Given the number of trees in the orchard, the number of trees in each row is 20 trees.
How to find the number of trees?Assuming that the number of rows is represented as x, the number of trees would be 2 less than the number of rows which makes it:
= x - 2
The number of trees is:
x ( x - 2) = 440
x² - 2x - 440 = 0
Solving for r can then be done quadratically which gives us:
x = (2 ± √(2² - 4(1) (- 440)) / 2 (1)
= 22, and -20
The number of rows in the orchard cannot be negative so the number of rows is 22.
The number of trees is therefore:
= Number of rows - 2
= 22 - 2
= 20 trees
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The CDC initially reported that the effectiveness of the Moderna Vaccine in preventing Covid-19 (after a second shot and two months time) could be given by the 95% confidence interval (.893, .967). Answer the following relating to this confidence interval.
a) The sample proportion would be of: 0.93.
b) The margin of error would be of: 0.037.
c) The critical value would be of: z = 1.96.
d) The standard error would be of: 0.0189.
e) The critical value for the 90% confidence interval would be of: z = 1.645.
f) The 90% confidence interval would be narrower.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.From the equation, the confidence interval can be described as follows:
The sample proportion plus/minus the margin of error.
For this problem, the interval is given as follows:
(.893, .967).
From the description, the sample proportion is the mean of the two bounds, hence:
Sample proportion = (0.893 + 0.967)/2 = 0.93.
The margin of error is the absolute value of the difference of each bound and the sample proportion, hence:
Margin of error = |0.967 - 0.93| = |0.893 - 0.93| = 0.037.
The critical values are found using the z-table, as follows:
95% confidence level -> p-value of 0.975 -> z = 1.96.90% confidence level -> p-value of 0.95 -> z = 1.645.The greater the critical value, the wider the interval, hence a 90% confidence interval would be narrower than the 95% confidence interval;
The standard error is the division of the margin of error by the critical value, hence:
Standard error = 0.037/1.96 = 0.0189 = 1.89%.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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4 Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0 Reset Next
The equation of the circle is x² + y² - 41 =0.
What is a circle?A circle is a round-shaped 2-dimensional geometrical figure in which the points on the boundary are equidistant from a fixed point called a center.
Given, a circle centered at O(0,0)and has a point B (4,5) on its circumference.
The radius of the circle is the distance between the points O(0,0) and B (4,5), therefore,
r = √((4-0)² + (5-0)²)
r = √(16+25)
r = √41
The equation of a circle, centered at the origin with a radius of r =√41 units, is given by,
x² + y² = √41²
x² + y² = 41
x² + y² - 41 =0
Hence, the equation of the circle is x² + y² - 41 =0.
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Find the equation of the inverse of the following function: f (x) = 7x + 3. State the answer in slope-intercept form
The equation of the inverse function is f⁻¹(x) = x/7 - 3/7
How to determine the inverse functions?The function f(x) is given as
f(x) = 7x + 3
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = 7x + 3
The next step is to switch/swap the positions of x and y in the above equation y = x + 5
The equation becomes
x = 7y + 3
The next step is to make y the subject of the formula in the above equation
The equation becomes
y = x/7 - 3/7
Express as an inverse function
f⁻¹(x) = x/7 - 3/7
Hence, the inverse is f⁻¹(x) = x/7 - 3/7
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Can you solve please
Answer:
Green x = 10
Purple x = 19
Step-by-step explanation:
Are we solve for x?
Green:
It is not staighted, but this looks like a straight angle. That would total 180
3x + 5 + 6x -5 +90 = 180 A right angle is 90 Combine like terms
9x + 90 = 180 Subtract each side by 90
9x = 90 Divide both sides by 9
x = 10
Purple:
5x - 19 + 2x + 5 = 119 Combine like terms
7x -14 = 119 Add 14 to both sides
7x = 133 Divide both sides by 7
x = 19
1. Jasmine buys 4 bottles of water for $1.30 each. She buys a large bag of popcorn for $3.75. How much more money did Jasmine spend on water than pop
Answer:
Jasmine spent 1.45$ more on water than popcorn.
Step-by-step explanation:
Jasmine buys 4 bottles of water and spends 1.30$ for each one individually. To find out how much all of these 4 costs, we multiply 4 by 1.30$ which is 5.20$
To find out how much more money Jasmine spent on the water than popcorn, we subtract 5.20$ - 3.75$ = 1.45$
6. Which shows the decimals in the
correct order?
A. 5.271> 5.217 > 5.38
B. 5.38 5.217 > 5.271
C.
5.271
5.38 > 5.217
D. 5.38
5.271 > 5.217
Answer: D. 5.38 > 5.271 > 5.217
There are 240 boxes with 25 bags of coffee each. I’d each bag weighs 0.62kg, what is the total weight of all the coffee? Round your answer to the nearest whole number
Answer:
3720 kg
Step-by-step explanation:
one bag of coffee weighs=0.62 kg
total no. of coffee bags= 240×25=600
total weight of coffee=6000×0.62= 3720
Simplify the expression (x)(6+x)−2x. Write products as powers when possible.
(x)(6+x)−2x=
Simplifying the expression (x)(6 + x)−2x gives x^2 + 4x
How to simplify the expressionInformation given in the question
the expression (x)(6 + x)−2x
The expression is simplified by first expanding
(x) (6 + x) − 2x
6x + x^2 - 2x
x^2 + 4x (products as powers when possible)
The result here is a quadratic equation without the constant variable. it can be simplified further to give
x(x + 4)
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i will give brainly if someone helps with thisIf △ABC is translated 3 units left and 2 units up, what would be the translated coordinates of Point C?
Answer: (-2, -2)
Step-by-step explanation:
Right now, the coordinates of point C are (1, -3).
It is first moved 3 units to the left, so the point C would change to (1 - 3, -3) = (-2, -3)
It is then moved 2 units up, so point C would change to (-2, -3 + 2) = (-2, -1)
Answer the questions on the function below:
What is the slope of the line?
What is the y-intercept?
What is the x-intercept?
Answer:
The slope of the line is 1/2.
The y-intercept of the line is 5.
The x-intercept of the line is 10.
Step-by-step explanation:
The y-intercept is where the line intercepts the y axis. (vertical line)
The x-intercept is where the line intercepts the x axis. (horizontal line)
The slope (rise over one) is a bit more complicated to find. First, pick two points on the line and determine their coordinates. Then, determine the difference in y-coordinates of these two points (rise). After that, determine the difference in x-coordinates for these two points (run). Then you have your slope!
Five hours and 20 minutes after a raft left a dock, a patrol boat left the dock and traveled in the same direction as the raft. The boat caught up to the raft 20 km away from their starting point. What was the speed of the raft if the speed of the patrol boat was 12 km/hr?
Answer:
20/7 km/hr
Step-by-step explanation:
To solve this problem, we use the formula of:
speed x time = distance
Both the raft and boat have their own speeds, times and distances, so we would write two equations based on the formula.
One for the raft: [tex](s_{r} )(t_{r} )=d_{r}[/tex]
And one for the boat: [tex](s_{b} )(t_{b} )=d_{b}[/tex]
Both vehicles travelled as total of 20 km, so both [tex]d_{r} =d_{b} =20[/tex]. We are also given that the boat goes 12 km/hr, so [tex]s_{b} = 12[/tex]. Lastly, the boat had been going for five hours and 20 minutes less than the raft. This is the same as 5 1/3 hrs. This can also be written as 16/3 hrs, so [tex]t_{r} = t_{b} +\frac{16}{3}[/tex]. We can now plug these in:
raft: [tex](s_{r} )(t_{b}+\frac{16}{3} )=20[/tex]
boat: [tex](12 )(t_{b} )=20[/tex]
We only have one variable in the boat equation, so we can solve for time:
[tex]t_{b} =\frac{20}{12} \\\\t_{b} = \frac{5}{3}[/tex]
Now, we can plug [tex]t_{b}[/tex] into the raft equation and solve for speed:
[tex](s_{r} )(t_{b}+\frac{16}{3} )=20\\\\(s_{r} )(\frac{5}{3} +\frac{16}{3} )=20\\\\(s_{r} )(\frac{21}{3} )=20\\\\(s_{r} )(7)=20\\\\s_{r}=\frac{20}{7}[/tex]
Therefore, the speed of the raft would be 20/7 km/hr
The speed of the raft if the speed of the patrol boat was 12 km/hr will be 20/7 km/hr.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
For example, if a car drives 50 meters for 10 seconds and it is constant then 50/10 = 5 meters/second will be the velocity.
It is known that,
Speed = total distance / total time taken
The time is taken by petrol boat to reach the raft craft
Time = total distance/speed
Time = 20/12 = 5/3 hour.
The time taken the raft boat to reach 20 km = (5 hour + 20 minutes) + 5/3 hour
⇒ 5 + 1/3 + 5/3
⇒ 16/3 + 5/3 = 21/3 = 7
The speed of the raft will be as,
Speed of raft = 20/7 km/hr
Hence "The speed of the raft, if the speed of the patrol boat was 12 km/hr, will be 20/7 km/hr".
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Help please
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions
The values of [tex]D, D_x, D_y[/tex] are, [tex]D = 13, D_x = 8, D_y = 19[/tex].
What is Cramer's rule?
One of the key techniques used to solve an equation system is Cramer's rule. The determinants of matrices are used in this method to derive the values of the system's variables. Thus, the determinant technique is another name for Cramer's rule.
Consider, the given system of equations
-3x + 4y = 4 ...(1)
2x = 7y - 9 ...(2)
equation (2) can be written as,
2x - 7y = -9 ..(3)
Using Cramer's rule, we have to find the determinant of the coefficient matrix
matrix,
D= [tex]\left[\begin{array}{ccc}-3&4\\2&-7\end{array}\right][/tex] = (-3)(-7) - 8 = 21 - 8 = 13
Secondly, find the determinant of x coefficient matrix,
[tex]D_x[/tex] = [tex]\left[\begin{array}{ccc}4&4\\-9&-7\end{array}\right][/tex] = (4)(-7) - (4)(-9) = -28 + 36 = 8
Similarly, find the determinant of y coefficient matrix,
[tex]D_y[/tex] = [tex]\left[\begin{array}{ccc}-3&4\\2&-9\\\end{array}\right][/tex] = (-3)(-9) - (4)(2) = 27 - 8 = 19
Hence, values of the determinants are, [tex]D = 13, D_x = 8, D_y = 19[/tex].
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a pitcher of water is three-fourths full. six cups of water are served from the pitcher. then the pitcher is two-thirds full. how many cups of water can the pitcher hold?
The total cups of water the pitcher can hold is 72
What is a fraction?A fraction is the ratio of two integers.
It is divided into two parts by a division line and the part above the line is called the numerator and the part below the line is called the denominator.
Fraction are of three types: proper, improper and mixed fractions.
Let the total number of cups to fill the pitcher be x.
The pitcher is 3-fourths full of water, that is 3/4 of x = [tex]\frac{3x}{4}[/tex]
when 6 cups were taken away from the Pitcher it became 2/3 of x = [tex]\frac{2x}{3}[/tex]
So that,
[tex]\frac{3x}{4}[/tex] - [tex]\frac{2x}{3}[/tex] = 6
multiply [tex]\frac{2x}{3}[/tex] by 4/4 and [tex]\frac{3x}{4}[/tex] by 3/3
it becomes
[tex]\frac{9x}{12}[/tex] - [tex]\frac{8x}{12}[/tex] = 6
simplifying the numerator
x/12 = 6
cross multiplying
x = 12 x 6
x = 72
In conclusion, the total number of cups to fill the pitcher is 72
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IXL Please Help Fast!
Equation of line c parallel to line d and passing through points (2, -6) is
How to equation of line dThe equation of line d will be written in the slope intercept form of the form just like line c,
the slope intercept form is as below
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
y = -5x + 3
slope
m = -5
slope of parallel lines are equal hence slope of line d = -5
using the formula for the slope intercept the equation is written
(y - y₁) = m (x - x₁)
point (2, -6) and m = -5
(y - -6) = -5 (x - 2)
y + 6 = -5x + 10
y = -5x + 4
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work
Find the savings plan balance after 4 years with an APR of 4% and monthly payments of $250.
The balance is
(Do not round until the final answer. Then round to the nearest cent as needed.)
The balance is $12989.90.
From the question, we have
[tex]A= P\times \frac{\left ( 1+\frac{APR}{n} \right )^{nt}-1}{\frac{APR}{n}}[/tex]
where,
A is the balance after t years,
P is the periodic payment,
APR is the annual percentage rate,
n is the number of periodic payments per year, and t is the number of years.
[tex]A=250\times \frac{\left ( 1+\frac{0.04}{12} \right )^{12\times 4}-1}{\frac{0.04}{12}}[/tex]
=$12989.90
The balance is $12989.90.
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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James is having a birthday party. It costs $350 to rent the hall plus $35 per person for food. Write an equation to show the total cost of the party (y) based on the number of guests (x) he invites.
y=35x+350 is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
James is having a birthday party.
It costs $350 to rent the hall plus $35 per person for food
We need to write an equation to show the total cost of the party (y) based on the number of guests (x) he invites.
y=35x+350
Where x represents the number of guests.
350 is a constant value because it is the cost of the hall.
As 35 is the cost per person, 35x
Hence y=35x+350 is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.
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You take out a home loan for $162359. The interest on this loan is fixed at 9.6% compounded
monthly for 30 years.
How much is your required monthly mortgage payment?
Round your final answer to the nearest cent (2 decimal places)
4
Answer:
$1377.06
Step-by-step explanation:
You want the monthly payment on a 30 year loan of $162359 at 9.6% interest.
AmortizationThe payment value can be computed by any spreadsheet and most graphing calculators using built-in financial functions. Numerous apps and web sites are available for the same purpose.
The monthly payment is $1377.06 according to the attached calculator output.
FormulaThe formula used for the purpose is ...
A = P(r/12)/(1 -(1 +r/12)^(-12·t))
where P is the loan value, r is the annual interest rate, and t is the number of years. For P=162359, r=0.096, and t=30, you have ...
A = 162359(0.096/12)/(1 -(1 +0.096/12)^-360) ≈ 1377.06
__
Additional comment
The formula assumes the payment is made at the end of the month. Spreadsheet and calculator functions often need to be told that's when the payment is made.
What expression represents the verbal phrase?
one-half times a number m plus twenty-five
Answer: m/2 + 25 or (0.5)m + 25
Step-by-step explanation:
Rhea has 36 homework problems to complete. She completes 12 on Monday. On Tuesday, she completes 2/3 of the remaining problems. How many problems does Rhea still have to complete after Tuesday?
The number of problems Rhea still have to solve is 8
What is a fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator and the number at the bottom is called denominator. It tells how many equal parts of the whole or collection are taken.
On Monday Rhea solved 12 out of 36 problems. This means she has 36-12 = 24 problems remaining. On Tuesday she solved 2/3 of the remainder, which means she did 2/3×24= 16problems on Tuesday.
Therefore she will have 24- 16= 8problems to complete after Tuesday.
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A bacteria culture initially contains 3000 bacteria and doubles every half hour.
1) Find the size of the baterial population after 80 minutes.
2) Find the size of the baterial population after 7 hours.
The size of the bacterial population after 80 minutes is 19048.81
The size of the bacterial population after 7 hours is 49152000.
Given,
A bacterial culture initially contains 3000 bacteria and doubles every half hour.
we are asked to determine the size of the bacterial population after 80 minutes.
The exponential growth law for this problem is
p(t) = 3000 (2)^t/30
where t is the time in minutes. To find the population after 80 minutes, plug in t=80 and evaluate P(80).
p(80) = 3000 (2)^80/30
p(80) = 3000(2)^8/3
p(80) = 19048.81
now, we are asked to determine the size of the bacterial population after 7 hours.
To find it after hours, plug in t=420 minutes (since 7 hrs equals 420 minutes) and evaluate p(420).
p(420) = 3000(2)^420/30
p(420) = 3000(2)^14
p(420) = 49152000
hence we get the required size of the population.
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a triangle has a base of 1.5
Answer: bro You need To add more about the question
Step-by-step explanation:
If point A is at (-2,-2) and point B is at (1,2), what is the distance between point A
and B?
The distance between point A and point B is 5 units.
According to the question,
We have the following information:
Point A = (-2,2)
Point B = (1,2)
Now, we know that the following formula is used to find the distance between two points:
Distance between two points = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} )}[/tex]
In this case, we have the values of x1 = -2, y1 = -2, x2 = 1 and y2 = 2.
Distance between two points = [tex]\sqrt{(2+2)^{2} +(1+2)^{2} )}[/tex]
(The sign has been changed from negative to positive because the multiplication of two negative integers is positive.)
Distance = [tex]\sqrt{(4)^{2} +(3)^{2} )}[/tex]
Distance = [tex]\sqrt{16+9}[/tex]
Distance = [tex]\sqrt{25}[/tex]
Distance = 5 units
Hence, the distance between point A and point B is 5 units.
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Write the equation of the line that passes through the points (2,-8)(2,−8) and (-1,4)(−1,4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The simplified point-slope form is y = 2x -12
A simple definition of point-slope form is a line equation written with only one point on the line and the slope of the line. (x, y) is the point form, and the slope is the rise over run or the ratio of the change in y values to the change in x values.
Given points (2,-8) and (-1,4)
We have to determine the answer in point-slope form
The slope formula provides the slope of the line:
m = (y2 -y1)/(x2 -x1)
m = (4 -(-8))/(-1-2) = 12/-3 = -4
the point-slope formula is given by
y-y1 = m(x-x1)
In terms of this formula:
m = 2
y1 = -8
x1 = 2
Let's simplify by plugging these values into the point-slope formula:
y - y1 = m (x - x1)
y - (-8) = (2)(x - 2)
y + 8 = 2(x - 2)
y + 8 = 2x -4
y = 2x -12
Therefore the simplified point-slope form is y = 2x -12
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Line g passes through points (2, 4) and (10, 1). Line h is parallel to line g. What is the slope of line h?
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line G
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 8 } \implies {\Large \begin{array}{llll} - \cfrac{3 }{ 8 } \end{array}}[/tex]
Which is the following rational functions is graphed below
Answer:
B.) 1/(x+3)(x+5)
Step-by-step explanation:
Look for the x-intercepts and asymptotes on the graph to get the numerator and denominator
There are no x-intercepts, so the numerator is an integer
The asymptotes are -3 and -5, so the denominator would be (x+3)(x+5) since if you were to set that = to 0 you would get -3 and -5.
Using Pythagoras' theorem, work out the
length of the hypotenuse of this right-angled
triangle.
Give your answer to the nearest centimetre.
7 cm
19 cm
Not drawn accurately
Answer: About 20.25 or [tex]\sqrt{410}[/tex]
Step-by-step explanation:
a²+b²=c²
c is the hypotenuse in this equation, so we can substitute the given side lengths for a and b.
7²+19²=c²
49+361=c²
410=c²
Then we take the square root to get
about 20.25 or [tex]\sqrt{410}[/tex] to be exact
Answer:
Step-by-step explanation:
a² + b². =. c²
7² + 19². =. c²
49 + 361 (400). =. c²
. c = √400= 20cm
The top of a 100 foot vertical tower is to be anchored by cables that make an angle of 60∘ with the ground. Please include units in your answers. All trig functions will be evaluated in degrees.
The horizontal distance which the cable is placed on is 57.74 feet
Trigonometric FunctionTrigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Data;
Height = opposite = 100ftangle = 60 degreeshorizontal distance = adjacent = xUsing tangent ratio;
tanθ = opposite / adjacent
tan 60 = 100 / x
x = 100 / tan 60
x = 57.74 ft
The distance which the cable is anchored to the ground is 57.74ft.
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Please help nobody wants to help me with this problem :,(
Answer:
x = 17
y = 2
Length of DF = 20
Step-by-step explanation:
Step 1: Solve x - 3
Since GH is the mid-segment it is equal to half of EFHalf of EF is 28/2 = 14x - 3 = 14x = 14 + 3x = 17Step 2: Plug x = 17 into x - 7 and solve
x - 7(17) - 7 = 10Since DH and HF are equal then x - 7 = y + 8So, 10 = y + 8y = 2Step 3: Find the length of DF
DF = y + 8 + x - 7DF = y + x + 1DF = 2 + 17 + 1 = 2012. Two functions are given below, one in equation form and the other in table form. Using these functions, give
the value of g (f (4)). Show how you arrived at your answer.
-2
f(x) -1
0
3
4
12
7
9
19
6
g(x)=3.25x+6
The composition of the fuctions g(x) and f(x) evaluated in x = 4 is equal to:
g( f(4)) = 45
How to find the value of the composition?Here we have two functions f(x) and g(x), such that:
g(x) = 3.25*x + 6
And f(x) is defined by the table:
x f(x)
-2 -1
0 3
4 12
7 9
19 6
And we want to find the composition of g(x) and f(x) evaluated in x = 4.
g( f(4))
By using the table of f(x), we can see that f(4) = 12
Then:
g( f(4)) = g(12)
Evaluating g(x) in x = 12 we get:
g(12) = 3.25*12 + 6 = 45
Then we conclude that g( f(4)) = 45
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Find the exact value of tan195
The exact value of tan195° is 0.2679.
The given trigonometric ratio is tan195°.
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.
Now, the value of trigonometric ratio is
tan195°=0.2679
Hence, the exact value of tan195° is 0.2679.
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