Answer: To find the height of the goalpost, we can use the information provided in the problem and the concept of similar triangles. Since Violet is looking down at the mirror, the line of sight from her eyes to the top of the goalpost forms a right angle with the ground. This right angle creates two similar triangles, one between her eyes, the ground, and the top of the goalpost, and the other one between the mirror on the ground, the goalpost, and a point on the ground that is the same distance from the mirror as the top of the goalpost is from Violet's eyes.
Since similar triangles have the same angle measures, we can set up the following proportion:
(distance from mirror to point on the ground) / (distance from mirror to top of goalpost) = (distance from Violet's eyes to ground) / (height of goalpost)
We can now use the information provided in the problem to solve for the height of the goalpost.
(6.65+4.25)/x = 1.75 / H
x = (6.65+4.25) * (1.75/H)
Where x is the distance from mirror to top of the goalpost.
Substitute the known values and solve for H
H = 1.75*(6.65+4.25) / x = 1.75*10.9 / x
We know that x = 4.25, so
H = 1.75*10.9 / 4.25 = 4.093 m
The height of the football goalp
Step-by-step explanation:
Erin combined 1 17/18 pounds of peanuts with 1 5/6 pounds of M&M's to create trail mix, then evenly distributed the mix in 8 bags. how many pounds of trail mix are in each bag?
There are 17/36 pounds of trail mix in each bag.
Finding out how much pounds of trail mix are in each bagTo find out how many pounds of trail mix are in each bag,you need to first add the weight of the peanuts and M&M's together.
1[tex]\frac{17}{18}[/tex] + 1 [tex]\frac{5}{6}[/tex] =([tex]\frac{35}{18}[/tex]) +([tex]\frac{11}{6}[/tex]) = [tex]\frac{35+33}{18}[/tex] =[tex]\frac{68}{18}[/tex]
which can be simplified to 3 [tex]\frac{14}{18}[/tex]
So there are 3 [tex]\frac{14}{18}[/tex]pounds of trail mix altogether.
To find out how many pounds of trail mix are in each bag, you will divide the total weight of the trail mix by the number of bags.3 [tex]\frac{14}{18}[/tex]÷ [tex]\frac{8}{1}[/tex] =
[tex]\frac{68}{18}[/tex] ÷ [tex]\frac{8}{1}[/tex]=[tex]\frac{68}{144}[/tex]
which can be simplified to [tex]\frac{17}{36}[/tex]
So there are [tex]\frac{17}{36}[/tex]pounds of trail mix in each bag.
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1. The football team at Vindale College is having a new stadium built that
will accommodate 49,697 people. According to one fan's calculations,
that is 67% more people than their old stadium could seat. How many
seats did the old stadium have? Round to the nearest whole number.
In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
The population of the city grew from 2010 to 2020 by 13.37%.
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
We have to given that;
In 2010, the population of a city was 237,000.
And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.
We know that;
Where, A = P (1+r)ⁿ
A = final population.
P = Initial population.
r = rate
n = time
Hence, The population in 2015 is, =
A = 237,000(1 + 0.076)⁵
A = 341829.629
And, The population in 2020 =
A = P (1 - r)ⁿ
A = 341829.629 (1 - 0.047)⁵
A = 268704.047
So, Percent grow = (268704.047 - 237,000) / 237,000 × 100
= 31704.047 / 237,000 × 100
= 13.37 %
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A financial analyst wants to set up a hypothesis test to determine if the mean yearly salaries of teachers, tutors, and professors are the same. What would be the correct setup for the null and alternative hypotheses for this test
Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.
Which null and alternative hypotheses are correct?The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.
Identify the null and alternative hypotheses.
As well as the sample size, specify.
Choose a suitable statistical test.
Gather information (note that the previous steps should be done prior to collecting data)
Based on the sample data, compute the test statistic.
Examine the null hypothesis, usually indicated by H0.
Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).
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I don’t know what to do for these whatsoever
please awnser the question below
The various statements regarding the given scatter plot is checked and found to be true or false.
What is a scatter plot?
A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities.
1)The equation of the line is y = 2500x - 125.
From the graph we can take two points on the line,
( 2,2250) and ( 10,1250)
Standard equation of line is y = mx + b
where b is y - intercept and m is slope
m = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex] = [tex]\frac{1250 - 2250}{10 - 2}[/tex] = -125
From graph, b = 2500
Equation of line is
y = -125x + 2500
Therefore the given equation is false.
2) The group of hikers descends about 250 feet every minute.
From the graph it is evident that for the interval between two points on y-axis is 250 feet and interval of x-axis is 1 minute.
So the hikers descend 250 feet every minute.
Therefore the given statement is true.
3) The hikers began at the elevation of 2500 feet.
The x-intercept of the graph is 2500 feet.
So the beginning elevation is 2500 feet.
Therefore the statement is true.
4) The graph shows a negative association.
Since the line in the graph is going down and the slope is negative, the graph shows a negative association.
Therefore the statement is true.
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When x²+(1/x)=3 find x⁴-2x³-x²-2x+1=
(without using calculator)
so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
we can start by squaring the equation x²+(1/x)=3
so we have x⁴ + 2x² + (1/x)² = 9
x⁴ + 2x² + 1 = 9x²
x⁴ - 7x² + 1 = 0
Now we can factor it
(x²-1)(x²-1) = 0
so x² = 1
now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1
x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1
= x⁴-2x³-2x-1
= (x⁴-2x³) - (2x+1)
= x⁴-2x³-2x-1
= (x²-x)² - (2x+1)
= (x-1)² - (2x+1)
so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)
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Solve the following system of equations using elimination:
-x+5y=8
And
3x+7y=-2
Answer:
x=-3, y=1. (-3, 1).
Step-by-step explanation:
-x+5y=8
3x+7y=-2
----------------
3(-x+5y)=3(8)
3x+7y=-2
--------------------
-3x+15y=24
3x+7y=-2
------------------
22y=22
y=22/22
y=1
-x+5(1)=8
-x+5=8
-x=8-5
-x=3
x=-3
how many solutions does y = 5x - 8 and y = 9x - 8 have
The equation y = 5x - 8 and y = 9x - 8 have one solution at
(0, -8)
How to find the solution of the equationThe equation is solved simultaneously by elimination method as follows
y = 5x - 8
y = 9x - 8
subtraction the equations
0 = -4x - 0
-4x = 0
x = 0
substituting x = 0 into y = 5x - 8
y = 5x - 8
y = 5 * 0 - 8
y =0 - 8
y = -8
The solution of the equation is at the point (0, -8)
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Darnel uses 8 fluid ounces of lemon juice in one batch of lemonade. How many batches can he make with 1 pint of lemon juice?
Answer:
16 ounces = 1 pint, 8 times 2 = 16
Step-by-step explanation:
Answer in explanation:
1 pint is 16 ounces so he could make 2 batches of lemonade with 1 pint of lemon juice.
(8 x 2 = 16
your answer is 2
Hope this helps!
A rectangular cake pan is 13 inches by 9 inches by 2 inches. A round cake pan has a diameter of 8 inches and a height of 2 inches. Which will hold more batter, one rectangular pan or two round pans?
Solve the equation by completing the squares.
x^2−10x = 11
x= __ and __
Answer:
x = 11 and x = -1
Step-by-step explanation:
We have x^2−10x = 11 and want to make a perfect square out of x^2−10x.
To do this, take half of the coefficient of x, square this half, and then add and then subtract the square immediately following x^2−10x:
Half of -10 is -5, and the square of -5 is 25.
x^2−10x = 11 becomes x^2 - 10x + 25 - 25 = 11
Rewrite x^2−10x + 25 as the square of a binomial: (x - 5)^2.
Then we have (x - 5)^2 - 25 = 11. Solve this for x -5:
(x - 5)^2 = 36. Taking the square root of both sides, we get
x - 5 = ±6
Then x = 11 and x = -1
The sum of two numbers is 50. the greater number is four less than five times the lesser number. Find the numbers
The required two numbers are 9 and 41.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
Let x be the lesser number, and y be the greater number.
From the question, we know that:
x + y = 50 (Equation 1: The sum of the two numbers is 50)
y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)
The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.
Then, two numbers are x = 9 and y = 41.
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20 POINTS!!! HELP ASAP!! What are the domain and range of the function graphed below?
What is the length of side AB as shown on the coordinate plane? On a coordinate plane, a rectangle has 4 points. Point A is (negative 2, 1), point B is (4, 1), point C is (negative 2, negative 3), and point D is (4, negative 3). 2 units 4 units 6 units 8 units please help???
Answer:
Step-by-step explanation:
Answer is 6 units
Answer:
6 units fs
Step-by-step explanation:
carman has saved 80% of the money she needs to buy a new video game. if she saved$36 how much does the video game cost
Carman buy the video game in the cost of $45.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Carman has saved 80% of the money she needs to buy a new video game.
And, she saved the cost $36.
Let total cost of the video game = x
So, We can formulate;
⇒ 80% of x = $36
⇒ 80/100 × x = 36
⇒ 8x = 360
⇒ x = $45
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If the equation of the line is y=-5.9x+91.9 . Which statement is false?
A. The slope of the line indicates that test score and the time spent watching tv are negatively correlated
B. The model predicts an approximate 6 - point drop in test score for one hour spent watching tv
C. The y-intercept or the line indicates that the student who spends no tv watching tv will get the highest test score possible
D.the liner model predicts an approximate test score of 92 if no time is spent watching tv
Answer:
. The slope of the line indicates that test score and the time spent watching tv are negatively correlated
Find the value of x in the isosceles triangle shown below. Please help asap!!
Answer:
B 12
Step-by-step explanation:
Using pythagoras theorem
What is the coefficient of x3y4 in 2x 3y2 5?
The coeficient of x^3+y^4 in the algebraic expression is the number 2
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
2x^3+ 2y^4
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.
2 is the coefficient of x^3+y^4
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classify the relationship between angles 1 and 2
Answer:
<1 and <2 are Complementary Angles
m<1 + <2 = 90 degrees
Step-by-step explanation:
<1 and <2 are Complementary Angles
m<1 + <2 = 90 degrees
Have a great day!
Since, angle 1 and 2 sums up to make 90 degrees, hence Angle 1 and 2 are complementary angles.
What is complementary angle?Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.
What is a supplementary angle?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. In the same way, complementary angles sum to 90 degrees.
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Find the length of the major arc in red
What is the value of the polynomial 5x − 4x^2 3 at x =- 1?
The value of the polynomial "5x - 4x^2 + 3" at x =- 1 is -6.
The polynomial is 5x - 4x^2 + 3, and it is required to find its value at x = -1,
Now solve the polynomial by putting the value of x equal to -1:
5(-1) - 4(-1)^2 + 3 , x = - 1
-5 - 4 ( 1 ) + 3 , squaring -1 gives + 1
minus 5 minus 4 plus 3
( - 9 + 3)
( - 6 )
Hence, is shown that the value - 6 is obtained when the given polynomial "5x - 4x^2 + 3" is solved for x = -1.
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Given the function f(x) = x² - x - 8, determine the average rate of change of the
function over the interval –4 < x < 3.
Answer:
Average Rate = -14/7
Step-by-step explanation:
f(3) = 3^2 - 3 - 8 = -2
f(-4) = (-4)^2 - (-4) - 8 = 12
interval: [-4, 3]
Average Rate = [f(b) - f(a)]/(b - a) interval: [a, b]
= [(-2) - 12] / [3 - (-4)]
= -14/7
What is the measure of angle ADC?
angle ADC equals 74 degrees
Please answer! Whoever does is a lifesaver and I wish they have a blessed day
Answer:
C = 31
Step-by-step explanation:
always do the parenthesis first so (2+4) = 6
3² + 4(6) x 6 ÷ 8 + 4 (Use PEMDAS)
9 + 4(6) x 6 ÷ 8 + 4, multiply 4 and 6
9 + 24 x 6 ÷ 8 + 4, multiply 24 and 6
9 + 144 ÷ 8 + 4, divide 144 and 8
9 + 18 + 4, now just add
31.
Answer:
c) 31
Step-by-step explanation:
9 + 4(6) * 6 / 8 + 4
9 + 24 * 6 /8 + 4
9 + 144 / 8 + 4
9 + 18 + 4
= 31
A juice container advertises it now contains 20% more juice. Originally, it had 27.5 ounces, how
much juice does it now contain?
Answer:
33 ounces
Explanation:
20% of 27.5 ounces is 5.5 ounces.
To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces
A circle has a diameter of 7.6 feet. What is the circumference of the circle in feet? Round to the nearest TENTH.
Answer:
23.88 feets
Step-by-step explanation:
C=2π2
=2×3.142×3.8
=23.8792 feets
rounded to the nearest TENTH
=23.88 feets
Are 6 8 and 9 12 equivalent?
Yes, 6/8 and 9/12 are equal. After simplifying both the fractions we got that both are equal and their value is 3/4.
Let's first try to understand what is a fraction.
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.
A fraction would be 5/10, for instance.
Here, the numerator is 5 and the denominator is 10.
6/8 is a fraction.
6/8 can be simplified further.
6/8 = 3/4
9/12 is also a fraction.
9/12 can be simplified further.
9/12 = 3/4
To compare 2 fractions first we try to make the same denominator.
we have the same value. so they are equivalent.
Given question is incomplete complete the question here:
Are 6/8 and 9/12 equivalent?
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Gillian feeds the goats the same amount of hay each day. On May 3, she has 72 pounds of hay left. On May 5, she has 60 pounds of hay left.
Based on the information and the graph provided, how many ponds of hay does Gillian most likely have left on the day that she has most likely 3 pounds of grain left? Provide evidence to support your answer. Include algebraic representations for each situation as part of your support
Answer:56
Step-by-step explanation:
Let ttt be the initial number of trees.
Hint #22 / 5
MacDonald now has t-5t−5t, minus, 5 trees and each one produced 210210210 oranges this harvest.
The total number of oranges produced is 210(t-5)210(t−5)210, left parenthesis, t, minus, 5, right parenthesis.
Hint #33 / 5
Since the trees produced a total of 417904179041790 oranges, let's set this equal to 417904179041790:
\qquad210(t-5)=41{,}790210(t−5)=41,790210, left parenthesis, t, minus, 5, right parenthesis, equals, 41, comma, 790
Now, let's solve the equation to find the initial number of trees (t)(t)left parenthesis, t, right parenthesis.
Hint #44 / 5
\begin{aligned}210(t-5)&=41790\\&\\ \dfrac{210(t-5)}{\blue{210}}&=\dfrac{41790}{\blue{210}}&&\text{divide both sides by $\blue{210}$}\\ \\ t-5&=199\\ \\ t-{5}\pink{+5}&=199\pink{+5}&&\pink{\text{add }} \pink{5} \text{ to both sides}\\ \\ t&=204\end{aligned}
210(t−5)
210
210(t−5)
t−5
t−5+5
t
=41790
=
210
41790
=199
=199+5
=204
divide both sides by 210
add 5 to both sides
Hint #55 / 5
The equation is 210(t-5)=41790.210(t−5)=41790.210, left parenthesis, t, minus, 5, right parenthesis, equals, 41790, point
MacDonald's farm initially had 204204204 orange trees.
Related content
Mandy bought a desktop computer system to start her business from home for $4,995. It is expected to depreciate at a rate of 10% per year. After how many years will the value of her home computer system depreciates to approximately $2150
Answer:
8.43 years
Step-by-step explanation:
Given data
Cost price P= $4995
Rate r= 10%
FInal amount A= $2150
The expression for the time/duration is given as
t= ln(A/p)/r
t= ln(2150/4995)/0.1
t= ln(0.430)/0.1
t= 0.843/0.1
t= 8.43
Hence the time it will take is 8.43 years