The proportion of the children identified orange as their favorite type of juice is 400 / 1000.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
From the table
Adults who like oranges= 600
and, Children who like oranges = 400
So, proportion of the children identified orange as their favorite type of juice
= 400/ 1000
Learn more about proportion here:
https://brainly.com/question/26974513
#SPJ1
An object was launched off the top of a building. The function f(x)=-16x^{2}+16x+96f(x)=−16x
2
+16x+96 represents the height of the object above the ground, in feet, xx seconds after being launched. Find and interpret the given function values and determine an appropriate domain for the function.
maximum height reached by the object is 100 feet.
Height of the building is 96 feet.
Appropriate domain is 0 ≤ x ≤ 3.
Given,
function for the height of the object above from ground is
[tex]f(x)=-16x^{2}+16x+96[/tex]
The domain can be determined for x for which the value of f(x) = 0
Therefore, when [tex]-16x^{2}+16x+96=0[/tex], we get;
[tex]-16x^{2}+16x+96=0\\\\-16(x^2-x-6)=0\\\\x^2-x-6=0\\\\x^2+2x-3x-6=0\\\\(x+2)(x-3)=0\\\\x=-2 or x=3[/tex]
The minimum value of time, x is 0 and when x = 3, the object is on the ground.
Therefore;
The appropriate domain is 0 ≤ x ≤ 3The maximum value of f(x) = a·x² + b·x + c, is given at [tex]x=-\frac{b}{2a}[/tex]
Therefore;
[tex]x=-\frac{16}{2*-16}=\frac{1}{2}[/tex]
Substituting 'x in f(x) we get,
[tex]f(1/2)=-16(\frac{1}{2} )^{2}+16(\frac{1}{2} )+96\\=-4+8+96=100[/tex]
The maximum height reached by the object, = 100 feetThe height of the building is given when the time, x = 0, as follows;
Height of building, [tex]f(0)=-16(0)^{2}+16(0)+96=96[/tex] feet.Hence, the appropriate domain of the function is 0 ≤ x ≤ 3.
To learn more about interpretation of domain refer here
https://brainly.com/question/20263812
#SPJ9
The bulbs are incandescent bulb for a and fluorescent bulb is for b
A 0.3kwh in 3 hours and 1.0kWh in 10 hours and for b is 0.35Kwh in 3 hours and in 10 hours it’s 0.9 kWh usage (pls help brainlist)
The graph has been shown where lines A and B meet each other at the coordinates (0.51, 5.2).
What are graphs?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.Bar graphs, circle graphs, and line graphs are the three most often used types of graphs. Different types of data can be displayed using different types of graphs.So, the coordinates where both lines meet are:
Coordinates for line A:
(0.3, 3)(1.0, 10)Coordinates for line B:
(0.35, 3)(0.9, 10)Now, plot the graph as follows:
(Refer to the graph attached below)
The coordinates where both lines meet are:
(0.51, 5.2)Therefore, the graph has been shown where lines A and B meet each other at the coordinates (0.51, 5.2).
Know more about graphs here:
https://brainly.com/question/28953186
#SPJ1
Randi takes the stairs at work whenever possible instead of the elevator. She must climb 51 steps from her office to get to the accounting department. The human resources
department is 34 steps below her office. How many steps are there between human
resources and accounting?
The steps between the human resource department and accountant department are 85 steps.
What is Human Resource?
The group of individuals who work for a given organization, business sector, industry, or economy is referred to as its human resources.
As given in the question,
Randi must climb 51 steps from her office to get to the accounting department, and
The HR department is 34 steps below her office.
Since, the HR department is below her office and accountant department is above her office so, we need to add the steps taken from her office to reach both department.
So,
Steps between HR department and accountant department = Steps between her office and HR department + Steps between her office and accountant department
Steps between HR department and accountant department = 51 + 34
Therefore,
Steps between HR department and accountant department = 85 steps
To know more about Human Resource, go to link
https://brainly.com/question/14419086
#SPJ13
6. A new hi-tech 3D Printer valued at $ 27,800 depreciates exponentially at a rate of 5% yearly. Write the logarithmic equation How long will it take until the machinery has value of $13,900
The logarithmic equation for the time taken until the machinery has a value of $13,900 is x = log₁₉/₂₀ 1/2
Given,
A new hi tech 3D printer valued at $27,800 depreciates exponentially at a rate of 5%.
we are asked to determine the logarithmic equation for the time taken until the machinery has the value of $13,900 = ?
based on the conditions, we formulate:
27800 × (1 - 5%)ˣ = 13900
solve the equation.
27800 × (1 - 0.05)ˣ = 13900
calculate the sum or difference.
27800 × 0.95ˣ = 13900
Divide both sides of the equation by the coefficient of variable.
0.95ˣ = 13900/27800
Reduce the fraction.
0.95ˣ = 1/2
convert exponential to logarithm form.
x = log₀.₉₅ 1/2
cross out the common factor.
x = log₉₅/₁₀₀ 1/2
x = log₁₉/₂₀ 1/2
hence we get the required equation.
Learn more about Logarithmic equation here:
brainly.com/question/28041634
#SPJ9
help me on this question (20pts)
The function with same rate of change as the function y = (7/4)x + 3 will be option C.
The rate of change for a function is nothing but rate of change of one thing over the second thing.
it can be calculated by [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
For a equation written in y = mx + c , m is nothing but the slope / rate of change of function.
So for function y = (7/4)x + 3
m = 7/4 which is the rate of change for this function.
Now let us find rate of change for each function.
For A rate of change will be = (-4 - 0) / (5 - 1)
= -4/3
For B it will be = ( 4 - 1) / (0 - (-1) )
= 3
For C it will be = (15 - 8) / (8 - 4)
= 7/4
For D it will be = (-2 - 0) / ( 0 - (-1) )
= -2
Therefore the rate of change which is same as the given function is of option C.
To know more about rate of change for a function
https://brainly.com/question/21335643
#SPJ1
Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the equation for the axis of symmetry.
f(x)=-3(x+2)²+1
Use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.
The equation of the axis of symmetry will be x = -2 and the curve is drawn below.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = -3(x + 2)² + 1
The equation of the axis of symmetry will be given as,
x + 2 = 0
x = - 2
The equation of the axis of symmetry will be x = -2 and the curve is drawn below.
More about the equation of the parabola link is given below.
https://brainly.com/question/20333425
#SPJ1
What is the slope of the line on the graph?
Answer:
The slope is 6
The slope-intercept form is y= 6x-1
Step-by-step explanation:
Homework: 4.2 Apply Pythagorean Theorem
Date
Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
Need help with this math please
The length of the side using the Pythagoras theorem is 4 mi
What is Pythagoras theorem?
Pythagoras theorem says sum of squares of side is equal to the square of the hypotenuse.
We are given one side of the triangle is 3 mi
And hypotenuse of the triangle is 5 mi
Let the another side of the triangle is x mi
By Pythagoras theorem,
3^2 + x^2 = 5^2
9 + x^2 = 25
x^2 = 16
x =4 mi
Using Pythagoras theorem the length of side of another side is 4cm
https://brainly.com/question/343682
#SPJ13
The height of liberty school is 8.85*10^3m.the height of festus school is 5.89*10^3m.write these in ordinary form,find the difference and write each height value correct to 2 sgf
The height of Liberty School in ordinary form is 8850m and height of Festus school is 5890m , the difference of the height of the schools is 2960m .
In the question ,
it is given that
the height of the Liberty school is 8.85×10³m .
we have to convert this height in the ordinary form ,
8.85 × 10³ = (885/100) × 1000
= 885 × 10
= 8850m
The height of the Festus school is 5.89 × 10³ m
in ordinary form it is
= 5.89×10³
= (589/100) × 1000
= 589 × 10
= 5890m
The difference in the height of the schools = (height of the Liberty school) - (height of Festus school) .
So , the difference = 8850 - 5890
= 2960m
Therefore , the height of Liberty School is 8850m and height of Festus school is 5890m , the difference of the height of the schools is 2960m.
Learn more about Ordinary Form here
https://brainly.com/question/13523230
#SPJ1
A horizontal trough is 16 meters long, and its ends are isosceles trapezoids with an altitude of 4 m, a lower base of 4 m, and an upper base of 6 m. If the water is being poured into the trough at the rate of10 m³/min. How fast is the water level rising when the water is 2m deep?
For the volume of through, the rate at which the water level (the depth) is decreasing, increases as more water is drawn from the trough and the rate at which water is being drawn from the through is 0.28cm/min
Volume:
Volume refers the mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Given,
A horizontal trough is 16 meters long, and its ends are isosceles trapezoids with an altitude of 4 m, a lower base of 4 m, and an upper base of 6 m.
Here we need to find the water level rising when the water is 2m deep if the water is being poured into the trough at the rate of10 m³/min.
While we looking into the given question we have identified that the values of length of the through, L = 16 m and the height of the through = 4 m
Lower base of the trapezoidal is a = 4 m
Upper base of the trapezoidal is b = 6 m
And the rate at which the water is decreasing at the depth of 3 m is 25 cm/min
Let us consider the length of the upper base at height is calculated as,
h = 4 + 2·x
So, the Volume of the through is,
=> Trapezoidal cross sectional area × Length
When we apply the value on the formula, then we get,
=> V = (4 + (4 + 2x)/2) x h
Now, if we include the water flow, then it can be written as,
=> V = (4 + (4 + 2x)/2) x h x L
Apply the value of L as 16, then we get,
=> V = (4 + (4 + 2x)/2) x h x 16
When we simplify this one then we get,
=> V = 8h (8 + 2x)
When we expand it then we get
=> V = 64h + 16hx
Here the value of x is not given, however we can express x in terms of h from Figure 3 using
So, by using the similar Triangles concept, we can get the value f x as,
=> x/h=1/4
=> 4x=h
Therefore, x = h/4
Now, Substituting x=h/4 into the Volume, V
=> V = 64h + 16h (h/4)
=> V = 64h + 4h²
When we differentiate this one, then we get,
=> dV/dt = 64 dh/dt + 8h dh/dt
Here we know that value of h=3m, dV/dt=25cm/min=0.25 m/min,
Then the equation is,
=> 0.25 = dh/dt (64 + 8 x 3)
=> 0.25 = 88 dh/dt
=> dh/dt = 0.002841m/min =0.28cm/min
Therefore, the rate is the water being drawn from the trough is 0.28cm/min.
To know more about Volume here.
https://brainly.com/question/1578538
#SPJ1
College tuition: A simple random sample of 35 colleges and universities in the United States has a mean tuition of $19,300 with a standard deviation of
$10,800. Construct a 95% confidence interval for the mean tuition for all colleges and universities in the United States. Round the answers to the nearest whole
number.
A 95% confidence interval for the mean tuition for all colleges and universities is
Answer:
The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and $22882.
Step-by-step explanation:
Sample size greater than 30, which means that we use the normal distribution to find the interval.
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
α = (1 - 0.95) / 2
= 0.025
Now, we have to find z in the table as such z has a pvalue of . So it is z with a pvalue of 1 - 0.025 = 0.975.
So, z = 1.96
Now, find M as such
M = z * (σ / √n )
In which σ is the standard deviation of the population and n is the size of the sample.
M = 1.96 * ( 10800 / √35 )
M = 3581.72
M ≈ 3582
The lower end of the interval is the sample mean subtracted by M. So it is 19300 - 3582 = $15718.
The upper end of the interval is the sample mean added to M. So it is 19300 + 3582 = $22882.
The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and $22882.
To know more about interval check the below link:
https://brainly.com/question/28112305
#SPJ13
A shop sells bottles of mango juice for
£1.80, but will take 20% off the total
cost when you buy more than 20
bottles. How much does it cost, in
pounds (£), to buy 40 bottles of
mango juice?
It cost £57.6 pounds to buy a 40 bottles of mango juice after 20% discount.
What is discount?
The difference between the purchase price and the item's par value is the discount. Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.
Here the cost of one bottle mango juice is £1.80 .
Then cost of 20 bottles mango juice = 20*1.80 = £36.
Now here we can get 20% discount then ,
=> cost of 20 bottles - 20% of cost of 20 bottles
=> 36- 20% of 36
=>36- [tex]\frac{20}{100}[/tex]*36
=>36-7.2
=>£28.8
Now here we have to buy 40 bottles then,
Cost of 40 bottles after 20% discount = 2*28.8=£57.6
Hence cost of 40 bottles of mango juice is £57.6.
To learn more about discount refer the below link
https://brainly.com/question/13660799
#SPJ9
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Correct vocabulary for theses two angles
Answer:
3: alternate exterior angles 4: supplementary angles
Step-by-step explanation:
3: that are outside and are on dif sides
4: they are interior and add up to 180 degrees
Twice a number n
Help
Lol
Answer:
2n
Step-by-step explanation:
2 x n = 2n
What's the probability of rolling 3 dice 10 times and landing on 1, 3, and 4? Please help 0-0
Answer:
it may have an even chance
Which Trinomials are perfect square trinomials?
A) 25a^2-40a+64
B) x^2-6x-16
C) 16z^4+48z^2+36
D) 9m^2+36m+36
Trinomials that are perfect square trinomials are (C) [tex]16z^{4}+48z^{2}+36[/tex] and (D) [tex]9m^{2}+36m+36[/tex].
[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]
We will check every trinomials in given options.
(A) [tex]25a^{2}-40a+64[/tex]
[tex]25a^{2} = (5a)^{2}[/tex]
[tex]64 = 8^{2}[/tex]
[tex]-40a \neq 2(5a)(8)[/tex]
Hence, its not a perfect square.
(B) [tex]x^{2}-6x-16[/tex]
[tex]x^{2} = (x)^{2}[/tex]
[tex]-16 \neq 4^{2}[/tex]
[tex]-6x \neq 2(x)(4)[/tex]
Hence, its not a perfect square.
(C) [tex]16z^{4}+48z^{2} +36[/tex]
[tex]16z^{4} = (4z^{2} )^{2}[/tex]
[tex]36 = 6^{2}[/tex]
[tex]48z^{2}=2(4z^{2} )(6)[/tex]
[tex]16z^{4}+48z^{2} +36 = (4z^{2}+6 )^{2}[/tex]
Hence, its a perfect square.
(D) [tex]9m^{2}+36m+36[/tex]
[tex]9m^{2} = (3m)^{2}[/tex]
[tex]36 = 6^{2}[/tex]
[tex]36m=2(3m)(6)[/tex]
[tex]9m^{2}+36m+36 = (3m+6)^{2}[/tex]
Hence, its a perfect square.
Therefore, only (C) and (D) are perfect square.
To learn more about trinomials here:
https://brainly.com/question/8985142
#SPJ1
. Answer questions (a – f) based on the following graph.
a. When x = -1, what is the value of y?
b. When y = 7, what is the value of x?
c. What is the y-intercept of the graph?
d. What is the x-intercept of the graph?
e. What is the slope of the line?
f. What is the equation of the line?
Answer:
are you asking for all the answers to this
Step-by-step explanation:
What is the quotient (6x^4-15x^3+10x^2-10x+4)/(3x^2+2)
Answer:
is 2x2 + 5x + 2.
Step-by-step explanation:
Y is greater than or equal to 2
The given statement in mathematical notation is Y≥2.
Given that the statement is Y is greater than or equal to 2.
We want to write the given statement in the mathematical notation.
In algebra, statements basically consist of true or false statements. These mathematical statements can consist of words and symbols.
The greater than in symbolic form is > and greater than or equal to ≥.
As it is given that Y is greater than or equal to 2 can be rewritten as Y≥2.
Hence, the given statement Y is greater than or equal to 2 is Y≥2.
Learn more about the mathematical statement from here brainly.com/question/20377088
#SPJ9
if sin α=1/3, pi/2 < α < pi and cos β = -1/3, pi < β < 3pi/2 find exact value of: (a) = (b) = (c) = (d) = (e)
The exact values of two trigonometric functions are listed below:
Case A: - 2√2 / 3
Case B: - 2√2 / 3
Case C: 7 / 9
Case D: 4√2 / 9
Case E: ± √6 / 3
How to determine the exact values of the trigonometric functions
In this problem we have the exact values of two trigonometric functions, and of which we need to determine the exact value of a set of trigonometric functions of more complexity, each of which can be found by understanding the nature of the trigonometric functions and trigonometric formulas.
Case A - cos α:
Since sin α > 0 for π / 2 < α < π, then cos α < 0. Then, by the fundamental formula:
cos α = - √(1 - sin² α)
cos α = - √[1 - (1 / 3)²]
cos α = - √(8 / 9)
cos α = - 2√2 / 3
Case B - sin β:
Since cos β < 0 for π < α < 3π / 2, then sin β < 0. Then, by the fundamental formula:
sin β = - √(1 - cos² β)
sin β = - √[1 - (- 1 / 3)²]
sin β = - 2√2 / 3
Case C - cos 2α:
cos 2α = cos² 2α - sin² 2α
cos 2α = (- 2√2 / 3)² - (- 1 / 3)²
cos 2α = 7 / 9
Case D - cos (α + β):
cos (α + β) = cos α · cos β - sin α · sin β
cos (α + β) = (- 2√2 / 3) · (- 1 / 3) - (1 / 3) · (- 2√2 / 3)
cos (α + β) = 2√2 / 9 + 2√2 / 9
cos (α + β) = 4√2 / 9
Case E - sin (β / 2):
sin (β / 2) = ± √[(1 - cos β) / 2]
sin (β / 2) = ± √[[1 - (- 1 / 3)] / 2]
sin (β / 2) = ± √6 / 3
To learn more on trigonometric functions: https://brainly.com/question/14746686
#SPJ1
What is the simplest form of this expression?
-b(-b³-1) +4b^4
Enter the correct answer.
Answer:
[tex]b(5b^{3}+1)[/tex]
Step-by-step explanation:
[tex]-b(-b^{3} -1)+4b^{4} =b^{4}+b+4b^{4}[/tex]
[tex]= 5b^{4} + b[/tex]
[tex]= b(5b^{3}+1)[/tex]
Write an expression for the sequence of operations described below.
raise 3 to the 9th power, then add the result to j
Do not simplify any part of the expression.
An expression for given sequence of operations is: j + 3^9
In this question, we need to write an expression for the sequence of operations described below.
raise 3 to the 9th power, then add the result to j
Consider the part of given statement,
raise 3 to the 9th power
We write this as: 3^9
then we add this result to j.
So, we get an expression: 3^9 + j
Therefore, an expression for given sequence of operations is: j + 3^9
Learn more about expression here:
https://brainly.com/question/1859113
#SPJ9
A book sold 33,500 copies in its first month of release. Suppose this represents 8.9% of the number of copies sold to date. How many copies have been sold to date?
Round your answer to the nearest whole number.
Answer:
376,404 copies sold.
Step-by-step explanation:
To find this answer, divide 33,500 copies by the 8.9%:
33,500 divided by 8.9% = 376404.494382
Now, if we round this number to the nearest whole number, it would be:
376,404 copies sold.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Felipa says she has an easy way to estimate the sales tax when she makes a purchase. The sales tax in her city is 9.05%. She knows this is a little less than 10%.
The estimate of the tax when a purchase is made in her city with a sales tax of 9.05% are as follows;
a) 10% converted to a fraction is [tex]\dfrac{1}{10}[/tex]
b) An estimate of the amount Felipa pays as tax is $9.5
What is an estimate?An estimate is a rough calculation that gives a value that is close to the actual value.
a)The sales tax in her city = 9.05
The sales tax is approximately 10%
To convert 10% to fraction we have;
10% = 0.1
[tex]0.1 = \dfrac{1}{10}[/tex]
[tex]10\% = \dfrac{1}{10}[/tex]
b) The estimate sales tax that Felipa would pay on a dress of $95 can be found as follows;
10% of $95 is found as follows;
[tex]\dfrac{1}{10} \times \$95 = \$9.5[/tex]
10% of $9.5 is found as follows;
The estimate of her tax is $9.5
The actual amount she pays as tax is found as follows;
[tex]\dfrac{1}{10} \times \$9.5 = \$0.95[/tex]
0.0005 = [tex]\frac{5}{10000}[/tex]
[tex]\dfrac{5}{10000} \times \$95 = \$0.0475[/tex]
9.05% = 0.0905
0.0905 = 0.10 - 0.01 + 0.0005
Her tax is $9.5 - $0.95 + $0.0475 = $8.5975
Felipa's tax if she buys a dress of $95 is $8.5975
Part of the question, based on a similar question online, includes;
a) To convert 10% into fractions
b) To provide an estimate of the tax payable on a $95 dress
Learn more about fractions and percentages here:
https://brainly.com/question/11562283
#SPJ1
Express
2x² + 20x + 7
in the form 2(x + p)² + q
The given expression is expressed in the form of 2(x + p)² + q as:
f(x) = (x + 5)² - 21.5
Given,
Express
2x² + 20x + 7
Step 1: Subtract both sides by 7
2x² + 20x = -7
Step: GCF and divide
2(x² + 10x) = -7
x² + 10x = -7/2
Step 3: Complete the Square
x² + 10x + 25 = -7/2 + 25
(x +5)² = 43/2
Step 4: Subtract 43/2 to both sides
(x + 5)² - 43/2
Hence we get the equation.
Learn more about Solving equations here:
brainly.com/question/26310043
#SPJ9
The mass of an empty bottle is 500g been filled with 1.0 L of mysterious to quit the masses 1400 G what is the density of the liquid what liquid might it be?
The liquid in this case is found to have a density of 900 g/L.
What is the density?The term density has to do with the ratio of the mass to the volume of the object. The density of an object is an intrinsic property of the material and it can be used to identify the kind of material that we have.
In this case we have;
Mass of the empty bottle = 500g
Mass of the bottle and the liquid = 1400 g
Volume of the bottle = 1.0 L
Mass of liquid = 1400 g - 500g = 900 g
Density of the liquid = mass/ volume
= 900 g/1 L = 900 g/L
Learn more about density:https://brainly.com/question/15164682
#SPJ1
8(4-a)=2a
Answer :16/5 or 3.2
I need help with the checking the answer not the equation. We check a solution to an equation by replacing the variable in the equation with the value of the solution. A solution should result in a true statement when simplified. This is what I need. Thank you.
Answer:
8(4-a)=2a
32-8a=2a
32=10a....dividing through by 10a we get..
32/10=10a/10
3.2=a
answer is 3.2
We know that the problem we are going to be dealing with is an equation. The big question is, what should we do? What steps should be taken to get to the answer? There are several steps. One of them is expanding the equation. We can't solve until we expand the left side. So the way we're going to do it is: the distributive property. This one states that if you have an [tex]a[/tex] term multiplied by the sum of [tex]b[/tex] and [tex]c[/tex] (the last two terms are in parentheses), then, in a sense, [tex]a[/tex] gets "distributed" and what results is this:
[tex]\darkblue{ab+ac}[/tex]. So now we apply that to our problem: [tex]8(4-a)=32-8a[/tex]. Now we make the replacement: [tex]32-8a=2a[/tex]. Then, notice that we have [tex]a[/tex] terms on both sides. What we do is we subtract [tex]2a[/tex] from the right and left and subtract [tex]32[/tex] from the left and add to the right: [tex]-8a-2a=-32[/tex]. Now let me share a little trick with you. First, we can add the [tex]a[/tex] terms together: [tex]-10a=-32[/tex]. Next, if you have minus signs on both sides, you clear them: [tex]10a=32[/tex]. Now divide both sides by 10. Here another trick comes into play: If you divide by 10 you move the decimal sign 1 place to the left.
[tex]a=3.2[/tex]
Now for the checking - put [tex]3.2[/tex] for [tex]a[/tex] and simplify. The answer should be a statement true for all values of [tex]a[/tex]. Let's go.
[tex]8(4-3.2)=2(3.2)[/tex]
[tex]8(0.8)=6.4[/tex]
[tex]6.4=6.4[/tex] is the result. Since the statement is true, we understand that the solution WAS correct and that [tex]3.2[/tex] IS the value of [tex]a[/tex] in the equation [tex]8(4-a)=2a[/tex].
Here are four triangles.
58°
C
23°
9 cm
23°
58°
9 cm
58°
B
D
9 cm
23°
Which two triangles are congruent
23⁰°
9 cm
58°
Total marks
Answer:
they will not be able to change the other owner of the property
Step-by-step explanation:
and the magazine costs m dollars Write down and other expenses for the ping by you
The population of a small town is decreasing at a rate of 4% each year.
The following table shows a projection of the population, N, after t
years.
0
1
2
3
4
header 2
13,000
12,480
11,981
11,502
11,042
If the population of the small town is currently 13,000 people, how
many years will it take for the population to reach 8,500 people?
Answer:
10.4 years
Step-by-step explanation:
Given the population of a small town is initially 13000 and decreasing at the rate of 4% per year, you want to know the number of years it will take for the population to reach 8500.
Exponential decayThe equation for exponential decay is ...
population = (initial population) · (1 - decay rate)^t
ApplicationHere, the initial population is 13000, the decay rate is 4%, and the population of interest is 8500. This gives an equation we can solve for t.
8500 = 13000 · (1 -0.04)^t
8500/13000 = 0.96^t . . . . . . . divide by 13000
log(17/26) = t·log(0.96) . . . . . take logs
t = log(17/26)/log(0.96) ≈ 10.408
It will take about 10.4 years for the population to reach 8500 people.
4 years is the total years will take to reach 8500 people.
Hence, The total is equal to 4 years.
What is exponential decay?If a quantity is subject to exponential decay, it is declining at a rate proportionate to its current value.
Given the population of a small town is initially 13000 and decreasing at the rate of 4% per year, you want to know the number of years it will take for the population to reach 8500.
Exponential decay
The equation for exponential decay is ...
population = (initial population) · (1 - decay rate)^t
Application
Here, the initial population is equal to 13000, the decay rate is equal to 4%, and the population of interest is 8500. This gives an equation we can solve for t.
8500 = 13000 · (1 -0.04)^t
8500/13000 = 0.96^t . . . . . . .
divide it by 13000
log(17/26) = t·log(0.96) . . . . .
take log
t = log(17/26)/log(0.96) ≈ 10.408
It will take about 10.4 years for the population to reach 8500 people.
To learn more about exponential decay, visit:
https://brainly.com/question/2193799
#SPJ1
A 9ft ladder lens against the side of a house the bottom of the ladder is 6ft from the side of the house how high is the top of the ladder from the ground round the answer to the nearest tenth
Answer:
6.7 feet
Step-by-step explanation:
You want to know the height of a 9 ft ladder above the ground where it leans against a house, and its base is 6 ft from the house.
Pythagorean theoremThe Pythagorean theorem relates the side length of a right triangle. The geometry of this problem can be modeled by a right triangle with hypotenuse 9 ft and one leg 6 ft.
a² +b² = c² . . . . sum of the squares of the legs is the square of the hypotenuse
6² +b² = 9²
b² = 81 -36 = 45
b = √45 ≈ 6.708
The top of the ladder is about 6.7 feet above the ground.
