Let's call the height of the building "h". We can use trigonometry to solve for "h" using the angle of elevation and the horizontal distance from the foot of the building to the point where the angle of elevation is measured.
In this case, we have a right triangle with the height of the building as one leg, the horizontal distance as the adjacent leg, and the angle of elevation as the angle opposite the height. So we can use the tangent function:
tan(60°) = h/55
Solving for "h", we get:
h = 55 tan(60°)
h ≈ 95.1
Rounded to the nearest tenth of a meter, the height of the building is approximately 95.1 meters.
HELP ASAPPPPPP PLESS
The coordinates of the vertices of △RST are R(−3, −1) , S(−1, −1) , and T(−4, −5) .
The coordinates of the vertices of △R′S′T′ are R′(3, −3) , S′(3, −1) , and T′(−1, −4) .
What is the sequence of transformations that maps △RST to △R′S′T′?
A sequence of transformations that maps △RST to △R′S′T′ is a (answer choice) area followed by a (answer choice) area
options:
translation 4 units right
rotation of about 180 degrees of origin
rotation 90 degrees clockwise about the origin
reflection across the y=x line
Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.
Which branches of mathematics employ coordinates?an arrangement of elements that faithfully represent an angle. The first number on a graph indicates the distance along, while the second number indicates the distance up or down. The point (12,5), for instance, is situated 12 below and 5 above.
A sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.
Explanation:
First, we need to reflect the original triangle RST across the y=x line. This will result in a new triangle that is congruent to the original one but with its vertices in different positions. The new vertices will be R(-1, -3), S(-1, -1), and T(-5, -4).
Next, we need to rotate this new triangle 90 degrees clockwise about the origin. This will result in another new triangle that is congruent to the previous one but with its vertices in different positions. The new vertices will be R'(3, -3), S'(3, -1), and T'(-1, -4), which are the vertices of △R′S′T′.
Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.
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The temperature in Austria was -5 degrees at 08:00 and increased by 2 degrees every hour what is the temperature at 11:30
Answer:
the answer is -2
Step-by-step explanation:
What is 273 - 8198 -274 + 8200 =
can you give step by step
The simplified value of the expression "273- 8198- 274+ 8200 is 1.
A Numerical Expression is a combination of numbers and mathematical operations such as addition, subtraction, multiplication, and division that can be evaluated to a single numerical value.
We have to evaluate the expression 273 - 8198 - 274 + 8200, step by step,
Step(i) : We start with the leftmost operation, which is the subtraction of 8198 from 273.
⇒ 273 - 8198 = -7925
Step(ii) : Next, we have to subtract 274 from the result of the step(i) ,
⇒ -7925 - 274 = -8199
Step(iii) : We add 8200 to the result of the step(ii),
⇒ -8199 + 8200 = 1
Therefore, the simplified value is 1.
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PLEASE HELP
A group of people living in either an apartment or a house are asked whether they own a pet or not. The data are collected in the table.
Pet No pet
Apartment 18 36
House 43 24
Drag and drop the correct percentages into each box to complete each statement.
Of the people living in an apartment, about _______ have a pet. Of the people living in a house, about______have no pet.
30%
33%
36%
40%
60%
64%
67%
70%
Answer:
Step-by-step explanation:
Firstline = 33%
Second line = 36%
Answer:
Firstline = 33%
Second line = 36%
Step-by-step explanation:
what is a base of square
A square is a base of a square pyramid.
What shape is known as a square pyramid?A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called a vertex) is called a square pyramid. It is called a pentahedron, due to its five faces.
A square base and four triangles joined at the vertex make up a square pyramid. It has a square base and triangular side faces with a central vertex.
A square pyramid has three components.
The top point of the pyramid is called the apex.The bottom square is called the base.The triangular sides are called faces.Properties of a Square Pyramid:
Let's go through the attributes we looked at in the graphic above. The definition of a pyramid is the source of all these characteristics.
It has 5 faces.It has 4 side faces that are triangles.It has a square base.It has 5 vertices.It has 8 edges.Learn more about square pyramid here:
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Complete question:
what is a base of a square pyramid?
Summary
How can the correlation coefficient help you determine how right (or justified) you are in using a line to
represent data?
The correlation coefficient, denoted by r, tells us how closely data in a scatterplot fall along a straight line. The closer that the absolute value of r is to one, the better that the data are described by a linear equation. If r =1 or r = -1 then the data set is perfectly aligned. Data sets with values of r close to zero show little to no straight-line relationship.
Due to the lengthy calculations, it is best to calculate r with the use of a calculator or statistical software. However, it is always a worthwhile endeavor to know what your calculator is doing when it is calculating. What follows is a process for calculating the correlation coefficient mainly by hand, with a calculator used for the routine arithmetic steps.
What is the total surface area of the rectangular prism shown?
Answer:
128 in^2
Step-by-step explanation:
L * W
16 * 8 = 128 in^2
Use the properties of logarithms to rewrite and simplify the logarithmic expression.
After using the properties of logarithms to rewrite and simplify the logarithmic expression ln((e⁸)/7) simplifies to 1.
What are natural logarithms?
Natural logarithms are a type of logarithm that uses the number e as its base. The natural logarithm of a positive number x (written as ln(x)) is the exponent to which e must be raised to get x. In other words, ln(x) represents the power to which e must be raised to obtain x.
The number e is a mathematical constant that is approximately equal to 2.71828. It is a special number that appears in many areas of mathematics, science, and engineering. Natural logarithms have a variety of applications in fields such as calculus, probability theory, and statistics.
Some properties of natural logarithms include:
ln(1) = 0
ln(e) = 1
ln(xy) = ln(x) + ln(y) for any positive numbers x and y
ln(x/y) = ln(x) - ln(y) for any positive numbers x and y
ln(xᵃ) = a ln(x) for any positive number x and any real number a
Natural logarithms can be evaluated using a calculator or by using the properties of logarithms to simplify expressions. They are commonly used in mathematical and scientific calculations that involve exponential growth or decay.
We can use the property of logarithms that states: log(aᵇ) = b log(a) for any base a and any real number b.
Using this property, we can rewrite ln((e⁸)/7) as:
ln((e⁸)/(e⁷))
[tex]= ln(e^{(8-7)})[/tex]
= ln(e)
= 1
Therefore, ln((e⁸)/7) simplifies to 1.
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A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d(t)=-16t²-4t+382
a. How tall is the building?
b.How high is the rock at its highest point?
c. How long does it take the rock to reach a height of 200 feet?
d. How long does it take the rock to hit the ground?
Please help! ASAP I am Terribly STUCK!!!!!
Answer:
a) The height of the building is 382 feet.
b) The rock is 382 feet above the ground at its highest point.
c) It takes the rock 3.25 seconds to reach a height of 200 feet.
d) Tt takes the rock 4.76 seconds to hit the ground.
Step-by-step explanation:
The function that models the distance (in feet) between the rock and the ground t seconds after it is thrown is a quadratic function.
As the leading coefficient of the quadratic function is negative, it is a parabola that opens downwards.
Part aThe rock is thrown from the top of the building. Therefore, the height of the building is the value of d(t) when t = 0. This is the y-intercept of the graphed function.
Substitute t = 0 into the given function:
[tex]\begin{aligned}\implies d(0)&=-16(0)^2-4(0)+382\\&=0+0+382\\&=382\; \sf feet \end{aligned}[/tex]
Therefore, the height of the building is 382 feet.
Part bThe highest point of the rock is the height of the building, since the rock is thrown down from the top.
Therefore, the rock is 382 feet above the ground at its highest point.
This can be proven by finding the vertex of the graph of the function.
The vertex (maximum point) of the graphed function is (-0.125, 382.25).
As the x-value of the vertex is negative, and time can only be positive, the path of the rock is on a downwards trajectory when t ≥ 0. Therefore, the highest point is the point at which the rock is thrown.
Part cTo calculate how long it takes for the rock to reach a height of 200 feet, substitute d(t) = 200 into the given function and solve for t.
[tex]\begin{aligned}\implies -16t^2-4t+382&=200\\-16t^2-4t+182&=0\\-2(8t^2+2t-91)&=0\\8t^2+2t-91&=0\\8t^2+28t-26t-91&=0\\4t(2t+7)-13(2t+7)&=0\\(4t-13)(2t+7)&=0\\\\\implies 4t-13&=0 \implies t=\dfrac{13}{4}=3.25\; \sf s\\\implies 2t+7&=0 \implies t=-\dfrac{7}{2}=-3.5\; \sf s\end{aligned}[/tex]
As time is positive, t = 3.25 s only.
Therefore, it takes the rock 3.25 seconds to reach a height of 200 feet.
Part dThe rock will hit the ground when d(t) = 0.
Therefore, to calculate how long it takes for the rock to hit the ground, substitute d(t) = 0 into the given function:
[tex]\implies -16t^2-4t+382=0[/tex]
Quadratic formula[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Solve for t using the quadratic formula.
[tex]\implies t=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(-16)(382)}}{2(-16)}[/tex]
[tex]\implies t=\dfrac{4 \pm \sqrt{24464}}{-32}[/tex]
[tex]\implies t=-\dfrac{4 \pm \sqrt{16 \cdot 1529}}{32}[/tex]
[tex]\implies t=-\dfrac{4 \pm \sqrt{16} \sqrt{1529}}{32}[/tex]
[tex]\implies t=-\dfrac{4 \pm 4\sqrt{1529}}{32}[/tex]
[tex]\implies t=-\dfrac{1 \pm \sqrt{1529}}{8}[/tex]
[tex]\implies t=-5.01280...,4.76280...[/tex]
As time is positive, t = 4.76 s only.
Therefore, it takes the rock 4.76 seconds to hit the ground.
The structure has a 382-foot height. The rock's highest peak is 39 1/2 feet high, or 195.5 feet. The time it takes for the rock to touch the ground is roughly 6.289 seconds.
What connection exists between height and separation?In arithmetic, we use angles and distance to determine an object's height. The distance between the items is measured horizontally, and the height of an object is determined by the angle of the top of the object with respect to the horizontal.
By setting t = 0, we can determine the rock's starting height:
d(0) = -16(0)^2 - 4(0) + 382
= 382
The highest point of the rock occurs at the vertex of the parabolic route, which is determined by the formula t = -b/2a
where a = -16 and b = -4.
t = -(-4) / 2(-16) = 1/8
d(1/8) = -16(1/8)^2 - 4(1/8) + 382
= 391/2
The equation d(t) = -16t^2 - 4t + 382 = 200 for t:
-16t^2 - 4t + 382 = 200
-16t^2 - 4t + 182 = 0
4t^2 + t - 45.5 = 0
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Factor the polynomial, if possible. If not possible, ttype "not factorable" y^(2)+49
We have to, the polynomial [tex]y^{(2)}+49.[/tex] is not factorable.
How do we prove that it is not factorizable?The given polynomial is [tex]y^{(2)}+49.[/tex]
This polynomial is not factorable because there are no two numbers that can be multiplied together to give a product of 49 and a sum of 0.
In other words, there are no two numbers that can be multiplied together to give 49 and added together to give 0. This means that the polynomial is not factorable.
Therefore, the answer is "not factorable".
In conclusion, the polynomial [tex]y^{(2)}+49[/tex] is not factorable.
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You are 14ft away from a flagpole and are looking up at if from an angle of 74.4 How is the flagpole ?
Answer:
23.4 ft tall
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given: Distance from the flagpole = 14 ft
Angle of elevation θ = 74.4°
To find: Length of the flagpole
Answer:
tan(74.4°) = [tex]\frac{L}{14}[/tex]
L = 14 tan(74.4°) = 50.142 ft
So the length of the pole is 50.142 ft.
Calculate the perimeter of a table that is 3m long an 2m wide
The perimeter of a table that is 3m long and 2m wide is 10m.
What is the perimeter of rectangle?The perimeter includes the total lengths (2 lengths and 2 breadths) of the four sides or the total distance around the rectangle.
For a rectangle, the perimeter can be determined using the following formula:
Perimeter = 2(l + w)
Length of the table = 3m
Width of the table = 2m
The perimeter of the table = 2(3 + 2)
= 10m
Thus, for a table that has lengths of 3 meters and width of 2 meters, the perimeter is 10 meters.
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10. A plane traveled 322 miles from El Paso in a direction 57° northeast as shown
below.
N
57°
322 miles
NE
E
El Paso
What is the height of the plane, to the nearest mile?
Answer:
To find the height of the plane, we need to use trigonometry. Let's call the height of the plane "h". We can use the given angle of 57° and the opposite side (height) to the angle to find the adjacent side (distance traveled east) using the tangent function:
tan(57°) = h / distance traveled east
We can rearrange this equation to solve for h:
h = distance traveled east x tan(57°)
To find the distance traveled east, we need to use the given distance of 322 miles and the direction traveled. Since the plane is traveling at a 57° angle northeast, we can split this into two right triangles, one facing northeast and the other facing southeast, as shown below:
N
|
|
|\ 57°
|
\
The distance traveled east is the adjacent side of the southeast-facing right triangle, which can be found using the cosine function:
cos(57°) = distance traveled east / 322
We can rearrange this equation to solve for the distance traveled east:
distance traveled east = 322 x cos(57°)
Now we can plug in this value for the distance traveled east into the equation for the height of the plane:
h = distance traveled east x tan(57°)
h = (322 x cos(57°)) x tan(57°)
Using a calculator, we can evaluate this expression to find:
h ≈ 389.4 miles
Therefore, the height of the plane to the nearest mile is 389 miles.
HURRY I NEED THIS PLEASE WORTH 60 points
Triangle ABC has been reflected over the x-axis to create triangle A'B'C'. Which of the following statements is true?
Answer: choose Answer B
Step-by-step explanation:
because if you flip the triangle back to what it was previously A B lines up with answer B so it’s B
The speed of light is approximately 2. 998 x 10^8 m/s, what is this number as a decimal
The decimal form of 2.998 x [tex]10^8[/tex] m/s is 29,980,000 m/s.
The number 2.998 x [tex]10^8[/tex] m/s represents the scientific notation of a very large number. It is a shorthand way of writing a number that is expressed as the product of a decimal number between 1 and 10 and a power of 10. In this case, the decimal number is 2.998 and the power of 10 is 8.
To convert this number to decimal form, we need to multiply the decimal number by 10 raised to the power of the exponent. So, we have:
2.998 x [tex]10^8[/tex] = 2.998 * 10,000,000
Multiplying 2.998 by 10,000,000, we get:
2.998 * 10,000,000 = 29,980,000
Therefore, the decimal form of 2.998 x [tex]10^8[/tex] m/s is 29,980,000 m/s.
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Use the 2021 marginal tax rates in the table to compute the tax owed by the person with the given filling status and taxable income single with a taxable income of $57000
Therefore, the total tax owed by a Single filer with a taxable income of equation $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.
What is equation?When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.
Assuming that the taxable income of $57,000 is for the tax year 2021 and the person is filing as Single, we can use the following marginal tax rates to compute the tax owed:
Tax Rate Taxable Income Range
10% $0 - $9,950
12% $9,951 - $40,525
22% $40,526 - $86,375
24% $86,376 - $164,925
32% $164,926 - $209,425
35% $209,426 - $523,600
37% $523,601 or more
To compute the tax owed, we need to apply each tax rate to the corresponding portion of the taxable income and add up the results. Here's how we can do that:
The first $9,950 of taxable income is taxed at 10%, so the tax on this portion is $9950 x 0.1 = $995.
The next $30,575 ($40,525 - $9,950) of taxable income is taxed at 12%, so the tax on this portion is $30,575 x 0.12 = $3,669.
The remaining $17,475 ($57,000 - $40,525) of taxable income is taxed at 22%, so the tax on this portion is $17,475 x 0.22 = $3,844.50.
Therefore, the total tax owed by a Single filer with a taxable income of $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.
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A baker can decorate one cake in 2/3 hour. What is the total of hours the baker needs to decorate 4 1/2cakes
The baker needs a total of 3 hours to decorate 4 1/2 cakes.
How to determine the time to decorate the cakesTo decorate one cake, the baker needs 2/3 hour.
To find out how long it takes to decorate 4 1/2 cakes, we need to multiply the time for one cake by 4 1/2 i.e. 9/2
Time for 4 1/2 cakes = (2/3) x (9/2)
When the products are evaluated, we have
Time for 4 1/2 cakes = 3
So, the time taken is 3 hours
Therefore, the baker needs a total of 3 hours to decorate 4 1/2 cakes.
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alice recipe for jam requires 4.8 of sugar. her kitchen weighing only gives measurements in pounds. taking 1kg = 2.205 lb, convert 4.8 kg to pounds
Alice needs to use 10.584 pounds of sugar for her jam recipe. This can be calculated using the conversion factor.
To convert 4.8 kg to pounds, we need to use the conversion factor of 1 kg = 2.205 pounds. This means that for every 1 kg, there are 2.205 pounds. To find out how many pounds are in 4.8 kg, we simply multiply 4.8 by 2.205.
The equation for this conversion is:
4.8 kg × 2.205 pounds/kg = 10.584 pounds
So, 4.8 kg is equivalent to 10.584 pounds.
Therefore, the correct answer is 10.584 pounds.
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Michelle's phone plan charges $0.22 per text message. Jeff's plan charges $0.12 a text plus an additional $1 a day. for what number of texts are the cost of the phone plans the same? write an algebraic equation and solve.
Answer:
Let's assume that the number of text messages sent in a day is x. Then the cost of Michelle's phone plan is:
Cost of Michelle's plan = 0.22x
And the cost of Jeff's phone plan is:
Cost of Jeff's plan = 0.12x + 1
We want to find the number of text messages for which the two plans have the same cost. So we can set the two expressions for the cost equal to each other and solve for x:
0.22x = 0.12x + 1
0.1x = 1
x = 10
Therefore, for 10 text messages per day, the cost of Michelle's plan and Jeff's plan will be the same.
We can also verify this by plugging x = 10 into the two expressions for the cost:
Cost of Michelle's plan = 0.22(10) = $2.20
Cost of Jeff's plan = 0.12(10) + 1 = $2.20
So the cost of the two plans is indeed the same for 10 text messages per day.
Answer:
Step-by-step explanation:
cost m = 0.22x
cost j = 0.12x+1
0.22x=0.12x+1
0.1=1
x=10
cost m = 0.22(10) = $2.20
cost J =0.12(10)+1=$2.20
So the answer is 10
6. A hiker looks down into a valley with binoculars. The angle of depression to the farthest edge of the river is 61. The angle to the closest edge of the river below is 63. If the valley is 1250
feet deep, how wide is the river? Round the answer to the nearest foot.
Answer:
w ≈ 640 feet
Step-by-step explanation:
Let's call the distance from the hiker's position to the closest edge of the river "x", and the width of the river "w". We can use trigonometry to set up two equations involving these values:
In the first triangle, the angle of depression is 63 degrees, and the opposite side is x + w. Therefore, we can use the tangent function:
tan(63) = (x + w) / 1250
In the second triangle, the angle of depression is 61 degrees, and the opposite side is x. Therefore, we can use the tangent function again:
tan(61) = x / 1250
Now we can solve these equations for "w" and "x", respectively:
w = 1250 * tan(63) - x
x = 1250 * tan(61)
Substituting the second equation into the first:
w = 1250 * tan(63) - 1250 * tan(61)
Plugging this into a calculator, we get:
w ≈ 640 feet
Therefore, the width of the river is approximately 640 feet rounded to the nearest foot.
1.Let f be a linear function. Given f(2) = - 7 and f(6) = - 17, find f(x).
2.FInd the slope of the line passing through the points A( 6, 3 ) and B( 15, - 3)
3. Find the equation of the line that contains point A(5,-3) and has slope m=3/5
4.Find the equation of the line that contains the point A ( 4 , - 8 ) and is parallel to the graph of the function :f(x)=1/4x+3
5. find the zero of the function f(x)=4x-2
By using the slope-intercept form it can be concluded that:
the equation of the line is f(x) = -2.5x - 2the slope of the line is -2/3the equation of the line is y = (3/5)x - 6the equation of the line is y = (1/4)x - 9the zero of the function is x = 1/2.The slope-intercept form of an equation is represented as follows:
y = mx + c or y - y₁ = m(x - x₁) , where
m = slope
c = y-intercept
(x₁, y₁) = point on the line
The slope of the line when given two points can be calculated as follows:
m = (y₂ - y₁) / (x₂ - x₁)
1. Given f(2) = - 7 and f(6) = - 17. To find f(x), we need to use the slope-intercept form of a linear function: f(x) = mx + b. First, we need to find the slope of the line by using the two given points:
m = (y₂ - y₁) / (x₂ - x₁)
= (f(x₂) - f(x₁)) / (x₂ - x₁)
= (-17 - (-7)) / (6 - 2)
= (-10) / (4)
= -2.5
Now, we can plug in one of the points to find the y-intercept:
f(x) = mx + b
f(2) = (-2.5)(2) + b
-7 = -5 + b
b = -2
Therefore, the equation of the line is f(x) = -2.5x - 2.
2. To find the slope of the line passing through points A(6,3) and B(15,-3), we use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
= (-3 - 3) / (15 - 6)
= (-6) / (9)
= -2/3
Therefore, the slope of the line is -2/3.
3. To find the equation of the line that contains point A(5,-3) and has slope m=3/5, we use the point-slope form of a linear function:
y - y₁ = m(x - x₁)
y - (-3) = (3/5)(x - 5)
y + 3 = (3/5)x - 3
y = (3/5)x - 6
Therefore, the equation of the line is y = (3/5)x - 6.
4. To find the equation of the line that contains the point A(4,-8) and is parallel to the graph of the function f(x)=1/4x+3, we know that the slope of the new line will be the same as the slope of the given function, which is 1/4. We can use the point-slope form of a linear function to find the equation of the new line:
y - y₁ = m(x - x₁)
y - (-8) = (1/4)(x - 4)
y + 8 = (1/4)x - 1
y = (1/4)x - 9
Therefore, the equation of the line is y = (1/4)x - 9.
5. To find the zero of the function f(x) = 4x - 2, we need to set the function equal to zero and solve for x:
f(x) = 0
4x - 2 = 0
4x = 2
x = 2/4
= 1/2
Therefore, the zero of the function is x = 1/2.
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How many roots does the polynomial equation have? 2x^(5)+6x^(4)-3x^(3)+x^(2)-9x-1=0
The polynomial equation 2x^(5)+6x^(4)-3x^(3)+x^(2)-9x-1=0 has 5 roots. This is because the degree of the equation is 5, and the number of roots of a polynomial equation is equal to its degree. Therefore, this equation has 5 roots. To find the roots of the equation, you can use the Rational Root Theorem, synthetic division, or other methods. However, finding the exact roots of a fifth-degree polynomial equation can be difficult and may require the use of a graphing calculator or computer software.
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Use substitution to solve
Answer:
x=4, y=5
Step-by-step explanation:
[tex]x=2y-6\\ x-2y=-6\\\\y=3x-7\\y-3x=-7\\\\\\\\-3x+y=-7\\-3(2y-6)+y=-7\\-6y+18+y=-7\\-5y+18=-7\\-5y=-25\\y=5\\\\\\x=2y-6\\x=2(5)-6\\x=4[/tex]
What is the fourth term in the geometric sequence 3, –9, 27, … ?
The fourth term in the geometric sequence is -81.
What is a geometric sequence?
In mathematics, a geometric progression, also known as a geometric sequence, is a set of non-zero numbers where each term after the first is derived by multiplying the previous one by a fixed, non-zero amount called the common ratio.
We are given a sequence as 3, –9, 27, ...
We can observe that each term is being multiplied by -3.
So, the common ratio i.e. r = -3
Here x = 4 and a₁ = 3.
Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get
⇒a₄ = a₁ r⁽⁴⁻¹⁾
⇒a₄ = a₁ r³
⇒a₄ = 3 (-3)³
⇒a₄ = 3 * -27
⇒a₄ = -81
Hence, the fourth term in the geometric sequence is -81.
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Kyra is making squares with toothpicks. She uses 4 toothpicks to make a square. Then she adds 3 more toothpicks to make two squares side by side. To build three squares in a line, she used a total of 10 toothpicks. If she continues this pattern, how many toothpicks will she use to make 90 squares in a straight line?
How many squares can Kyra make in this pattern if she has a box of 1,000 toothpicks?
The toothpicks she will use to make 90 squares in a straight line are 271. Squares can Kyra make if she has a box of 1,000 toothpicks are 333.
How many toothpicks are needed for making the first three squares?A total of 4 toothpicks are needed.
A total of 9 toothpicks are needed for further 3 squares.
So, the number of toothpicks needed to make 87 squares = [tex]\frac{87*9}{3}[/tex]
= 261
Hence, the number of toothpicks needed to make 90 squares = [tex]261+10[/tex]
= 271
The number of squares formed by 261 toothpicks = 87
So, the number of squares formed by 1000 toothpicks = [tex]\frac{996*87}{261} + 1[/tex]
= 333
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Q2: Small bakery have sold the following number of bread loafs for the last six months.
Month Number of bread loafs
October 1,200
November 1,230
December 1,450
January 1,410
February 1,420
March 1,380
a. Apply four period moving average forecast method to calculate demand for the month of April 2020?
b. What should Al Artz Bakery decide to do with capacity? justify your opinion.
c. If the bakery calculated forecasts for all products it makes, would this forecast be more accurate than the one you just d. calculate? justify your opinion.
e. If bakery decides to use qualitative methods, what sources of opinion it could use in these methods?
A2: a. The four period moving average forecast method is a technique that is used to calculate the demand for a particular month based on the average demand for the previous four months. In this case, to calculate the demand for the month of April 2020, we will take the average of the demand for the months of December, January, February, and March. The formula for this method is:
Four period moving average forecast = (Demand for December + Demand for January + Demand for February + Demand for March) / 4
= (1,450 + 1,410 + 1,420 + 1,380) / 4
= 5,660 / 4
= 1,415
Therefore, the demand for the month of April 2020 is 1,415 loafs.
b. Based on the demand forecast for the month of April 2020, Al Artz Bakery should decide to maintain their current capacity as the demand is relatively stable and there is no significant increase or decrease in demand. This will ensure that they are able to meet the demand without overproducing or underproducing.
c. If the bakery calculated forecasts for all products it makes, the forecast would be more accurate than the one calculated for just one product. This is because it would take into account the demand for all products and would give a more comprehensive view of the overall demand for the bakery.
d. If the bakery decides to use qualitative methods, it could use sources of opinion such as customer feedback, expert opinion, and market research. These sources of opinion can provide valuable insights into the demand for the bakery's products and can help to improve the accuracy of the demand forecast.
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The three angles of a quadrilateral are 60°,80° and 120° find the fourth angle?
Answer:
Step-by-step explanation:
Angles in a quadrilateral add to 360°. So
[tex]60+80+120+x=360[/tex] (where [tex]x[/tex] is the fourth angle)
[tex]260+x=360[/tex]
[tex]x=100[/tex]° (after subtracted 260 from both sides of equation)
Mr. Katz is designing a flower garden in the shape of a trapezoid. What is the value of x? Round to the nearest hundredth.
In response to the query, we can state that Rounding to the nearest parallel lines hundredth, the value of x is approximately 4.89 inches. Therefore, the answer is not provided in the options.
what is parallel lines?In geometry, parallel lines are non-intersecting coplanar infinite lines. Parallel planes are ones that never intersect in a certain three-dimensional space. The term "parallel" refers to curves that have a fixed minimum distance between them and neither points of contact nor junction. In geometry, two lines are said to be parallel if they are in the same plane, equally spaced apart, and never intersect. Both horizontal and vertical can be used. Railroad tracks, columns of notebooks, and pedestrian crossings are examples of commonplace things that have parallel lines.
A = (a + b)h/2
where a and b=lengths of the parallel sides of the trapezoid,
h =height
a = 550 in
b = 10 in
h = x in
A = (a + b)h/2 = (550 + 10)x/2 = 280x
And we know that the area of the trapezoid is 1,370 square inches:
A = 1,370
280x = 1,370
x = 1,370/280
x ≈ 4.89
Rounding to the nearest hundredth, the value of x is approximately 4.89 inches. Therefore, the answer is not provided in the options.
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Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e}. If A = {1,
2, a, e} and B = {1, 2, 3, 4, a, b, c}, find the following.
(c) n(A ∪ Bc)
(d) n(Ac ∩ Bc)
The answers are n(A ∪ Bc) = 10 and n(Ac ∩ Bc) = 6.
To solve this question we need knowledge of set theory, union and intersection.
(c) To find n(A ∪ Bc), we first need to find the complement of B, which is Bc = {5, 6, 7, 8, 9, d, e}. Now, we can find the union of A and Bc, which is A ∪ Bc = {1, 2, a, e, 5, 6, 7, 8, 9, d}. The number of elements in this set is n(A ∪ Bc) = 10.
(d) To find n(Ac ∩ Bc), we first need to find the complement of A, which is Ac = {3, 4, 5, 6, 7, 8, 9, b, c, d}. Now, we can find the intersection of Ac and Bc, which is Ac ∩ Bc = {5, 6, 7, 8, 9, d}. The number of elements in this set is n(Ac ∩ Bc) = 6.
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Charlotte wants to know which website has more user engagement per a
single writer.
1) Charlotte thought of two different ways to define this quantity. Identify
these two definitions among the following options.
A. Avg number of likes per writer
B. Total number of comments
C.Avg number of people words per writer
D. Avg number of comments per writer
The average number of likes per writer and the average number of comments per writer can be used to determine which website has more user engagement per a single writer
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the average number of likes per writer be L
Let the average number of comments per writer be C
Now , the number of writers for website A = 5
The number of writers for website B = 11
The average number of likes per post for A = 3500 likes
So , the average number of likes per writer A = ( 3500 / 5 ) = 700 likes
And , the average number of likes per writer B = ( 3500 / 5 ) = 700 likes
The number of comments per writer A = ( 500 / 5 ) = 100 comments
The number of comments per writer B = ( 450 / 11 ) = 40.90 comments
Hence , the average number of likes per writer and the average number of comments per writer are solved
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