To find the height of the column of water in the Fountain Hills fountain, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of elevation to the top of the fountain, the distance from the surveyor to the base of the fountain, and the height of the column of water to form a right triangle.
We can then use the tangent function to find the height of the column of water as follows:
tan(29.7°) = opposite/adjacent
opposite = tan(29.7°) * adjacent
opposite = tan(29.7°) * 980 feet
opposite = 0.56 * 980 feet
opposite = 548.8 feet
Therefore, the height of the column of water in the Fountain Hills fountain is approximately 549 feet. To the nearest 10 feet, this is 550 feet.
Express the confidence interval 71.6% ± 8.2% in the form of a trilinear inequality.
The confidence interval, expressed as a trilinear inequality, is 71.6%
What does a confidence interval mean?
The range of values we see in our sample and expect to find the value that most accurately represents the population are referred to as a confidence interval.
The lower bound is 71.6% - 8.2% = 63.4% and the upper bound is 71.6% + 8.2% = 79.8%.
Thus the confidence interval, expressed as a trilinear inequality, is 63.4% < p < 79.8%, where p= 71.6%.
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PLEASE HELP
ALGEBRA
The explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].
What is a geometric sequence?
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given:
[tex]a_4=8573.75\\\\a_6=7731.81[/tex]
Now by using the formula for the nth term of a GP, we get
[tex]a_n = ar^{n-1}\\\\a_4=ar{4-1}\\\\8573.75=ar^3[/tex]
Now for n = 6, we get
[tex]a_n = ar^{n-1}\\\\a_6=ar{6-1}\\\\7737.81=ar^5[/tex]
Now divide we get
[tex]\frac{ar^5}{ar^3} =\frac{7737.81}{8573.35} \\\\r^2=0.9025\\\\r=0.95[/tex]
Now we can get the value of a,
[tex]8573.75=ar^3\\\\a = \frac{8573.75}{(0.95)^3}\\\\a = \frac{8573}{0.8573}\\\\a = 10000.87[/tex]
So we can prepare the explicit formula as
[tex]a_n =10000.87\times (0.95)^{n-1}[/tex]
Hence, the explicit formula for the geometric sequence would be [tex]a_n =10000.87\times (0.95)^{n-1}[/tex].
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y varies inversely as x. y = 18 when x = 7. Find y when x = 6.
The value of y is 21, when x = 6.
What are Inverse variations?
The link between two variables known as "inverse variation" occurs when the value of one variable rises while the value of the other variable falls.
Here, we have
Inverse variations look like this: y = k/x
We need to make our own inverse variation given y = 18 and x = 7. We can plug this into the standard inverse variation with variables.
y = k/x
18 = k/7
k = 126
We've determined that k =126. Now we have what it takes to create an inverse variation. This is our final equation:
y = 126/x
We still need to find what y equals when x is 6. Let's plug in 6 for x
y = 126/6
y = 21
Hence, the value of y is 21, when x = 6.
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If M is the centroid of triangle ABC, AM = 44, CE =54, and DM
= 23, find each missing measure.
The missing sides of triangle ABC, If M is the centroid of triangle ABC, AM = 44, CE =54, and DM = 23, are FM = 22, AM = 44.
What is the centroid of the triangle?Three medians of a triangle intersect to produce the centroid of the triangle. It is one of a triangle's four points of concurrency. When the midpoints of the triangle's opposite sides are linked, the triangle's vertices become the triangle's medians.
Given:
The [tex]M[/tex] is centroid of triangle ABC, AM = 44, CE = 54, and DM = 23,
The centroid of a triangle divides the median in the ratio [tex]2 : 1[/tex]
Therefore, [tex]AM : FM = 2 : 1[/tex]
Let AM = 2x and FM = x
Since, AM = 44
Hence, 2x = 44
x = 44 / 2
x = 22
FM = 22
Therefore, the missing sides are FM = 22 and AM = 44.
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The missing figure is attached below.
It takes Stacy 0.75 hours to drive to school. Her route is 40km long. What is Stacy’s average speed on her
drive to school?
Answer:
Step-by-step explanation:
160/3
Can someone please help me? I’ll give brainly thank you so much :)
Answer:
B (192 ft^2)
Step-by-step explanation:
The area of the blue shaded region: total area - small rectangle
This is:
(11x20) - (4x7)
= 220 - 28
= 192 ft^2
Hope this helps,
:]
Answer:
A.
Explanation:
20*11=220
Please vote for Brainliest and I hope this helps!
Simplify 6.5m(3m + 1.8) using the distributive property.
19.5m + 11.7m
19.5m + 1.8
19.5m2 + 11.7m
19.5m2 + 1.8
Answer:
C.
19.5m2+11.7m
Step-by-step explanation:
hope this helps
Answer:
C.
19.5m2+11.7m
Step-by-step explanation:
what i got on the test
Line t passes through points (9, 9) and (2, 5). Line u is perpendicular to t. What is the slope of line u?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Write the sentences as an equation. 140 is the same as a multiplied by 319
140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.
What is an equation?An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.
Hence, the sentence as an equation for 140 is the same as multiplying by 319 is, 140 = a x 319.
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To express the given numbers in equation form it can be written as =
140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.
What is an equation?
An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.Hence, the sentence as an equation for 140 is the same as multiplying by 319 is, 140 = a x 319.A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.To know more about equations check out,
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there are 80 houses being built in a neighborhood last month 1/4 of them were sold. This month 2/5 of the remaining houses were sold. How many houses are left to be sold?
36 houses are left to be sold.
Step-by-step explanation:Here are the steps to find out the answer to your question:We need to convert 1/4 and 2/5 into decimals. We do this by dividing the numerator by the denominator:
1 ÷ 4 = 0.25
2 ÷ 5 = 0.4
Now, we can set up this equation to find out how many were sold in the first month:
0.25 x 80 = 20
Now, 20 isn't the answer, it is 60 houses left, because 80 - 20 = 60.
Let's do the next one:
0.4 x 60 = 24
60 - 24 = 36
Solution:
36 houses are left to be sold.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Simplify the expression by using a double-angle formula.
sinπ/7·cosπ/7
After using the trigonometry method the answer is sin 2 (pi/7)/2
What principle underlies trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the branch of mathematics known as "trigonometry." Therefore, using trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.
What distinguishes geometry from trigonometry?
The study of triangle properties, particularly those of right triangles, is known as trigonometry. But the study of geometry focuses on the characteristics of all geometrical figures.
Given that:
sinπ/7·cosπ/7
if we can divide and multiply 2 so it can be converted to sin 2 theta
sin 2 (pi/7)/2
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To convert Celsius temperatures to Fahrenheit temperatures, the function F defined by F(x) = 32 + 1.87 is useful. Confirm this, then find a formula for the function C (which could also be called F-1) that converts Fahrenheit temperatures to Celsius temperatures.
Answer: The function F(x) = 32 + 1.87x converts Celsius temperatures to Fahrenheit temperatures. To confirm this, you can plug in a few different values for x (the Celsius temperature) and see if the corresponding value of F(x) (the Fahrenheit temperature) is correct.
For example, if x = 0, the function gives us F(0) = 32 + 1.87 * 0 = 32, which is the correct conversion from Celsius to Fahrenheit for 0 degrees Celsius.
If you want to find a formula for the function C that converts Fahrenheit temperatures to Celsius temperatures, you can start by rearranging the formula for F(x). The Fahrenheit temperature is equal to the Celsius temperature plus 32, multiplied by 1.8.
If we solve for the Celsius temperature, we get:
x = (F - 32) / 1.8
This is the formula for the function C that converts Fahrenheit temperatures to Celsius temperatures. To use this function, you would plug the Fahrenheit temperature into the function as the input, and it will give you the corresponding Celsius temperature as the output.
For example, if you want to convert 100 degrees Fahrenheit to Celsius, you would plug 100 into the function as the input:
C(100) = (100 - 32) / 1.8 = 37.78 degrees Celsius.
ASAP!!!
Find the perimeter of the square
Answer:
156
Step-by-step explanation:
4x + 3 = 3(2x - 5)
4x + 3 = 6x - 15
3 = 2x - 15
2x = 18
x = 9
4(9) + 3
= 36 + 3
= 39
39 * 4 = 156
Hope it helps!
Answer: 156 inches
Step-by-step explanation:
So we know that all of the sides are equal to each other.
Now we need to know what x equals.
4x + 3 = 3(2x -5)
4x + 3 = 6x - 15
3 = 2x -15
18 = 2x
9 = x
Plug 9 into one of the equations.
4(9) + 3
36 + 3 = 39
39 * 4 = 156
Perimeter = 156 inches
Hope this helps!!! :)
9 + a - 5b - 2 combine The like terms to create an equivalent expression
Answer:
Your answer is 7 + a - 5b.
Step-by-step explanation:
All you have to do is subtract the numbers.
Hope this helped! :D
Complete the square by adding the correct missing term on the left, then factor as indicated:
x²+x+________=(______)²
Answer:
Missing term [tex]\dfrac{1}{4}[/tex]
Factored term on RHS: [tex]$(x+\dfrac{1}{2})^{2}$[/tex]
Step-by-step explanation:
Write an equation in solve-intercept form of the line that passes through the point (2, -2) and is parallel to the line y= -x-2.
The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as,
ax + by + d = 0
The equation of the line is given below.
y = - x - 2
x + y + 2 = 0
Then the equation of the line that is parallel to x + y + 2 = 0 is given as,
x + y + d = 0
The line is passing through (2, -2), then we have
2 + (-2) + d = 0
d = 0
The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.
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Seven more than the quotient of a number and 2 equals 9 .
Answer:
4
Step-by-step explanation:
n/2 + 7 = 9
n/2 + 7 - 7 = 9 - 7
n/2 = 2
n = 4
Jo leaves some money in a bank account that pays
interest. Each year, the balance of her account is
15% more than it was the year before.
If she starts with £400 in her account, work out
her balance for the next three years. Give your
answers in order and rounded to the nearest
pound.
If she starts with £400 in her account, her balance for the next three years IS; $608.35
How to solve exponential equation?
The general formula for exponential equation is;
y = a(b)ˣ
where;
a represents an initial value or amount
b is the constant multiplier, is a growth factor or factor of decay.
We are given;
Initial value; a = £400
constant multiplier; b = an increase of 15% yearly = 1.15
Thus, her balance for the next three years is;
y(3) = 400(1.15)³
y(3) = $608.35
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PLS answer this i need it asap
Answer:
b
step by step explanation
solve for the length of the diagonal of the rectangular prism
The diagonal can be written as -
d = √{(L)² + (B)² + (H)²}
What is a right rectangular prism? What is a mathematical equation? What is constant of proportionality?The right rectangular prism has two parallel end faces and four lateral faces, each one of which is a rectangle; the faces are perpendicular to each of its bases. The faces of a non-right rectangular prism (oblique prism) are parallelograms. A right rectangular prism is also called a cuboid.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a graph as shown in the figure.
Since the dimensions of a right rectangular prism are not given, assume the length, width and height to be [L], [W] and [H]. Then the diagonal can be written as -
d = √{(L)² + (B)² + (H)²}
Therefore, the diagonal can be written as -
d = √{(L)² + (B)² + (H)²}
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How much money does Dana Jones have after 7 years if she invests $ 1100 at 5 % interest compounded continuously? Use the formula A =Pе⁺ to solve.
Dana Jones has $____ after 7 years.
(Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)
The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
When compounded continuously , the Compound Interest Amount is calculated by the formula ,
A = Pe^rt
Given data ,
Let the investment be P
The value of P = $ 1100
The rate of interest r = 5 %
The number of years t = 7 years
The Compound Interest Amount when compounded continuously is calculated by the formula ,
A = Pe^rt
Substituting the values in the equation , we get
A = 1100 x e ^ 0.05 x 7
A = 1100 x e ^ 0.35
A = 1100 x 2.718 ^ 0.35
A = 1100 x 1.419067
A = $ 1560.97
Therefore , the value of the amount is A = $ 1560.97
Hence ,
The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97
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Ride and simplify two division expressions they have a negative quotient used to fractions -2/3 5/6 and negative one show your work
The simplification of complex fraction -⅔/⅚ is - 4/5
What are complex fractions?A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.
In fraction when the numerator is bigger than the denominator , then it is called improper fraction, when a fraction consist of whole number and proper fraction is called mixed fraction
-2/3 ÷ 5/6
= -2/3×6/5
= -4/5
Therefore -⅔/⅚ can be simplified to -⅘
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Factor 132w + 55 using the Distributive Property.
Answer:
11(12w+5)
Step-by-step explanation:
common factors of 132 and 55 is 11
So we can take it out by dividing both terms by 11
11(12w+5)
Hopes this helps
Answer:I hope this is helps
good luck
Step-by-step explanation:
132w+55
Factor out from the expression
11(12w+5) this is the distributive Property
The sum of a number and seven is one more than twice the number. What is the number
Answer: x+7=1+2x
Step-by-step explanation:
If x represents the number,The sum of a number and 7 is x + 7One more than twice the number is 1 + 2xThe IS in the middle of the sentence means =So, x + 7 = 1 + 2x Solve this equation,If you need further assistance message me.
Debbie has 4,000 in an account the interest rate is 15% compounded annually to the nearest and how much interest will she earn in 2 years
need answers fast please and thank you
Answer:
Step-by-step explanation:
The formula you want is: fv=p(1+int/c)^(nc)
future value
principal
int
compound
years
fv=4000(1.04/4)^(16)=$4690.31
The cost of buying gas varies directly with the number of gallons
Suppose that Lena bought 12.2 gallons of gas for $35.99. Write an equation that could be
used to find the unit cost per gallon of gas. Then find out how much 9.5 gallons of gas
would cost. Round to the nearest cent.
Answer:
1 gallon of gas is $2.95
9.5 gallons of gas is $28.025
Step-by-step explanation:
[tex]\frac{12.2}{35.99} =\frac{1}{y}[/tex]
Cross Multiply.
12.2 · y = 1 · 35.99
12.2y = 35.99
12.2y ÷ 12.2 = 35.99 ÷ 12.2
y = 2.95
1 gallon of gas is $2.95.
[tex]\frac{1}{2.95} =\frac{9.5}{y}[/tex]
1 · y = 2.95 · 9.5
y = 28.025
9.5 gallons of gas is $28.025.
hi!! can someone do 14 and 16 or just one if you’d rather do that?? thank you sm i’m just trying to get some of my assignments done by tomorrow and i don’t understand how to do these things
In a survey of 1000 eligible voters selected at random, it was found that 100 had a college degree. Additionally, it was found that 80% of those who had a college degree voted in the last presidential election, whereas 45% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random will have the following characteristics. (Round your answers to three decimal places.) (b) The voter did not have a college degree and did not vote in the last presidential election.
The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is 49.5%.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
The no. of people who don't have a college degree is (1000 - 100) = 900.
45% of the people who did not have a college degree voted in the last presidential election hence (100 - 45) = 55% of the people who did not have a college and did not vote in the last presidential election.
∴ (55/100)×900.
= 495 people.
∴ The probability that an eligible voter selected at random did not have a college degree and did not vote in the last presidential election is,
= 495/1000.
= 0.495.
= 49.5%.
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Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours
ŷ= 6.45x + 31.5 is the equation of the regression line for the given data
How to find the equation of the regression line for a given data?Construct the table of the data as follows:
x >>>> y >>>> x² >>>> y² >>>> xy
1 39 1 1521 39
2 45 4 2025 90
3 52 9 2704 156
4 49 16 2401 196
5 61 25 4096 305
5 72 25 5184 360
................................................................................................
20 318 80 17931 1146
.................................................................................................
∑x = 20, ∑y = 318, ∑x²= 80, ∑xy = 1146, n = 6 (number data points)
The linear regression equation is of the form:
ŷ = ax + b
where a and b are the slope and y-intercept respectively
a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )
a = (6×1146 - 20×318) / ( 6×80-20² )
a = 6876-6360 / 480-400
a = 516 / 80
a = 6.45
x' = ∑x/n
x' = 20/6 = 10/3
y' = ∑y/n
y' = 318/6 = 53
b = y' - ax'
b = 53 - 6.45×(10/3)
b = 53 - 21.5
b = 31.5
ŷ = ax + b
ŷ= 6.45x + 31.5
Thus, the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)
(a) x=3 hours
ŷ= 6.45(3) + 31.5 = 50.85
(b) x=4.5 hours
ŷ= 6.45(4.5) + 31.5 = 60.525
(c) x=13 hours
ŷ= 6.45(13) + 31.5 = 115.35
(d) x=1.5 hours
ŷ= 6.45(1.5) + 31.5 = 41.175
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Solve linear differential equations.
a. (x + 2)² (dy/dx) = 5-8y - 4xy
The value of y for the linear differential equation is:
y= [5(x³+6x²+12x)/3(16+32x+24x²+8x³+4x⁴)] + c₁ /(16+32x+24x²+8x³+x⁴)
How to solve the differential equation?You should know that a differential equation is in which we find the value of y with respect to x
The given parameter is
(x-2)² dy/dx = 5-8y-4xy
Differentiate y with respect to x to have
y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]
Recall that the differential equation is (x-2)² dy/dx = 5-8y-4xy
Solving the Ordinary Differential Equation we have
y= y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]
In conclusion, the value of y is: y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]
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