The expression that represents the area of the triangle is given as follows:
A = (c - a)[8 - (c - a)]/4.
How to obtain the area of a triangle?The area of a triangle is obtained as half the multiplication between the base b and the height h, that is:
A = 1/2 x b x h.
For the triangle in this problem, the base is composed by these following vertices:
(a, 0).(c, 0).Hence the length of the base is of:
b = c - a.
The height is given by the difference between the y-coordinate of the vertex (b,4) and the midpoint of the base ac, hence:
h = 4 - (c - a)/2 = [8 - (c - a)]/2
Hence the area is given as follows:
A = 1/2 x (c - a) x [8 - (c - a)]/2
A = (c - a)[8 - (c - a)]/4.
Missing InformationThe problem asks for which expression gives the area of the triangle with these vertices.
More can be learned about the area of a triangle at https://brainly.com/question/21735282
#SPJ1
we get statistics of 2017-2018 average starting teacher salaries by state measured by nea. given that the salary of arkansas is 33323, the sample size is 3,600 and the standard deviation is 399.876. a. what is the margin of error for a 80% confidence interval in arkansas? symbolic expression b. if we want to get a 80% confidence interval with a small margin of error, say only 7%. how many people do you need to sample?
a) The margin of error for an 80% confidence interval in Arkansas is 0.1041
b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359
The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.
n = 3600
standard deviation = 399.876
Confidence Interval = 80%
a) α = 0.20
The margin of error = Zα/2 (σ / √n)
Zα/2 = 1.4395 --- (From the tabular value)
The margin of Error = 1.4395 + 399.876 / √3600
Therefore, the Margin of Error = 8.1041
b) Margin of Error = 0.07 = 7%
α = 0.20
Critical Value = 1.2816
Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²
n = [(1.2816 * 399.876) / 0.07]²
n = 53599358.98
Therefore, Sample size, n = 53599359
To know more about the Margin of Error, refer to this link:
https://brainly.com/question/11832344
#SPJ4
if two numerical variables x and y have a correlation coefficient of 0.90, what percentage of the variation in one variable can be accounted for by the other variable?
The percentage of variation in variable can be accounted for by the other variable is 81%.
What is variation in statistic?
The statistical distance between the values of the observations (data points) is what makes up a measure of variance. There are various ways to measure variation.
What is correlation coefficient?
A statistical indicator of the strength of a linear link between two variables is the correlation coefficient.
The formula of percentage of variation is:
(correlation coefficient × correlation coefficient × 100)%.
Given that the correlation coefficient is 0.90.
Thus the percentage of variation is (0.90 × 0.90 × 100)% = 81%
To learn more about correlation coefficient, you can visit below side
https://brainly.com/question/15577278?
#SPJ4
There are 150 students in the marching band , and 30 of them play trumpet . Which number line represents the percent of the students in the marching band who play trumpet
By using the rule of 3 we wills ee that the percentage of students who play the trumpet is 20%
How to get the percentage of students who play the trumpet?We know that there are 150 students in the marching band, that will be our 100% in this case, and we know that 30 of them play the trumpet.
These 30 students represent a percentage X that we want to find, so we can write a little system of equations and use the rule of 3.
30 = X
150 = 100%
Taking the quotient between the two equations we get:
(30/150) = X/100%
Solving for X we get:
(30/150)*100% = X = 20%
So we can say that 20% of the students play the trumpet.
Learn more about percentages:
https://brainly.com/question/843074
#SPJ1
EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the slope intercept form of the equation of the line through the given point with the given slope
through (-1, -4) slope = 5
Answer:
y=5x+1
Step-by-step explanation:
we already know the slope so we can put it in the slope intercept form
y=5x
And now we can put the coordinate points in there to find the y intercept
-4=5(-1)
-4=-5
We need to add 1 to make this equation true so the y intercept is 1
The equation will be
y=5x+1
Hopes this helps please mark brainliest
Answer:
y=5x+1
Steps are in the picture
which one would be the correct answer?
3x²-2x+5 is the other factor of the above polynomial (6x³-x²+8x+5) other than (2x+1).
Describe a polynomial.In mathematics, a polynomial is an equation made up of coefficients and indeterminates, also referred to as variables. Only addition, subtraction, multiplication, and powers of positive-integer variables may be utilized to solve it. An example of a polynomial with one uncertain x is x² + 4x + 7.
Polynomials are commonly used in calculations in both mathematics and science. For instance, in the fundamental sciences of chemistry, physics, economics, and social science, they are used to define polynomial functions. They are also used in numerical analysis and calculus to approximate other functions. Simple word problems to complex scientific conundrums are all represented by polynomial equations. Polynomials are used in advanced mathematics.
To know more about polynomials, visit:
brainly.com/question/11536910
#SPJ13
WILL GIVE BRAINLIST TO BEST ANSWER! EASY POINTS
write the point slope form of the equation of the line through the given points.
through (-5, -1) and (-4, -5)
Answer:
y+1=-4(x+5)
Step-by-step explanation:
it changed to point slope form so now it’s different
the equation is y-y1=m(X-x1)
y-(-1)=m(x-(-5)
y+1=m(x+5)
Now to find slope y2-y1/x2-x1
-5+1/-4+5
-4/1
-4 is the slope so we just fill it in
y+1=-4(x+5)
Hopes this helps please mark brainliest
The number of avocados used by a restaurant in a day varies directly with the number of orders of guacamole that day. It takes 6.5 avocados to make 4 orders of guacamole. How many avocados would it take to make 14 orders of guacamole?
Proportionately, it would take the restaurant 22.75 avocadoes to make 14 orders of guacamole since it takes 6.5 avocados to make 4 orders.
What is the proportion?Proportion refers to the quantity of a value or variable contained in another value.
Proportion is a fractional value like a ratio that shows the numerical relationship between two or more values.
Proportions are depicted using fractions, decimals, or percentages.
The number of avocados required for 4 orders of guacamole = 6.5
The total number of orders of guacamole required = 14
The number of avocados to make 1 order = 6.5/4
The number of avocadoes required to fill 14 orders = 22.75 (6.5/4 x 14)
Thus, in proportion, it would take 22.75 avocados to make 14 orders of guacamole.
Learn more about proportions at https://brainly.com/question/1496357
#SPJ1
find the intervals of increase and decrease of 3/512(x-4)^2(x-8)(x-10)(x^2+16)
The given function is strictly decreasing in interval (−∞, 4) & trictly increasing in interval (4, −∞).
What is an increasing and decreasing functions?
For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
We have,
[tex]\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]
[tex]\frac{d}{dx}\left(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]
[tex]=\frac{5}{512}\frac{d}{dx}\left(\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]
[tex]f'(x)=\left(x-4\right)^2,\:g=\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]
[tex]=\frac{5}{512}\left(\frac{d}{dx}\left(\left(x-4\right)^2\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\frac{d}{dx}\left(\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\left(x-4\right)^2\right)[/tex][tex]=\frac{5}{512}\left(2\left(x-4\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\left(4x^3-54x^2+192x-288\right)\left(x-4\right)^2\right)[/tex]
[tex]f'(x)=\frac{5\left(x-4\right)\left(3x^4-53x^3+300x^2-816x+1856\right)}{256}[/tex]
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
x = 4, 4i, −4i, 10, 8
∴ f′(x) = 0
x = 4,
Now, the point 4 divides the real line into two disjoint intervals i.e., (−∞, 4) and (4, −∞)
In interval (−∞, 4), f′(x) < 0
Hence, the given function (f) is strictly decreasing in interval (−∞, 4)
In interval (4, −∞), f′(x) > 0
Hence, the given function (f) is strictly increasing in interval (4, −∞)
To learn more about the increasing and decreasing functions visit,
https://brainly.com/question/13157110
#SPJ9
Help! Consider the following three systems of linear equations.
Answer:
b & d
Step-by-step explanation:
assume that blood pressure readings are normally distributed with and a blood pressure reading of 145 or more may require medical attention. what percent of people have a blood pressure reading greater than 145?
0.08891% percent of people have a blood pressure reading greater than 145.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
145) = (145-120)/8 = 25/8.P(x > 145) = P(z > 27/8) = 0.0008891.. = 0.08891%Hence, 0.08891% percent of people have a blood pressure reading greater than 145.
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ4
First, complete the story below so that it can be represented by the equation 5000-50x=4800-30x
Pool A started with 5000 liters of water, and 50 liters per minute are being (Drained out or Pumped back in)
Pool B started with 4800 liters of water, and 30 liters per minute are being (Drained out or Pumped back in)
The amount of water after x minutes is more in which pool? Pool A or Pool B?
Amount of water after x minutes is more in pool B.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Pool A started with 5000 liters of water, and 50 liters per minute are being.
Pool B started with 4800 liters of water, and 30 liters per minute are being.
5000-50x=4800-30x
Add 30x on both sides
5000-50x+30x=4800-30x+30x
5000-20x=4800
5000-4800=20x
200=20x
Divide both sides by 20
20=x
Now substitute x in pool A equation
5000-50x
5000-50(20)=5000-1000
Pool A =4000
Now substitute x in pool B equation
4800-30x
4800-30(20)
4800-600
Pool B =4200
4200>4000
Pool B> Pool A
Hence amount of water after x minutes is more in pool B.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
A right triangle has a hypotenuse of 1 meter and a leg of 1/2 meter. What is the area of the triangle to the nearest hundredth of a square meter?
The area of the triangle to the nearest hundredth of a square meter is 0.217m²
A right triangle has a hypotenuse of 1 meter and a leg of 1/2 meter
Hypotenuse = 1
base = 0.5
We need to calculate the perpendicular
h² = b² + p²
1² = 0.5² + p²
p² = 1 - 0.25
p = √0.75
p = 0.866
area of the triangle = 1/2 base x height
area = 1/2 (0.5 x 0.866)
area = 0.2165m²
Therefore the area of the triangle to the nearest hundredth of a square meter is 0.217m²
To learn more about area refer here
https://brainly.com/question/17335144
#SPJ9
Answer both of um I'll mark you brainliest
Answer:
1) 71.83
2) 43
3) 41
4) 755.66
5) 458
6) 1757.12
7) 123 meters
Help I need this for my homework
Answer:
6.6
Step-by-step explanation:
you subtract 6.6 from both sides to cancel it out on one side
Hopes this helps please mark brainliest
Can someone help me with this please! I really need it done PLS
increase the amount of the ingredients by 5 and by 20
Answer:
it's 50 g
Step-by-step explanation:
it's like a multiplying assberry kehe
How do you find if the vertical or horizontal asymptote is going to be approaching negative infinity or positive infinity. Provide examples.
Answer:
to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.
Step-by-step explanation:
9) Willie took a trip to Oman. Upon leaving he decided to convert all of his Rials back into dollars. How many dollars did he receive if he exchanged 12 Rials at the rate of 1 Rial to $3?
10) A rectangle is 2 in wide and 1 in tall. If it is enlarged to a width of 14 in then how tall will it be?
number 9 is 36 12x3 is 36
pls help me with algebra
a hospital director is told that 31% of the emergency room visitors are uninsured. the director wants to test the claim that the percentage of uninsured patients is below the expected percentage. a sample of 380 patients found that 95 were uninsured. find the value of the test statistic. round your answer to two decimal places.
The test statistic is -2.60 as a sample of 380 patients found that 95 were uninsured.
What is test statistic?A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. For instance, the Z-statistic, which has the typical normal distribution under the null hypothesis, is the test statistic for a Z-test. Here,
n=380
x=95
p=95/380
p=0.25
test=(0.25-0.31)/√(0.28(1-0.28)/380)
test=-2.60
The test statistic is -2.60 because 95 out of 380 patients in the sample did not have insurance.
To know more about test static,
https://brainly.com/question/4675410?referrer=searchResults
#SPJ4
How do you write 11+5(3x-2)-8x in the sum of two terms
The simplified for of the Algebraic expression which is the sum of two terms is 1 + 7x
What is an Algebraic expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms which can either be a variable or a constant .
11 + 5(3x - 2) -8x
multiply out the bracket we have,
11 + 15x - 10 -8x
collect like terms and simplify
11 - 10 + 15x - 8x
1 + 7x
In conclusion, the expression 11 + 5(3x - 2) as a sum of two terms is 1 + 7x
Learn more about Algebraic expressions: https://brainly.com/question/2164351
#SPJ1
8/5 + 7/3 Please put step by step
Answer:
59/15
Step-by-step explanation:
8/5 + 7/3 Multiply the numerator and denominator by the LCF of the denominator
(3/3) 8/5 + 7/3 (5/5) Multiply
24/15 + 35/15 Add the numerators
59/15
correct answer gets brainliest!
Answer:
x = 14
Step-by-step explanation:
the inscribed angle JKL is half the measure of its intercepted arc, that is
83 = [tex]\frac{1}{2}[/tex] arc JL = [tex]\frac{1}{2}[/tex](9x + 40) ← multiply both sides by 2 to clear the fraction
166 = 9x + 40 ( subtract 40 from both sides )
126 = 9x ( divide both sides by 9 )
14 = x
A group of friends wanted to compare their average running speeds. They recorded the distance and amount of time each person ran one Saturday morning.
Select all the runners whose speeds are in a proportional relationship with each other.
Name Time (seconds) Distance (miles)
Liam 306.6 0.5
Taylor 756.36 1.2
Sarah 504.35 0.7
Ashley 459.9 0.75
Connor 600.5 1
Nathan 942.75 1.5
Juan 827.82 1.35
Katie 429.48 0.6
The runners whose speeds are in a proportional relationship with each other:
the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed of Sarah and Katie are equal.
In this question, we have been given the data for the distance and amount of time each person ran one Saturday morning.
We need to select all the runners whose speeds are in a proportional relationship with each other.
We find the speed using formula, speed = distance / time
Name Time (seconds) Distance (miles) Speed(mps)
Liam 306.6 0.5 0.5/306.6 = 0.0016
Taylor 756.36 1.2 1.2/756.36 = 0.0016
Sarah 504.35 0.7 0.7/504.35 = 0.0014
Ashley 459.9 0.75 0.75/459.9 = 0.0016
Connor 600.5 1 1/600.5 = 0.0017
Nathan 942.75 1.5 1.5/942.75 = 0.0016
Juan 827.82 1.35 1.35/827.82 = 0.0016
Katie 429.48 0.6 0.6/429.48 = 0.0014
Therefore, the runners whose speeds are in a proportional relationship with each other:
the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed of Sarah and Katie are equal.
Learn more about proportional relationship here:
https://brainly.com/question/13910860
#SPJ1
PLEASE HELP! WILL GIVE BRAINLIEST!
1. The linear function .f(2) = 79.4, therefore, test average for maths class after 2 test is: 79.4
2. Using the function table, the test average for science class is after the second test is: 84.
3. f(4) = 79.8
4. g(4) = 80
5. Science class was higher.
What is a Linear Function?The equation of a linear function is given as .f(x) = mx + b, given that m represents the slope/unit rate, and b is the y-intercept or starting value.
The linear function for average test score in maths class is given as, .f(x) = 0.2x + 79
Write the linear function for science class;
Slope (m) = change in y/change in x = (84 - 82)/(2 - 3) = 2/-1
Slope (m) = -2
Substitute m = -2 and (x, y) = (3, 82) into y = mx + b:
82 = -2(3) + b
82 = -6 + b
82 + 6 = b
88 = b
b = 88
Substitute m = -2 and b = 88 into g(x) = mx + b:
g(x) = -2x + 88
Part 1:
Substitute x = 2 into .f(x) = 0.2x + 79
.f(2) = 0.2(2) + 79
.f(2) = 79.4
Test average for maths class after 2 test is: 79.4
Part 2:
Using the function table, when x = 2, the test average for science class is: 84.
Part 3:
Substitute x = 4 into .f(x) = 0.2x + 79
.f(4) = 0.2(4)+ 79
.f(4) = 79.8
Part 4:
Substitute x = 4 into g(x) = -2x + 88
g(4) = -2(4) + 88
g(x) = 80
Part 5:
Science class had a higher test 4 average of 80.
Learn more about linear functions on:
https://brainly.com/question/15602982
#SPJ1
If 8^y =16^y+2what is the value of y?
O-8.
O-4.
O-2.
O-1.
Answer:
-8
Step-by-step explanation:
Graph each side of the equation. The solution is the x-value of the point of intersection.
solve for x 4{x+1 1/3]=9 2/3
The solution for the expression is X =87/ 48 or 1.812
To solve for x in the equation we follow the step below:
Step 1: Open the bracket by multiply 4
= 4x +4x/3 = 9 2/3
= 4x + 4x /3 = 29/3
Step 2: Evaluate for X
= [tex]\frac{12x + 4x}{3}[/tex] = [tex]\frac{29}{3}[/tex]
= [tex]\frac{16x}{3}[/tex] =[tex]\frac{29}{3}[/tex]
Step 3: Cross multiply
: 3 (16x) = 3(29)
48x = 87
Step 3: Divide both sides by 48
=[tex]\frac{48x}{48}[/tex] =[tex]\frac{87}{48}[/tex]
x = [tex]\frac{87}{48}[/tex] = 1.812
Therefore, the solution for the expression is X =87/ 48 or 1.812
Learn more about expression here; https://brainly.com/question/4344214
#SPJ1
what is the correct postulate to prove these two triangles congruent?
A. SAS
B. ASA
C. SSS
D. AAS
E. HL
Ms. Lewinsky’s math class has k students. If p students earned a C or better on the last test, what fraction of the class did NOT eat a C or better on the last test?
Answer:
its "a" your welocome
Step-by-step explanation:
i did the test
i need help asap i need an awncer
3x=y-4z=-22
2x+3y+4z=32
x-y+2z=16
Answer:
3x + y - 4z = -222x + 3y + 4z = 32x - y + 2z = 16 Write and number each equation. Eq 1 3x+y-4z = 16. Eq 2 -222x+3y+4z = 16. Eq 3 32x-y+2z = 16
Step-by-step explanation:
Hope it helps you buddy(:
Answer: 16
You already got the answer- But whatever.
The values of [x], [y] and [z] are 2, 0 and 7.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written to express proportional relationship as -
y = kx {k is constant}
We have the following system of equation -
3x+y-4z=-22
2x+3y+4z=32
x-y+2z=16
We can write -
x - y + 2z = 16
x = 16 + y - 2z
So, we can write 3x + y - 4z = -22 as -
3(16 + y - 2z) + y - 4z = -22 ...eq[1]
and we can write 2x + 3y + 4z = 32 as -
2(16 + y - 2z) + 3y + 4z = 32 ...eq[2]
Plot eq[1] and eq[2], and find [y] and [z]. Refer to graph.
We get y = 0 and z = 7
So -
x = 16 + 0 - 14
x = 2
Therefore, the values of [x], [y] and [z] are 2, 0 and 7.
To solve more questions on system of equations, visit the link below-
https://brainly.com/question/20067450
#SPJ2
find two positive numbers whose product is 25 and whose sum is a minimum. (enter your answers as a comma-separated list.)
The required positive number whose product is 25 and whose sum is minimum is 5, 5
Sum of Two numbers
Sum of two numbers means adding two same or different number together
Let two positive numbers xy = 25
Divide both side by x
y = [tex]\frac{25}{x}[/tex] ----------Equation (1)
Sum of two positive numbers s = x + y -------Equation (2)
Substitute equation (1) into equation (2)
S = x + [tex]\frac{25}{x}[/tex]
differentiate with respect to x
[tex]\frac{ds}{dx} = \frac{d}{dx} (x + \frac{25}{x} ) = 1 - \frac{25}{x^{2} }[/tex]
[tex]\frac{ds}{dx} = 1-\frac{25}{x^{2} }[/tex] ---------- Equation (3)
[tex]\frac{ds}{dx} = 0[/tex]
[tex]1[/tex][tex]- \frac{25}{x^{2} }[/tex] = 0 ⇒ [tex]x^{2}[/tex] = 25
x = 5
Differentiate equation (3) again
[tex]\frac{d^{2}s }{dx^{2} } = 0 + \frac{50}{x^{2} }[/tex]
hence, at point x = 5, [tex]\frac{d^{2} s}{dx^{2} } = \frac{50}{5^{2} }[/tex] [tex]= \frac{50}{25} = 2[/tex]
Value of s minimum at point x = 5.
substitute the value of x into equation (1)
[tex]y = \frac{25}{x} = \frac{25}{5} = 5[/tex]
Therefore the required positive numbers are 5, 5.
Learn more about sum of two positive numbers here: https://brainly.ph/question/99369
#SPJ1