Any percentage can be written as that number divided by 100. As a decimal, you find that quotient. You can quickly divide any number by 10 by moving the decimal place to the left for every 0 in that multiple of 10. 100 has 2 zeros, so all you need to do to divide by 100 is to move the decimal place 2 places to the left. Therefore, 60% is .6 as a decimal.
Let's say the number we want to find is x. In word problems, "of" indicates multiplication, so 60% of our number would be 6x.
We then add our number to that, giving us .6x + x
We know the result is 160, so
.6x + x = 160
Since any number multiplied by 1 is itself, that x can be written as 1x.
.6x + 1x = 160
Now, we combine our like terms; we add the numbers in front of the x's (aka coefficients).
(.6 + 1)x = 160
1.6x = 160
We want x by itself. 1.6 is multiplied by our number, so to undo multiplication, we do division. This leaves us with
x = 160/1.6
x=100
Find the critical value ze necessary to form a confidence interval at the level of confidence shown below.
c=0.97
Zc =
(Round to two decimal places as needed.)
The critical value Zc is ±2.170.
What is a confidence interval?
An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
Here, we have
Given: a confidence interval at the level of confidence shown below.
c=0.97
We have to find the critical value Zc.
c = 0.97
we get a = 1 - c
a = 1 - 0.97
a = 0.03
Critical value Zc = ±2.170
Hence, the critical value Zc is ±2.170.
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Need help will give brainliest and 5 stars for the fastest answers with work.
The answer of A is The point (-2,2) is included in the graph of g(x) regardless of the value of b and c.The answer of B the point (2,2) would be transformed to the point (2,1) on the graph of h(x).
What is graph?
A graph is a visual representation of data, functions, or relationships between variables. It is a way of displaying information in a way that is easy to interpret and understand. Graphs typically consist of two axes, the x-axis and y-axis, and points or lines plotted on the graph to represent the data or function being displayed.
There are many different types of graphs, including line graphs, bar graphs, pie charts, scatter plots, and more. Each type of graph is used for different purposes and can display different types of data.
Graphs are commonly used in many fields, including science, economics, finance, engineering, and more. They allow researchers and analysts to easily visualize data and identify trends or patterns, making it easier to draw conclusions and make informed decisions based on the data.
A. To include the point (-2,2), we need to shift the graph of f(x) two units to the right and two units upwards. So we have:
g(x) = a f(x - (-2)) + 2
g(x) = a f(x + 2) + 2
Now we need to find the value of "a". Since the point (3,4) on the graph of f(x) is mapped to the point (2,2) on the graph of g(x), we have:
g(3) = a f(3 + 2) + 2 = 2
4a + 2 = 2
4a = 0
a = 0
Therefore, the function g(x) is:
g(x) = 0 f(x + 2) + 2
g(x) = 2
So the point (-2,2) is included in the graph of g(x) regardless of the value of b and c.
B. The function h(x) is a linear function with slope 2 and y-intercept -1. To find where the point (2,2) would end up after the transformations, we plug in x=2 into h(x) and get:
h(2) = 2(2+1)-3 = 1
So the point (2,2) would be transformed to the point (2,1) on the graph of h(x).
The transformations made to f(x) to obtain h(x) are a horizontal shift to the left by one unit (x+1), a vertical stretch by a factor of 2 (2(x+1)), and a vertical shift downwards by three units (-3).
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La cafetería de Jina prepara una mezcla que es una combinación de dos tipos de café. El café del tipo A le cuesta 5.75 por cada libra, y café del tipo B 4.3 por cada libra. En la mezcla de este mes utilizó tres veces más la cantidad de libras de café del tipo B que del tipo A, con un costo total de 503.55. ¿Cuántas libras de café del tipo A se utilizaron?
The amount of coffee of type A that was used is given as follows:
27 lbs.
How to obtain the amounts?The amounts of each type of coffee used are obtained using a system of equations, for which the variables are given as follows:
Variable x: amount of coffee of type A used.Variable y: amount of coffee of type B used.The total cost was of 503.55, hence:
5.75x + 4.3y = 503.55.
The amount of coffee B used was the triple of the amount of coffee A used, hence:
y = 3x.
Replacing the second equation into the first, the amount of coffee A used is given as follows:
5.75x + 4.3(3x) = 503.55
x = 503.55/18.65
x = 27 lbs.
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add [-6 -22] + [-3 2 1]
A [-903]
B [-603]
C [-303]
D[-9-3 -5]
Answer:
I think its C. sorry if I'm wrong.
EXACTLY how big is your dictionary?
QUICKLY!!!!!!!!!!!!!!!!!
Answer:
960 pages
Step-by-step explanation:
Name the Verticals of the polygon
By answering the presented question, we may conclude that There are polygon four vertex designated HT , HB, TE and EB in the provided picture.
What is a polygon?A polygon is a two-dimensional shape that is formed by joining three or more points in a closed loop. Triangles, tetrahedra, pentagons, hexagons, and other forms are examples of polygons. Polygons are a fundamental geometric concept used to define and analyze a wide range of real-world forms and structures, such as buildings, layouts, and computer graphics. Polygons are examined not just for their perimeter, area, and angles, but also for their symmetry.
The vertex of the polygon in the image are the line segments that link the polygon's opposing vertices and are perpendicular to its base. There are four vertex designated HT , HB, TE and EB in the provided picture.
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MY NOTES
PRACTICE ANOTHER
1. [-/1 Points]
DETAILS
HARMATHAP12 6.3.005.
Find the future value of an annuity of $1300 paid at the end of each year for 10 years, if interest is earned at a rate of 5%, compounded annually. (Round your answer to the
nearest cent.)
$
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Question
In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB = 7 and
BC= 6, what is the area of the shaded region? Write your answer as a decimal, if necessary. Do not include units in your
answer.
evious
D
E
B
Answer:
The area of the shaded region is 21.
Step-by-step explanation:
Since point E lies halfway between AB and BC, the area of the shaded region (As) consists of two identical triangles with base equal to AB and height equal to half the measure of BC:
[tex]A_s=2\times A_t[/tex]
Where At is the area of each triangle.
[tex]A_t=\dfrac{AB\times BC/2}{2}[/tex]
[tex]A_t=\dfrac{AB\times BC}{4}[/tex]
We know AB=7 and BC=6, thus:
[tex]A_t=\dfrac{7\times6}{4} =\dfrac{42}{4}[/tex]
Simplifying:
[tex]A_t=\dfrac{21}{2}[/tex]
Finally:
[tex]A_s=2\times\dfrac{21}{2}[/tex]
[tex]A_s=21[/tex]
The area of the shaded region is 21.
Note the area of the shaded region is half the area of the rectangle.
ACT/SAT A passenger in a hot-air balloon spots a small fire on the ground. The angle of depression to the fire is 30°, and the height of the hot-air balloon is 150 feet. To the nearest foot, what is the horizontal distance from the hot-air balloon to the fire?
Step-by-step explanation:
law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a,b,c being the sides of the triangle, A, B, C are the corresponding opposite angles in the triangle.
the angle of depression is the external angle of the triangle vertex at the balloon. that means the internal angle is 60°, as both together must be 90° (the angle between the height of the balloon and the horizontal line at the balloon).
the angles at the ground at the fire are mirrored : the internal angle there is 30°, the external angle is 60°.
and so,
height/sin(30) = 150/0.5 = distance/sin(60)
distance = sin(60)×150/0.5 = sin(60)×300 =
= 259.8076211... ft ≈ 260 ft
Find the value of x.
33
30°
x =
Which expression is equivalent to g/2h
Answer:g/2h
Step-by-step explanation:
g/2h x g/2h= g/2hSuppose a State of California bond will pay $1,000 eight years from now. If the going interest
rate on these 8-year bonds is 4.5%, how much is the bond worth today?
a. $682.09
b. $597.71
c. $703.19
d. $829.76
e. $675.06
Answer:
a. $682.09
Step-by-step explanation:
We can use the present value formula to find the value of the bond today:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.
Substituting the given values, we get:
PV = 1000 / (1 + 0.045)^8 = $682.09
Therefore, the bond is worth $682.09 today, which is option (a).
Which of the following are solutions to the quadratic equation below?
Check all that apply.
x²+7x-8=0
A. -1
B. 2
C. -4
D. -8
E. 1
Therefore, the solutions to the quadratic equation x² + 7x - 8 = 0 are -8 and 1. The answers are D and E.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations. Equations can be solved by manipulating the expressions to find the value of the variables that satisfy the equation. Equations can be used to model real-world situations, and they are an important tool in many fields, including mathematics, physics, engineering, and economics.
Here,
To check which values are solutions to the quadratic equation, we can substitute each value into the equation and see if it equals zero.
Substituting -1 into the equation:
(-1)² + 7(-1) - 8 = 1 - 7 - 8 = -14, which is not equal to zero.
Substituting 2 into the equation:
2² + 7(2) - 8 = 4 + 14 - 8 = 10, which is not equal to zero.
Substituting -4 into the equation:
(-4)² + 7(-4) - 8 = 16 - 28 - 8 = -20, which is not equal to zero.
Substituting -8 into the equation:
(-8)² + 7(-8) - 8 = 64 - 56 - 8 = 0, which is equal to zero. Therefore, -8 is a solution to the equation.
Substituting 1 into the equation:
1² + 7(1) - 8 = 1 + 7 - 8 = 0, which is equal to zero. Therefore, 1 is a solution to the equation.
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someone please help me. alg 2. spam comments will be reported and deleted.
The answer of the given question based on series to match the correct summation is the given series matches with option 2: 1 + 0.5 + 0.25 + 0.125 + ...
What is Infinite series?In mathematics, an infinite series is a sum of infinitely many terms. An infinite series can be thought of as the limit of the sequence of partial sums, which is obtained by adding only the first n terms of the series. If the limit of the sequence of partial sums exists and is finite, then the infinite series is said to be convergent; otherwise, it is said to be divergent.
Infinite series have many applications in mathematics, science, and engineering, and are used to approximate functions, solve differential equations, and model physical phenomena.
The given infinite series is: 3 - 9/4 + 27/16 - 81/64 + ...
This series is a geometric series with first term a = 3 and common ratio r = -3/4.
The formula for the sum of an infinite geometric series with first term a and common ratio r (|r| < 1) is given by:
S = a / (1 - r)
Plugging in the values of a and r, we get:
S = 3 / (1 - (-3/4)) = 3 / (7/4) = 12/7
Therefore, the given series matches with option 2: 1 + 0.5 + 0.25 + 0.125 + ...
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Write the equation for each line
Answer:
y = -x
Step-by-step explanation:
We can use two points on the line to write the equation.
Using ( 0,0) and (2,-2), we can find the slope.
m = ( y2-y1)/(x2-x1)
= ( -2-0)/(2-0)
= -2/2
= -1
The y intercept is 0.
y = mx+b where m is the slope and b is the y intercept.
y = -x+0
y = -x
Triangle JKL, with vertices J(-7,-9), K(-4,-8), and L(-5,-6), is drawn inside a rectangle, as shown below.
Triangle JKL's area is 3 square units as a result.
How is area of triangle determined in coordinate geometry determined?The vertices' coordinates and the following formula must be used to determine the area of triangle JKL:
Area equals 1/2*base*height
We must first determine the triangle's height and base length. The distance between points J and K, which is the base, is:
base = √[(x2 - x1)² + (y2 - y1)²]
= √[(-4 - (-7))² + (-8 - (-9))²]
= √[3² + 1²]
= √10
The height is calculated as the distance between point L and the base-containment line. To calculate it, we can use the following formula for the separation between a point and a line:
height = |(y2 - y1)x0 - (x2 - x1)y0 + x2y1 - y2x1| / √[(y2 - y1)² + (x2 - x1)²]
= |(-9 - (-8))(-5) - (-7 - (-4))(-6) + (-4)(-9) - (-8)(-7)| / √[(1)² + (3)²]
= 6 / √10
Now, we can enter the height and base values into the triangle's area formula:
Area = 1/2 * √10 * 6 / √10
= 3
Triangle JKL's area is 3 square units as a result.
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Give a solution to 3x+7y=11 as an ordered pair, (x,y)
After solving the given equation 3x+7y=11 we know that (A) (6, -1) lies on the graph of the given equation.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2.
A noun that counts.
When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.
So, we are asked to identify the point on its graph.
(6, -1)
Adding "x=6" and "y=-1"
3x+7y=3×6+7×(-1)
= 18-7
= 11
Thus, on the graph of 3x+7y=11, (6, -1) is located.
(1,-2)
X = 1 and Y = -2
3x+7y=3×1+7×(-2)
= 3-14
= -11
As a result, the graph of 3x+7y=11 does not contain (1, -2)
(0,-4)
X = 0 and Y = -4
3x+7y=3×0+7×(-4)
= -28
Hence, the graph of 3x+7y=11 does not contain (0, -4)
(0,4)
By setting x=0 and y=4,
3x+7y=3×0+7×4
= 28
In light of this, the graph of 3x+7y=11 does not contain (0, 4)
Therefore, after solving the given equation 3x+7y=11 we know that (A) (6, -1) lies on the graph of the given equation.
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Complete question:
Which ordered pair is on the graph of equation 3x+7y=11?
a. (6,-1)
b. (1,-2)
c. (0,-4)
d. (0,4)
Time in minutes a. Define variables and write an equation to represent the relationship between the quantities b. How far would the biker travel in 20 minutes? c. If the biker traveled 48 miles, how many minutes did he bike? Round to the nearest tenth.
A. The equation that relates these variables is:
d = s * t. B. The biker would travel 10 miles in 20 minutes. C. The biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.
How did we get the values?a. Let's define the variables:
t = time in minutes
d = distance traveled by the biker in miles
s = speed of the biker in miles per minute
The equation that relates these variables is:
d = s * t
b. If the biker travels for 20 minutes, we can use the equation above to find the distance traveled:
d = s * t
d = s * 20 (since t = 20 minutes)
We need to know the speed of the biker to calculate the distance traveled. Let's assume that the biker's speed is 0.5 miles per minute (which is equivalent to 30 miles per hour):
d = 0.5 * 20
d = 10
Therefore, the biker would travel 10 miles in 20 minutes.
c. If the biker traveled 48 miles, we can rearrange the equation above to find the time:
d = s * t
t = d / s
We need to know the speed of the biker to calculate the time. Let's assume that the biker's speed is still 0.5 miles per minute:
t = 48 / 0.5
t = 96
Therefore, the biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.
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find the 40% Axo value of x Lage:
Use the method of Lagrange multipliers to find the dimensions of the least expensive packing crate with a volume of 240 cubic feet when the material for the top costs $2 per square foot, the bottom is $3 per square foot and the sides are $1.50 per square foot.
Answer:
a hard one
Step-by-step explanation:
Find the slope of the following line:
y=−7x−6
Answer: -7
Step-by-step explanation:
in the linear equation, y=mx+b, m represents the slope of the line, so when looking at an equation the best way to find the slope is to find where the m variable would be
Graph each function between 0 and 2
The function oscillates between two horizontal asymptotes, y=3 and y=-3, as x approaches the vertical asymptotes.
How to study graph?
To graph the function y=3cot(x) between 0 and 2, we can start by identifying the key characteristics of the cotangent function. The cotangent function is defined as the ratio of the adjacent side to the opposite side of a right triangle, with respect to a given angle. As such, the cotangent function is periodic with a period of π and has vertical asymptotes at x=nπ, where n is an integer.
The coefficient of 3 in the given function y=3cot(x) vertically stretches the function by a factor of 3, and does not affect the period or the vertical asymptotes.
Between 0 and 2, there are two vertical asymptotes at x=0 and x=π. To graph the function, we can plot a few points along the curve, using the symmetry properties of the cotangent function. Specifically, the cotangent function is odd, meaning that cot(-x)=-cot(x), and thus the graph is symmetric about the origin.
At x=π/4, we have cot(π/4)=1, and thus y=3cot(π/4)=3. Similarly, at x=3π/4, we have cot(3π/4)=-1, and thus y=3cot(3π/4)=-3. Using the symmetry property, we can also plot points at x=-π/4 and x=-3π/4, with y=3cot(-π/4)=-3 and y=3cot(-3π/4)=3, respectively.
Connecting these points with smooth curves, we can see that the graph of y=3cot(x) oscillates between two horizontal asymptotes, y=3 and y=-3, as x approaches the vertical asymptotes at x=0 and x=π.
Overall, the graph of y=3cot(x) between 0 and 2 can be summarized as follows:
There are two vertical asymptotes at x=0 and x=π.
The function oscillates between two horizontal asymptotes, y=3 and y=-3, as x approaches the vertical asymptotes.
The graph is symmetric about the origin.
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Find sum of g(x) and h(x) where g(x) = 5x³ + 3x²y + 2xy² -9y³x² and h(x) = 10x³ - 2xy² - 2xy² - x²y + 5y³x² also find the degree.
polynomial
Answer:
differentiate between tropical and subtropical climate zone on the basis of climate and economic activities in 4 points class 10
. A bread recipe calls for 3/4 cup rye flour, 2/4 cup wheat flour,
and ¾ cup white flour. How much flour is in the bread? Show
your work
Answer:
2 cups of flour
Step-by-step explanation:
We want to find the total amount of flour, which means we need to add.
3/4 + 2/4 + 3/4 =
8/4
We can simplify this term.
8/4 =2
2 cups of flour
Answer:
2 cups of flour
Step-by-step explanation:
A bread recipe has,
3/4 cup of rye flour
2/4 cup of wheat flour
3/4 cup of white flour
So, to find the total amount of flour, add all the given fractions together.
[tex]\sf Total\: amount\: of\: flour = rye \:flour + wheat\: flour + white \:flour\\\\\sf Total\: amount\: of\: flour =\frac{3}{4} +\frac{2}{4} +\frac{3}{4} \\\\\sf Total\: amount\: of\: flour =\frac{3+2+3}{4} \\\\\sf Total\: amount\: of\: flour =\frac{8}{4} \\\\\sf Total\: amount\: of\: flour =2 \:cups[/tex]
a-1/a=2/3 for some real number a. Find a^4+1/a^4
Answer:
[tex]1 \frac{1}{81} \ [/tex]
Solution:
[tex] \frac{a - 1}{a} = \frac{2}{3} [/tex]
1) 2a = 3(a - 1)
2a = 3a - 3
2a - 3a = -3
-a = -3 / * (-1)
a = 3
2) Replace the a with 3 in this:
[tex] \frac{ {a}^{4} + 1}{ {a}^{4} } [/tex]
[tex] \frac{ {3}^{4} + 1}{ {3}^{4} } = \frac{81 + 1}{81} = \frac{82}{81} = 1 \frac{1}{81} [/tex]
I don't know if I got this right, but at least I tried
For f(x) = x-5 and g(x)=x^2+3 find f[g(-2)].
Show all work
f[g(-2)] = 2 as the function f(x) = x - 5 must then be used to evaluate the function f[g(-2)] .
what is function ?A function is a mathematical construct that transforms a set of inputs (referred to as the domain) into a single output from another set (called the range). A function is, in other words, a rule that allots precisely one output to each input in the domain. The notation f(x) is frequently used to denote functions, where f stands for the function name and x for the input value. As an illustration, the function f(x) = 2x + 1 doubles any input x, adds 1, and returns the result.
given
To begin, we must calculate g(-2) using the formula g(x) = x2 + 3:
[tex]g(-2) = (-2)^2 + 3 = 4 + 3 = 7[/tex]
The function f(x) = x - 5 must then be used to evaluate the function f[g(-2)]:
f[g(-2)] = f(7) = 7 - 5 = 2
Hence, f[g(-2)] = 2.
f[g(-2)] = 2 as the function f(x) = x - 5 must then be used to evaluate the function f[g(-2)] .
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A jet travels 2576 miles against a jetstream in 4 hours and 3216 miles with the jetstream in the same amount of time. What is the rate of the jet in still air and what is the rate of the jetstream?
Answer: 80 mph fet stream
Step-by-step explanation:
2576/4 + the jet stream=3216/4- jet stream
simplified, 80 mph
a) Determine the edge length of this cube Volume =91 125 cm 3
b) Determine the side length of this square Area = 3969 cm²
PLS HELP!!!
The lengths of the edges of the cubes are 45cm and 63cm respectively.
EquationsTo determine the edge length of a cube with a volume of 91,125 cm³, we can use the formula:
Volume of a cube = edge length³
Plugging in the given value, we get:
91,125 = edge length³
Taking the cube root of both sides, we get edge length
edge length ≈ 45
Therefore, the edge length of the cube is approximately 45 cm.
To determine the side length of a square with an area of 3,969 cm², we can use the formula
Area of a square = side length²
Plugging in the given value, we get:
3,969 = side length²
side length = √3,969
Using a calculator, we can simplify this to
side length ≈ 63
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189=-6x+3(-7x-18) what is x
Answer:
x = -9
Step-by-step explanation:
To solve for x in this equation, we first need to simplify the right-hand side by distributing the 3:
189 = -6x + (-21x - 54)
Next, we can combine like terms on the right-hand side:
189 = -27x - 54
Adding 54 to both sides:
243 = -27x
Dividing both sides by -27:
x = -9
Therefore, the solution to the equation 189=-6x+3(-7x-18) is x = -9.
Answer:
To solve for x in the equation 189=-6x+3(-7x-18), we can use the following steps:
Distribute the 3 to the terms inside the parentheses:
189 = -6x + (-21x - 54)
Combine like terms on the right side of the equation:
189 = -27x - 54
Add 54 to both sides of the equation:
189 + 54 = -27x
Simplify the left side of the equation:
243 = -27x
Divide both sides by -27:
x = -9
Therefore, x is equal to -9.
Hope This Helps!
Choose the correct simplification of the expression −5x2(4x − 6x2 − 3).
30x4 − 20x3 + 15x2
−11x4 − x3 − 8x2
−30x4 + 20x3 − 15x2
30x4 + 20x3 + 15x2
Answer:
first option (30x4 − 20x3 + 15x2)