a sphere is [tex]V = (4/3)πr^3[/tex] , where r is the radius of the sphere.
Since we are given the diameter of the sphere, we can find the radius by dividing the diameter by 2:
[tex]r = 21.6 cm / 2 = 10.8 cm[/tex]
Substituting this value into the formula, we get:
[tex]V = (4/3)\pi(10.8)^3[/tex]
[tex]= 4.18879 \times (10.8)^3[/tex]
[tex]= 5276.794 cm^3[/tex]
Rounding to the nearest tenth, we get:
[tex]V \approx 5276.8 cm^3[/tex]
Therefore, the answer is D) 5276.7 cm3.
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The given question is incomplete. the complete question is given below.
The diameter of a sphere is 21.6 cm. What is the sphere's volume? Round to the nearest tenth, if necessary. A) 693.2 cm3 B) 1453.8 cm3 C) 1868.5 cm3 D) 5276.7 cm3
explain how you can find the difference between the most common and least common amounts on a line plot
who ever gets this right is the brainlest in the Universe
Therefore, the difference between the most common and least common amounts on the line plot is 8.
What is least common?"Least common" refers to the item or value that appears the fewest number of times in a given set or group. For example, if you have a set of numbers {2, 4, 2, 5, 3, 4, 1}, the least common number in the set is 1 because it appears only once, while the most common number is 2 and 4 because they both appear twice. In a line plot, the least common amount is the one that appears the fewest number of times on the p.
Given by the question.
To find the difference between the most common and least common amounts on a line plot, follow these steps:
Look at the line plot and identify the most common amount. This is the amount that appears the most frequently on the plot.
Look at the line plot and identify the least common amount. This is the amount that appears the least frequently on the plot.
Subtract the least common amount from the most common amount. The result will be the difference between the most common and least common amounts on the line plot.
For example, if the most common amount on the line plot is 10 and the least common amount is 2, then the difference would be:
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The design dept is planning a new model of tent in the shape of a triangular pyramid. They intend to make two sizes of the new model
By taking these factors into account, they can create a product that meets the needs of potential customers and is a success in the market. the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.
What is the design dept is planning a new model ?Triangular Pyramid Tent Design:
The triangular pyramid tent design is a unique shape that could potentially offer better stability against wind and other weather conditions. However, it may also require more complex construction and assembly than a traditional rectangular tent.
The design department should consult with engineers and experienced tentmakers to ensure that the triangular pyramid tent can be manufactured in a cost-effective and user-friendly manner.
Size options:
The design department has decided to make two sizes of the triangular pyramid tent. They should consider the intended use of the tents and the needs of potential customers when determining the size options.
For example, a smaller size might be suitable for backpackers or solo campers, while a larger size could accommodate families or groups.
Therefore, the tent design, size options, materials, features, and pricing when planning the new model of triangular pyramid tents.
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For a standard normal distribution, find:
P(z > -0.25)
Accοrding tο the standard nοrmal distributiοn, the prοbability that z is greater than -0.25 is 0.5987.
What is a standard nοrmal distributiοn?Nοrmal distributiοn, alsο knοwn as Gaussian distributiοn οr bell curve, is a prοbability distributiοn that describes the randοm variatiοn οf a cοntinuοus variable in a pοpulatiοn. In a standard nοrmal distributiοn, the mean is 0 and the standard deviatiοn is 1, and the curve is fully described by the parameters οf mean and standard deviatiοn. The nοrmal distributiοn is used in many statistical applicatiοns tο mοdel and analyze cοntinuοus data.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the area tο the right οf z=-0.25 is apprοximately 0.5987.
Therefοre,
[tex]$$P(z > -0.25) = 1 - P(z \leq -0.25) = 1 - 0.4013 = 0.5987$$[/tex]
Sο the prοbability that z is greater than -0.25 is 0.5987.
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Complete Question
Find P(Z > 0.25), using the standard normal distribution. The average number of calories in a 1.5-ounce chocolate bar is 250. Suppose that the distribution of calories is approximately normal with standard deviation 10. Find the probability that a randomly selected chocolate bar will have between 230 and 260 calories. A single die is rolled 5 times. Find the probability of getting at least one number which is greater than 4. Given data values: 11, 3, 5, 12, 17, 13, 10, 6, 8, 21, 14, 20, 9, 15, 7. (a) Find the percentile rank for 10. (b) What value corresponds to the 70th percentile? A survey found that the American family rates an average of 25 pounds of glass garbage each year. Assume the standard deviation of the distribution is 7pounds. Find the probability that the mean of a sample of 49 families will be between 19 and 26 pounds.
Justin purchased his dream car worth $18500 on a finance for 4 years. He was offered 6% interest rate. Assuming no other charges and no tax, we want to find his monthly installments.
Using simple interest his monthly installments are $1243.38
What is simple interest?The amount on Simple interest is given by A = P(1 + rt) where
P = principal, r = interest rate and t = timeNow, since Justin purchased his dream car worth $18500 on a finance for 4 years. He was offered 6% interest rate. Assuming no other charges and no tax, we want to find his monthly installments.
His installments are his principal. so, making P subject of the formula, we have that
P = A/(1 + rt)
Given that
A = $ 18500r = 6% = 0.06 and t = 4 yearsSubstituting the vales of the variables into the equation, we have
P = A/(1 + rt)
P = $ 18500/(1 + 0.06 × 4)
P = $ 18500/(1 + 0.24)
P = $ 18500/1.24
P = $ 14919.35 per year
To find his monthly installments, we divide P by 12.
So, P' = P/12
= $ 14919.35/12
= $1243.38
So, his monthly installments are $1243.38
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Help with this problem guys
no trolling please i really need it
Answer:
[tex]\textsf{1.}\quad \sf \overline{AZ} = 28 \; meters[/tex]
[tex]\textsf{2.}\quad \sf \overline{AM} = 28 \; meters[/tex]
[tex]\textsf{3.}\quad b = \sf 4[/tex]
[tex]\textsf{4.}\quad \sf Perimeter = 112\; meters[/tex]
[tex]\textsf{5.}\quad \sf \overline{MX} = 22\; meters[/tex]
[tex]\textsf{6.}\quad \sf \overline{AX} = 10\sqrt{3}\; meters[/tex]
[tex]\textsf{7.}\quad \sf \overline{EX} = 10\sqrt{3}\; meters[/tex]
[tex]\textsf{8.}\quad \sf \overline{AE} = 20\sqrt{3}\; meters[/tex]
Step-by-step explanation:
Side lengths and value of bAll sides of a rhombus are the same length. Therefore, for rhombus MAZE:
[tex]\sf \overline{AZ} = \overline{AM} = \overline{ZE} = \overline{EM}[/tex]
Given:
[tex]\overline{\sf AZ} =8b-4[/tex][tex]\overline{\sf AM} =5b+8[/tex]As the sides of a rhombus are the same length, we can equate the expressions for sides AZ and AM, and solve for b:
[tex]\begin{aligned}\overline{\sf AZ}&=\overline{\sf AM}\\8b-4&=5b+8\\8b-4-5b&=5b+8-5b\\3b-4&=8\\3b-4+4&=8+4\\3b&=12\\3b \div 3&=12 \div 3\\b&=4\end{aligned}[/tex]
Therefore, the value of b is 4.
To find the length of AZ and AM, substitute the found value of b into one of the expressions:
[tex]\begin{aligned}\overline{\sf AZ}&=8b-4\\&=8(4)-4\\&=32-4\\&=28\end{aligned}[/tex]
Therefore, as AZ = AM, then AZ = 28 and AM = 28.
[tex]\hrulefill[/tex]
PerimeterAs the sides of a rhombus are equal in length, each side length is 28 meters (as found previously).
The perimeter of rhombus MAZE is the sum of its side lengths. Therefore:
[tex]\begin{aligned}\sf Perimeter\;MAZE&=\sf \overline{AZ} +\overline{AM} +\overline{ZE}+ \overline{EM}\\&=28+28+28+28\\&=112\; \sf meters\end{aligned}[/tex]
Therefore, the perimeter of rhombus MAZE is 112 meters.
[tex]\hrulefill[/tex]
DiagonalsThe point of intersection of the diagonals of rhombus MAZE is point X.
As the diagonals of a rhombus are perpendicular bisectors of each other, then:
[tex]\sf \overline{AX}=\overline{EX}\quad and \quad \overline{AX}+\overline{EX}=\overline{AE}[/tex]
[tex]\sf\overline{MX}=\overline{ZX}\quad and \quad\overline{MX}+\overline{ZX}=\overline{MZ}[/tex]
Given MZ = 44 meters, and MX is half of MZ, then:
[tex]\sf \overline{MX}=\overline{ZX}=22\;meters[/tex]
As the diagonals bisect each other at 90°, m∠MXA= 90°. Therefore, ΔMXA is a right triangle with hypotenuse AM = 28 and leg MX = 22.
As we know the lengths hypotenuse AM and leg MX, we can use Pythagoras Theorem to calculate the length of the other leg, AX:
[tex]\begin{aligned}\sf \overline{AX}^2+\overline{MX}^2&=\sf \overline{AM}^2\\\sf \overline{AX}^2+22^2&=\sf 28^2\\\sf \overline{AX}^2&=\sf 28^2-22^2\\\sf \overline{AX}&=\sqrt{\sf 28^2-22^2}\\\sf \overline{AX}&=\sf 10\sqrt{3}\; meters\end{aligned}[/tex]
As the diagonals bisect each other, AX = EX. Therefore:
[tex]\sf \overline{EX}=\sf 10\sqrt{3}\; meters[/tex]
The length of diagonal AE is the sum of segments AX and EX. Therefore:
[tex]\begin{aligned}\sf \overline{AE}&=\sf \overline{AX}+\overline{EX}\\&=\sf 10\sqrt{3}+10\sqrt{3}\\&=\sf 20\sqrt{3}\; meters\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Note: The attached diagram is drawn to scale.