Answer:
23/99 as a decimal is 0.23232323232323.
Step-by-step explanation:
In fractions, the numerator is the number above the line and the denominator is the number below.
The line in a fraction that separates the numerator and the denominator represents division.
To convert a fraction to a decimal, divide the numerator by the denominator.
a bar of dark chocolate is advertised to contain 60 % of pure cocoa the total weight of the bar is 8 ounces how many ounces if the bar are pure cocoa
Answer:
4.8
Step-by-step explanation:
60 percent of 8 is 4.8
I hope this helps!
how to solve for problem 14
m∠ AEM = 20°
How to determine the angle
From the given figure, we can see that m∠ AEM is alternate to m∠ ACE
Note that m∠ ACE = 20°
Alternate angles are equal.
If m∠ ACE is alternate to m∠ AEM
Then, m∠ AEM = 20°
Hence, m∠ AEM = 20°
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A rectangular piece of land measures 4.5 km long and 2.5 km wide
Calculate the ratio of
1.It's width to its length
2.Its length to its perimeter
The ratio of its width to its length is; 5 :9.
The ratio of its length to its perimeter is; 9: 28.
What is the ratio of its width to its length?1). From the task content, the land measures 4.5 km long and 2.5 km wide. Hence, the ratios is; 2.5: 4.5.
Therefore, we have; 5: 9 by expression as whole number ratios.
2) Since the perimeter of the rectangle is; 2(2.5+4.5) = 14.
The ratio of length to perimeter expressed simply is therefore; 9: 28.
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A: Describe a relationship that can be modeled by the function represented by the graph, and explain how the function models the relationship.
B: Identify and interpret the key features of the function in the context of the situation you described in part A.
The function represented is analyzed below.
How to illustrate the function?The function represented by the graph is related to a piecewise function.
The key features of the function include:
The function has a constant value in interval (0, 15) which is 40.
It decreases at first and then increases from 45 to 65.
It increases linearly from 65 to 90.
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Select the correct answer.
(1, √3) to polar form.
A. (√3, 30°)
B. (2,60°)
C. (4,30°)
D. (2,240°)
Answer:
(2, 60°)
Step-by-step explanation:
A point in polar form (a,b) is represented by a radius and an angle (r, ϴ). To convert, use the formula r² = a² + b² to get r, and [tex]tan^{-1}[/tex](b/a) = ϴ
[tex]r = \sqrt{1^{2} + \sqrt{3} ^{2} }[/tex]
[tex]r = \sqrt{1+3}[/tex]
[tex]r = \sqrt{4}[/tex]
= 2
[tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]/1) = ϴ
= 60°
John is looking at the top of a building and thinking it would be great to make a zipline from the top to your current location. He measures the angle of elevation as 28and is 182 feet from the base of the buildingHow long a zipline is needed if John is 71.5 inches tall? Include a sketch that shows all known information and clearly shows what you need to findShow all work and give the answer rounded to the nearest tenth of a foot
Answer:
Step-by-step explanation:
sin(28) = 2184 / x
x= 2184/ sin(28) = 2184 / 0.4694 = 4652.75
4652.75 / 12 = 387.7 ft
ANSWER: 387.7ft
In the given case, The length of the zipline needed is approximately 96.7 feet.
To find the length of the zipline needed, we can use trigonometry. Let's start by drawing a sketch to visualize the problem. | | zipline | | | | | | | | | | John | Building 28°
John's location, with the angle of elevation labeled as 28°. John is 182 feet away from the base of the building, and he is 71.5 inches tall.
To find the length of the zipline, we can use the tangent function.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is John's height, and the adjacent side is the distance between John and the building. Using the tangent function, we have: tan(28°) = opposite / adjacent
We want to find the length of the zipline, which is the hypotenuse of the right triangle formed by John, the building, and the zipline. Let's call this length "x".
Therefore, we can rewrite the equation as: tan(28°) = 71.5 inches / 182 feet To solve for x, we need to convert the units so that they match.
Let's convert inches to feet: 71.5 inches = 71.5 inches * (1 foot / 12 inches) ≈ 5.96 feet (rounded to the nearest hundredth)
Now, let's solve for x: tan(28°) = 5.96 feet / 182 feet
To isolate x, we can multiply both sides by 182 feet: x ≈ tan(28°) * 182 feet Using a calculator, we find that tan(28°) ≈ 0.5317.
Multiplying this by 182 feet, we get: x ≈ 0.5317 * 182 feet ≈ 96.7 feet (rounded to the nearest tenth) .
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Which is the best estimate of -14 1/9 (-2 9/10) ?
Answer:
42
Step-by-step explanation:
-14 1/9 is about -14.
-2 9/10 is about -3.
Multiplying these, we get (-14)(-3)=42.
9 boys can paint a basketball court in 3 hours how long should 5 boys take working at the same rate
Answer:
100 minutes
Step-by-step explanation:
3 hours= 180 min
180/9 = 20
20 x 5 =100 min
Rearrange the equation so a is the independent variable.
−3a+6b=a+4b
Answer:
6b-4b=a+3a
2b=4a
4a=2b
a=2b/4
a=b/2
What is the standard equation for the circle with center (1,-3) that passes through the point (2,2)?
The standard equation for the circle is (x - 1 ) ^2 + (y + 3)^2 = 2 ^2
A circle is a closed curve that is drawn from a fixed point called the center in which all points on the curve are the same distance from the center of the center. The equation of a circle with center (h, k) and radius r is given by:
(x-h)^2 + (y-k)^2 = r^2
This is the standard form of the equation. So if we know the coordinates of the center of the circle and also its radius, we can easily find its equation.
Consider any point P(x, y) on the circle. Let "a" be the radius of the circle which is equal to OP.
We know that the distance between the point (x, y) and the origin (0,0) can be found using the distance formula which is equal to -
√[x^2+y^2]= a
Therefore the equation of a circle with center as origin is,
x^2+y^2= a^2
Where "a" is the radius of the circle.
An alternative method
Let's derive another way. Assume that (x,y) is a point on the circle and the center of the circle is at the origin (0,0). Now, if we draw a perpendicular from the point (x,y) to the x-axis, we get a right triangle, where the radius of the circle is the hypotenuse. The base of the triangle is the distance along the x-axis and the height is the distance along the y-axis. Applying the Pythagorean theorem here, we therefore obtain:
x^2+y^2 = radius^2
We need to find the standard equation for the circle with center (1,-3) that passes through the point (2,2)
Standard equation for circle is
(x-h)^2 + (y-k)^2 = r^2................(1)
Here h = 1 , k = -3 and r = 2
put this value of h, k and r in equation (1), we get
(x - 1 ) ^2 + (y + 3)^2 = 2^2
Hence the standard equation of the circle is
(x - 1 ) ^2 + (y + 3)^2 = 2 ^2
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A survey of several 10 to 11 year olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46 Construct the 98% confidence interval for the average amount spent by 10 to 11 year olds on a trip to the mall. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The 98% confidence interval for the average amount spent by 10 to 11-year-olds on a trip to the mall is 23.36 ± 2.933.
How to calculate the confidence interval and its critical value?The confidence interval for a given level of percentage is given by
C. I = μ ± Z(σ/√n)
Where,
μ - mean, σ - standard deviation, n - sample size, and z - critical value.
The critical value is calculated by
step 1: 100% - (the confidence level)
step 2: Converting the step 1 result into decimal value
step 3: dividing the step 2 result by 2
This is indicated by α/2. So, from the normal distribution table, the z-value at α/2 is said to be the required critical value and denoted by Z_(α/2) or Z.
Calculation:It is given that,
A survey of several 10 to 11-year-olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46
Sample size n = 6
Step 1: Finding the mean for the given amounts of the survey:
Mean μ = (18.31 + 25.09 + 26.96 + 26.54 + 21.84 + 21.46)/6
= 23.36
Step 2: Finding the standard deviation:
Standard deviation σ = √summation(x - mean)²/n
On calculating, we get σ = 3.09
Step 3: Finding the critical value:
It is given that the confidence level is 98%
So, (100% - 98%) = 2%
Converting into decimal gives 0.02
So, α/2 = 0.02/2 = 0.01
Thus, at 0.01, the critical value Z = 2.326
Step 4: Constructing the confidence interval:
C.I = 23.36 ± (2.326) × (3.09/√6)
= 23.36 ± (2.326 × 1.261)
= 23.36 ± 2.933
So, the lower bound = 23.36 - 2.933 = 20.427
the upper bound = 23.36 + 2.933 =26.293
Therefore, the 98% confidence interval lies from 20.427 to 26.293.
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Which lines can you conclude are parallel given that M<7 m<11=180 Justify your conclusion with a theorem. Line c is parallel to line d by the Converse of the Alternate Interior Angles Theorem. Line c is parallel to line d by the Converse of the Same-Side Interior Angles Theorem. Line a is parallel to line b by the Converse of the Alternate Interior Angles Theorem. Line a is parallel to line b by the Converse of the Same-Side Interior Angles Theorem. 23
Lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,
What is the Converse Same-Side Interior Angles Theorem?The Converse of Same-Side Interior Angles Theorem states that, if the sum of two interior angles on same side of a transversal equals 180 degrees, then the lines they lie on are parallel to each other.
Since M<7 + m<11 = 180, lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,
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find the values of A and B
PLEASE HELP GIVING BRAINLIEST
Factoring the roots, the values of A and B are given as follows:
A = 3z.B = 2.What are the values of A and B?The expression is:
[tex]\sqrt{\frac{45\alpha z^3}{40y}} = \frac{A\sqrt{\alpha z}}{B\sqrt{2y}}[/tex]
We have that:
[tex]\frac{45}{40} = \frac{9}{8}[/tex]
Hence:
[tex]\sqrt{\frac{45\alpha z^3}{40y}} = \sqrt{\frac{9\alpha z^3}{8}} = \sqrt{\frac{9\alpha z^2 \times z}{4 \times 2}} = \frac{A\sqrt{\alpha z}}{B\sqrt{2y}}[/tex]
Hence, comparing the last two equalities:
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The functions u and w are defined as follows. u(x)=2x+2 w(x)=-2x^2+2 find the value of w(u(4)).
The value of w(u(4)) is 73.
u( x ) = - 2*x + 2
w( x ) = 2*x^2 + 1
w( u( x ) ) = w( - 2*x + 2 )
⇒ w( u( x ) ) = 2*( - 2*x + 2 )^2 + 1
⇒ w( u( x ) ) = 2*[ 2^2 + ( 2*x )^2 - 2*2*( 2*x ) ] + 1
⇒ w( u( x ) ) = 2*[ 4 + 4*x^2 - 8*x ] + 1
⇒ w( u( x ) ) = 8 + 8*x^2 - 16*x + 1
⇒ w( u( x ) ) = 8*x^2 - 16*x + 9
⇒ w( u( 4 ) ) = 8*4^2 - 16*4 + 9
⇒ w( u( 4 ) ) = 8*16 - 16*4 + 9
⇒ w( u( 4 ) ) = 128 - 64 + 9
⇒ w( u( 4 ) ) = 73
In mathematics, a feature from a set X to a fixed Y assigns to each detail of X exactly one detail of Y. The set X is called the domain of the function and the set Y is referred to as the codomain of the function. features were firstly the idealization of how various quantity relies upon any other quantity.
These elementary functions include
rational functions, exponential functions, basic polynomials, absolute values square root function.A function is defined as a relation between a set of inputs having one output each. In simple phrases, a function is a courting among inputs wherein every entry is associated with exactly one output. every function has a site and codomain or range. A characteristic is normally denoted through f(x) in which x is the input.
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(05.02 MC)
Solve 2 log x = log 64.
Ox= 1.8
Ox=8
Ox= 32
Ox = 128
Answer:
x = 8
Step-by-step explanation:
[tex]2logx=log64\\logx^2=log64[/tex]
now that both sides has log, you can remove them and leave it as:
[tex]x^{2} =64\\[/tex]
take the square root of both sides:
[tex]x = [8, -8]\\x = 8[/tex]
logarithmic equations can't have negative solutions, plus -8 isn't an option
i hope this helped!
Instructions: Find the measure of the indicated angle to the nearest degree.
Identify each expression that represents the slope of a tangent to the curve y = 1/x+1 at any point (x,y)
The expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.
How to find an expression for the slope at any point of a function
The slope at any point of the function can be found by definition of derivative following algebraic handling:
[tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex]
[tex]m = \lim_{h \to 0} \frac{\frac{x+1 - x - h - 1}{(x + h + 1)\cdot (x + 1)} }{h}[/tex]
[tex]m = -\lim_{h\to 0} \frac{1}{(x + h + 1)\cdot (x + 1)}[/tex]
[tex]m = -\frac{1}{(x + 1)^{2}}[/tex]
Thus, the expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.
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each of 16 students in a class made a poetry book. each book contained 24 poems. how many poems are in 16 books
HELP PLS 5. Find the missing side lengths. Leave the answers as radicals in simplest form.
Answer:
[tex]a=22, b=11\sqrt{3}[/tex]
Step-by-step explanation:
Given a 30-60-90 triangle, the shortest side is always opposite of the smallest angle, in this case 11 is opposite the 30° angle. The largest side of a 30-60-90 triangle will always be twice the smallest, giving [tex]a[/tex] a measure of [tex]22[/tex]. To get the side across the 60° angle we multiply the smallest side by the square root of 3. Meaning [tex]b=11\sqrt{3}[/tex]
Find the area of the polygon formed whe these points are connected a(3,7)b(3,3)c(7,3)d(7,7)
Here, given
sides of polygon= a(3,7)b(3,3)c(7,3)d(7,7)
Let, 3 = x1 & 7= y1 , 3= x2 & 7= y2 , 7= x3 & 3= y3 , 7= x4 & 7= y4
[tex]\frac{1}{2}[/tex] [det.(9-21)+det.(9-21)+det.(49-21)+det.(49-21)] {we took determinants of all the given sides}
[tex]\frac{1}{2}[/tex] (32)
16cm^2
Hence, the area of the polygon is 16cm2.
The formula for calculating the area of a regular polygon is: area = (number of sides x 1 side length x apothem distance) / 2, where the value of the apothem is the formula apothem = [(1) Length side). / {2 × (tan (180 / number of sides))}].
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The volume of this cylinder is 7500cm3.
find the missing length x.
give your answer rounded to 1 dp.
V = π r2h. Volume Calculations. Round ( Cylinder) Tanks. Example 1. Find the Volume in cubic feet of a tank having a radius of 10 feet and ...
Missing: 7500m Give SF.
In the case of a hollow cylinder, we measure two radii, one for the inner circle and one for the outer circle formed by the base of a hollow cylinder. Suppose, r1 and r2 are the two radii of the given hollow cylinder with 'has the height, then the volume of this cylinder can be written as; V = πh(r12 – r22).
To find the volume of a box, simply multiply the length, width, and height — and you're good to go! For example, if a box is 5×7×2 cm, then the volume of a box is 70 cubic centimeters.
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Your ship has steamed 1651 miles at 20 knots using 580 tons of fuel oil. The distance remaining to your next port is 1790 miles. If you increase speed to 25 knots, how much fuel will be used to reach that port
The 680 tons of fuel needed to cover the next 1790 miles distance.
According to the statement
We have given that the ship covered a 1651 miles distance at 20 knots by a 580 tons of fuel oil.
And distance remaining to next port is 1790 miles and speed increases to 25 knots.
And we have to find that how much fuel used to reach that port.
So, Distance covered = 1651 mile
fuel used = 580 tons
distance covered with 1 tons fuel = 1651/580
distance covered with 1 tons fuel = 2.85 mile at a speed of 20 knots.
so, The fuel consumption for 1790 mile is = 1790/2.85
The fuel consumption for 1790 mile is = 628 tons of fuel needed.
So, The 680 tons of fuel needed to cover the next 1790 miles distance.
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PLS HELP PLSSS HELP
I NEED THIS SOLVED
PLSS DO IT
PLSSSS HELPP
ITS SO HARD
I WILL FAIL
HELP PLSSS
Answer:
x² + 5x - 14 = (x + 7)(x - 2)
x² - 3x - 54 = (x - 9)(x + 6)
x² + 8x + 12 = (x + 2)(x + 6)
x² - 11x + 30 = (x - 5)(x - 6)
x² - 25 = (x + 5)(x - 5)
x² + 8x - 9 = (x - 1)(x + 9)
Step-by-step explanation:
To factor x² + ax + b, look for two numbers whose sum is a and whose product is b.
The factorization of x² - a² is (x + a)(x - a).
x² + 5x - 14 = (x + 7)(x - 2)
x² - 3x - 54 = (x - 9)(x + 6)
x² + 8x + 12 = (x + 2)(x + 6)
x² - 11x + 30 = (x - 5)(x - 6)
x² - 25 = (x + 5)(x - 5)
x² + 8x - 9 = (x - 1)(x + 9)
The factored form of the given expressions are
y = (x -2)(x +7)
y = (x +6)(x -9)
y = (x +2)(x +6)
y = (x -5)(x -6)
y = (x +5)(x -5)
y = (x -1)(x +9)
y = (x +4)(x -4)
Factoring quadratic expressionsFrom the question we are to factor the given quadratic expressions
y = x² + 5x - 14y = x² +7x -2x - 14
y = x(x +7) -2(x +7)
y = (x -2)(x +7)
y = x² -3x - 54y = x² -9x +6x - 54
y = x(x -9) +6(x -9)
y = (x +6)(x -9)
y = x² +8x + 12y = x² +6x +2x +12
y = x(x +6) +2(x +6)
y = (x +2)(x +6)
y = x² -11x +30y = x² -6x -5x +30
y = x(x -6) -5(x -6)
y = (x -5)(x -6)
y = x² - 25y = (x +5)(x -5)
y = x² + 8x - 9y = x² +9x -x -9
y = x(x +9) -1(x +9)
y = (x -1)(x +9)
y = x² - 16y = (x +4)(x -4)
Hence, the factored form of the given expressions are
y = (x -2)(x +7)
y = (x +6)(x -9)
y = (x +2)(x +6)
y = (x -5)(x -6)
y = (x +5)(x -5)
y = (x -1)(x +9)
y = (x +4)(x -4)
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A triangle is given by A ( 3,2 ) B (-1,5) and C (0,-1) . What is the equation of the line through B parallel to AC ( give ans and how it works pls )
Answer:
Step-by-step explanation:
Solution :
hello :
note :
Use the point-slope formula.
y - y_1 = m(x - x_1) when : x_1= -1 y_1= 5
m= the slope is : (YC - YA)/(XC -XA)
(-1-2)/(0-3) = -3/-3 =1
( parallel to AC means same slope)
an equation in the point-slope form is : y -5 = 1(x+1)
y=x+6
PLEASE HELP ME IM STUCK
The slope-intercept formula of the linear equation is:
[tex]y = \frac{3}{7}x + 7[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The y-intercept is of b = 7. The line also goes through point (0,-3), hence the slope is:
m = 3/7.
Thus the equation is:
[tex]y = \frac{3}{7}x + 7[/tex]
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Because computers operate so quickly, developers often measure time in milliseconds (which are 1000th of a second). Which operation could we perform in order to find the number of milliseconds in a year
The operation is 365*24*60*60*1000 = 31536*10^6.
As we know the year has 365 days.
Each day has 24 hours.
Each hour has 60 minutes.
Each minute has 60 seconds.
Each second has 1000 millisecond.
Therefore number of milliseconds in a year is
365*24*60*60*1000 = 31536*10^6.
Hence we get the The operation is 365*24*60*60*1000 = 31536*10^6.
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HELP MEEEEEEEEEEEEEEEE
Step-by-step explanation:
Well first let's find the derivative in using the power rule
h'(t) = (-4.9)t + 157
h'(t) = -9.8t + 157
we can see from the image above that the maximum height is 1452.602 so that is the answer to the second question.
h'(1452.602) = -9.8(1452.602) + 157
h' = 14,078.500
Hi! It’d be really helpful if someone could explain he two questions below, thanks!
so confused pls help>>>> there’s a pic
Answer:
(c) 25/4
Step-by-step explanation:
A perfect square trinomial is obtained by "completing the square." The constant in a perfect square trinomial is the square of half the x-coefficient.
Square of a binomialA "perfect square trinomial" is the square of a binomial.
(x +a)² = x² +2ax +a²
Of note here is that the constant (a²) is the square of half of the x-term coefficient:
((2a)/2)² = a²
Completing the squareThe given expression (x² +5x) has an x-term coefficient of 5. The square of half that is ...
(5/2)² = 25/4
The constant that must be added to make x² +5x into a perfect square trinomial is 25/4.
(x² +5x) +25/4 = x² +5x +25/4 = (x +5/2)²
Jenny draws the path to walk from her house over to her grandmother's house. She knows that she has to avoid the end of the segment where construction is taking place. If she wants to use equations to identify her path on the coordinate plane, what should her answer look like?
Her answer should look like y = x + 2, x ≤ 2
How to determine the equation?The complete question is added as an attachment
From the attached graph, we have the following points
(x, y) = (2, 4) and (0, 2)
See that the difference between the y and x values is 2 where y > x
So, we have
y - x = 2
Add x to both sides
y = x + 2
The highest value of x in the graph is 2.
So, we have
x ≤ 2
Hence, her answer should look like y = x + 2, x ≤ 2
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