Answer:
92
Step-by-step explanation:
We first do 12x7 which equals to 84
Then we add 8 which equals to 92
In the diagram below of triangle DEF, G is the midpoint of DF and H is the midpoint of EF. If GH = 3x + 2, and DE = 18 + 4x, what is the measure of GH?
the wildlife game commission poured 5 cans of fish (each can contained approximately 100 fish) into a farmer's lake. the function n defined by n ( t )? A, The number of fish gets larger each year, but does not exceed 1200. B. The number of fish gets smaller every year but does not get smaller then 1200. C. The number of fish gets arger each year, but does not exceed 600. D. The number of fish gets larger each year, but does not exceed 500. E. The number of fish gets smaller every year, but does not get smaller than 500.
The function representing number of fish each 't' year
n ( t ) = (600t + 500) / ( 0.5t + 1) best defines option A. The number of fish get larger every year , but does not exceed the number 1200.
Let 'n' represents the number of fish.
't' represents the year.
The function representing the number of fish in 't' years is :
n ( t ) = (600t + 500) / ( 0.5t + 1)
Number of cans poured in the lake by farmer is equal to 5
Number of fish in each can = 100
Let t = 1
n(1) = 600(1) + 500 / 1.5
= 733.33
t= 2
n(2) = 600(2) + 500 / 2
=850
n(3) = 600(3) + 500 / 2.5
= 920
Therefore, the function n ( t ) = (600t + 500) / ( 0.5t + 1) best describes the option A. The number of fish get larger every year , but the number does not exceed 1200.
The above question is incomplete, the complete question is:
The wildlife game commission poured 5 cans of fish (each can contained approximately 100 fish) into a farmer's lake. the function n defined by
n ( t ) = (600t + 500) / ( 0.5t + 1) represents the approximate number of fish in the lake as a function of time (in years).Which one of the following best describes how the number of fish in the lake changes over time?
A. The number of fish gets larger each year, but does not exceed 1200.
B. The number of fish gets smaller every year but does not get smaller then 1200.
C. The number of fish gets larger each year, but does not exceed 600.
D. The number of fish gets larger each year, but does not exceed 500.
E. The number of fish gets smaller every year, but does not get smaller than 500.
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which of the following statements are true of an event listener's callback function? (select all that apply) A.It will be called every time the event listener is triggered B.Idon't know It must always define a parameter for the event object C.It must be passed to the event listener as the second argument D.It can be either an anonymous or a named function
Out of the following statements A)It will be called every time the event listener is triggered, C. It must be passed to the event listener as the second argument and D.It can be either an anonymous or a named function that is true of the event listener's callback function.
An event listener's callback function is a function that is triggered when an event is fired and the callback function is responsible for handling the event. A callback function must be passed to the event listener as the second argument, and it can be either an anonymous or a named function.
The callback function will be called every time the event listener is triggered, and it must always define a parameter for the event object. This allows the callback function to access the event object's properties and methods to handle the event accordingly. The event object contains information about the event, such as the type of event, the target element, and more. By accessing this information, the callback function can determine how to handle the event.
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Find a solution to the initial value problem, xy' + y = 8e", y(1) = -1 + 8e. [Hint: Interpret the left-hand side of the equation as the derivative of the product of two functions.] y =
The solution of the initial value problem xy' + y = 8e is equal to
log (x ) = - log ( 8e - y ) .
Solution of the initial value problem is:
xy' + y = 8e
⇒ x (dy /dx ) + y = 8e
⇒ x (dy/dx ) = 8e -y
⇒ dx / x = ( 1 / (8e -y ) ) dy
Integrate both the sides we get,
⇒ log (x ) = - log ( 8e - y ) + c ____(1)
Now , we have y ( 1 ) = -1 + 8e
Substitute the value y ( 1 ) = -1 + 8e in (1) we get,
⇒ log ( 1 ) = - log ( 8e - ( -1 + 8e )) + c ( value of log (1) = 0 )
⇒ 0 = - log ( 8e + 1 - 8e ) + c
⇒ 0 = log ( 1 ) + c
⇒ c = 0
Now substitute c =0 in (1) we get,
log (x ) = - log ( 8e - y )
Therefore, the explicit solution of the initial value problem is equal to
log (x ) = - log ( 8e - y ) .
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5y+8-2y=4y-y+5
Can someone please help im failing math (like explain the steps pls)
Answer: false
Step-by-step explanation: 1st we collect the Like Terms which would make the new equation 3y + 8 = 3y + 5 then we can cancel the 3y's bc they're equal and leaves us with 8 = 5 which we could see is false, so this equation is false
A jar contains 7 poker chips: 4 blue, 2 red and 1 white. You randomly select two chips from the jar. What is the probability that your selection includes two different colored chips? Report your answer to three decimal places.
The probability of selecting two different coloured chips is the fraction 14/49.
What is probability?Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.
total possible outcome = 7
blue chips = 4
red chips = 2
white chips = 1
probability of selecting blue chips = 4/7
probability of selecting red chips = 2/7
probability of selecting white chips = 1/7
probability of selecting two coloured chips at random = 4/7 × 2/7 + 4/7 × 1/7 + 2/7 × 1/7
probability of selecting two coloured chips at random = 8/49 + 4/49 + 2/49
probability of selecting two coloured chips at random = 14/49
Therefore, the probability of selecting two different coloured chips is the fraction 14/49
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Please help me with this question.
The answers are k = 12√2 and [tex]\theta=\frac{\pi }{2}+2\pi n[/tex]
What are trigonometric functions?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given are questions related to trigonometric functions:
a) k cos² (π/6) - k sin² (π/6) = 6√2
Finding k,
k cos² (π/6) - k sin² (π/6) = 6√2
Taking k common,
k [cos² (π/6) - sin² (π/6)] = 6√2
Since, cos²x-sin²x = cos2x
Therefore,
k[cos2(π/6)] = 6√2
k[cos(π/3)] = 6√2
Since, cos(π/3) = cos 60° = 1/2
Therefore,
k[1/2] = 6√2
k = 6√2 × 2
k = 12√2
b) sinx / cscx+cotx
[tex]\frac{sinx}{cscx+cotx}= \frac{sinx}{\frac{1}{sinx}+\frac{cosx}{sinx}}= \frac{sinx}{\frac{1+cosx}{sinx}}= \frac{sin^2x}{1+cosx}= \frac{1-cos^2x}{1+cosx}= \frac{(1+cosx)(1-cosx)}{1+cosx}\\\\= 1-cosx[/tex]
Hence, proved.
c) sinθ = 2cos²θ + 1
Solving for θ
[tex]\sin \left(\theta\right)-2\cos ^2\left(\theta\right)-1=0[/tex]
[tex]-3+\sin \left(\theta\right)+2\sin ^2\left(\theta\right)=0[/tex]
[tex]\sin \left(\theta\right)=1,\:\sin \left(\theta\right)=-\frac{3}{2}[/tex]
[tex]\sin \left(\theta\right)=1 : \theta=\frac{\pi }{2}+2\pi n\\\sin \left(\theta\right) = -\frac{3}{2} : no solution\\\theta=\frac{\pi }{2}+2\pi n[/tex]
Where n is any integer,
Hence, the answers are k = 12√2 and [tex]\theta=\frac{\pi }{2}+2\pi n[/tex]
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Find y'(-1) if y = (4x² - 5)³
The value of expression y ' (-1) is, 24.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ y = (4x² - 5)³
Now, We can differentiate with respect t x as;
⇒ y (x) = (4x² - 5)³
⇒ y' (x) = 3(4x² - 5)² × (4×2x - 0)
⇒ y' (x) = 3 (4x² - 5)² × 8x
⇒ y' (x) = 24x (4x² - 5)²
Substitute x = 1, we get;
⇒ y ' (1) = 24 × 1 (4 × 1² - 5)²
⇒ y' (1) = 24 (- 1)²
⇒ y' (1) = 24
Thus, The value of expression y ' (-1) = 24
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scores on the mathematics part of the sat exam in a recent year were roughly normal with mean 515 and standard deviation 114. you choose an srs of 100 students and average their sat math scores. suppose that you do this many, many times. which of the following are the mean and standard deviation of the sampling distribution of a) Mean =515,SD=114 (b) Mean =515,SD=114/√100 (c) Mean =515/100,SD=114/100 (d) Mean =515/100,SD=114/√100 (e) Cannot be determined without knowing the 100 scores.
The mean and standard deviation of the sampling distribution of the sample mean (average) of the SAT math scores are:
(b) Mean = 515, SD = 114/√100
SAT Math Scores Mean, SDThe mean of the sampling distribution of the sample mean is equal to the population mean (515), because the expected value of the sample mean is equal to the population mean. The standard deviation of the sampling distribution of the sample mean is called the standard error, and it is equal to the population standard deviation divided by the square root of the sample size (114/√100).
The result (b) is determined based on the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, the population mean is 515 and the population standard deviation is 114, so the standard deviation of the sampling distribution of the sample mean is equal to 114/√100. This result can be mathematically proven using the formula for the standard deviation of the sample mean:
SD of sample mean = σ/√n, where σ is the population standard deviation and n is the sample size.
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A scale drawing of th statue of abraham lincoln in the lincoln memorial uses a scale of 1 inch =3 feet if the statue is 19 feet tall how tall is the statue on the drawing ?
The length of the statue on the drawing is 6.33 inches.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 inch = 3 feet
The length of the statue = 19 feet
Now,
3 feet = 1 inch
Multiply 19/3 on both sides.
19 feet = 6.33 inch
Thus,
The statue on the drawing is 6.33 inches.
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Amanda rented a bike from Ted's Bikes. It costs $10 for the helmet plus $3.75 per hour. If Amanda paid about $41.88, how many hours did she rent the bike? a) Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem. b) Now solve your equation Amanda rented the bike for an hour.) hours. (Round your answer to the nearest tenth of Enter an integer or decimal number [more..]
Answer:
a) The equation to solve this problem would be:
10 + 3.75h = 41.88
b) To solve for h, we first need to subtract 10 from both sides:
3.75h = 31.88
Then, divide both sides by 3.75:
h = 8.50 (rounded to the nearest tenth)
So Amanda rented the bike for 8.5 hours.
Step-by-step explanation:
Answer: a) To solve the problem, we can use the equation:
Cost = 10 + 3.75h
Where h is the number of hours Amanda rented the bike.
b) We know that the cost is about $41.88, so we can plug that in for the cost and solve for h:
41.88 = 10 + 3.75h
31.88 = 3.75h
h = 31.88/3.75
h = 8.5 hours
So Amanda rented the bike for 8.5 hours. (rounding to the nearest tenth)
Step-by-step explanation:
Can anyone help with this question? I'm so lost
The amount of taxes a city collects is proportional to the population of the city. In 2005 the population was 2 million and it had increased to 3 million by 2017. If 4 billion dollars in taxes were collected in 2005, how much was collected in 2017?
The amount of taxes collected is proportional to the population, so if the population increased by 3 million - 2 million = 1 million, the amount of taxes collected should increase by the same factor.
So, in 2017, 4 billion * (3 million / 2 million) = 6 billion dollars in taxes were collected.
Answer:
Since the amount of taxes collected is proportional to the population of the city, we can write the relationship between the amount of taxes and the population as:
T = kP
where T is the amount of taxes, P is the population, and k is the constant of proportionality.
From the information given, we can find the value of k:
4 billion = k * 2 million
k = 4 billion / 2 million = 2
So, for the population of 3 million in 2017, the amount of taxes collected would be:
T = k * P = 2 * 3 million = 6 billion
So, in 2017 the city collected 6 billion dollars in taxes.
Please help me with this question.
The amount of rainfall in Nashville than in Miami would be 0.67.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the rainfall in Albany is 0.33. The amount of rainfall in Miami is calculated as:-
Rainfall = 1 - 0.33
Rainfall = 0.67
Hence, the amount of rainfall in Nashville than in Miami would be 0.67.
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Task 8
gifts &
entertainment
12%
clothes 5%
misc. 7%
debt 5%
savings
10%
Spending
Guidelines
(% of net incomes)
housing 30%
food 20%
transportation
11%
Jonathan makes a monthly net income
of $6,100 through his job as a manager.
He spends the following each month:
Monthly Expenditures
$2200
$350
$750
$150
$75
$50
Rent
Student Loans
Food
Car payment
Car insurance
Savings
1: How much is he over or under in each
category?
2: What advice would you give to Jonathan?
With the help of given pie chart, He is Under for some categories and over for other categories.
What is a pie chart?
The “pie chart” is also known as a “circle chart”, dividing the circular statistical graphic into sectors or sections to illustrate the numerical problems. Each sector denotes a proportionate part of the whole. A pie chart requires a list of categorical variables and numerical variables. To find out the composition of something, Pie-chart works the best at that time. In most cases, pie charts replace other graphs like the bar graph, line plots, histograms, etc.
The total value of the pie is always 100%.
Now,
Categories Spend value Spending guidelines Over/Under(O/U)
Rent $2200 $1830 O-$370
Student
Loan $350 $305 O-$45
Food $750 $1220 U-$470
Car payment $150 Together in transportation
and Car +
insurance $75 $671 U-$446
Savings $50 $610 U-$560
I would suggest Jonathan to save more and spend less on rent and more on food for better health.
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MATH for 53 POINTS
Find m∠DEC.
Answer:
118°
Step-by-step explanation:
Alexandra bought a pair of sunglasses online for $24. She used a coupon code to get a 20% discount. The website also applied a 10% processing fee to the price after the discount. How much was the discount, in dollars and cents?
$2.4 is the discount used to purchase a pair of sunglasses
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Alexandra bought a pair of sunglasses online for $24.
She used a coupon code to get a 20% discount.
The website also applied a 10% processing fee to the price after the discount.
20%-10%=10%
Now 10% of price is 24
10/100×24=x
2.4=x
24+2.4=26.4 is the actual price.
Hence, $2.4 is the discount used to purchase a pair of sunglasses
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if monique wanted to run 7/8 mile and she went to the school track which was one quater of a mile long how lany laps would she have to run
Which of the following questions could I use to find the answer check all that apply.
A. L x 1/4=7/8. YES OR NO
B. 7/8 x 1/4 = L. YES OR NO
C. 7/8 X 4=L. YES Or NO
D. L/ 7/8 = 1/4. YES OR NO
hURRY
if Monique wanted to run 7/8 mile and she went to the school track which was one quarter of a mile long. The number of lap Monique will complete is
C. 7/8 X 4 = L. What is a lap in race?One complete lap around a track or across a pool, from one end to the other: The track has 400 meters or approximately 25 mile per lap.
A lap is end to end of a track and in the problem a lap is 1/4 mile and Monique wants to complete 7/8 miles'. the comparison is as follows
assuming the number of laps is L
1 lap = 1/4 mile
L laps = 7/8 miles
cross multiplying
1 * 7/8 = L * 1/4
multiplying by 4 for each side
1 * 7/8 * 4 = L * 1/4 * 4
1 * 7/8 * 4 = L * 1
7/8 * 4 = L
hence option C is correct
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What is the volume of the cube shown?
WILL GIVE BRAINLEST
Answer:
11.390625 in^3
Step-by-step explanation:
2.25^3 = 11.390625 in^3
The width of a rectangle is 8 in. less than its length. The perimeter is 52 in.
What is the width of the rectangle?
Answer:
The width of the rectangle is 9
Step-by-step explanation:
l + l + w + w = perimeter
(x - 8) + (x - 8) + (x) + (x) = 52
We don't know the length so put it as a variable
x + x + x + x - 8 - 8 = 52 Group together like-terms.
4x - 16 = 52 Combine like-terms
4x = 68 Add 16 to both sides
x = 17 Divide both sides by 4
We now have the value for the length (x = 17) however we need the value for the width. Just subtract 17 - 8 since the width is 8 in. less than its length.
17 + 17 + 9 + 9 = 52
Given the following diagram what can you conclude?
Answer:
YXZ=AXZ
because if you see the letters they form triangle
Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.
[1 h 4
3 6 8]
The value of h can be any value other than 2.
Value of h for Consistent SystemThe augmented matrix of a consistent linear system must have a unique solution, which means the determinant of the coefficient matrix must be non-zero.
For the given matrix, the coefficient matrix is:[1 h
3 6]
The determinant of this matrix is (1 * 6) - (3 * h) = 6 - 3h.
For the determinant to be non-zero and the system to be consistent, 6 - 3h must not be equal to zero, so h cannot be equal to 2.
Therefore, the value of h can be any value other than 2.
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Going into the final examwhich will count as two testsBrandi has test scores of 79,80, 74, 63, and 92. What score does Brandi need on the final in order to have an average score of 80?
Answer:
Brandi needs to receive a score of 46 on the final to have an average score of 80.
Step-by-step explanation:
First, let's understand what is being told to us. We are being asked to find the score Brandi needs on the final, or x. Since the final is worth 2 tests, the final is equal to twice the score she receives, or 2x. Next, we need the average of all the tests, including the final, to be equal to 80. It's important to also note that we will be taking the average of 6 scores. Now, let's use all of our information to write an equation to solve:
( 79 + 80 + 74 + 63 + 92 + 2x ) / 6 = 80. [Combine like terms]
( 388 + 2x ) / 6 = 80 [Multiply by 6]
388 + 2x = 480 [Subtract 388 from both sides]
2x = 92 [Divide both sides by 2]
x = 46
So, Brandi needs to receive a score of 46 on the final to have an average score of 80.
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Which solution for the value of x is right? 4x - 2 = 3x + 6 or 4x - 2 +3x+6=180
Answer:
Step-by-step explanation:
4x+3x=6+2
7x/7=8/7
=1.143
Answer: X=22
According to equation given :-
4x-2=3x+6 ----------------------(1)
4x - 2 +3x+6=180 -------------(2)
hence put equation (1) in (2) which that
4x - 2 +4x-2=180
2* ( 4x-2 ) = 180
4x-2 =90
4x = 88
x= 22 (answer)
HELP ASAP MY MOMS ABOUT TO CHECK MY MATH WORK AND I HAVE THIS STILL
Find the percent equivalent to 96 over 160.
60%
64%
75%
80%
Answer:
0.6
Step-by-step explanation:
96/160 = 0.6
Just divide.
The decimal is 0.60, which is 60% of 1.
Answer:
96 of 160 is 60%
102.4 of 160 is 64%
120 of 160 is 75%
128 of 160 is 80%
Hope this helped!
Step-by-step explanation:
xFind the radian measure of the central angle of a circle of radius 6 yards that intercepts an arc of length 8 yards.
The measure of the central angle associated to the circular arc is equal to 4 / 3 rad.
How to determine the central angle associated to the arc of a circle
Herein we find the information of the radius of a circle and the length of its circular arc, whose relationship is shown by the following formula:
s = θ · r
Where:
r - Radius, in yards.s - Length of the circular arc, in yards. θ - Measure of the central angle, in radians.If we know that r = 6 yd and s = 8 yd, then the measure of the central angle is:
θ = s / r
θ = (8 yd) / (6 yd)
θ = 4 / 3 rad
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A radio tower is located 300 feet from a building. From a window in the building, a person determines that
the angle of elevation to the top of the tower is 38° and that the angle of depression to the bottom of the
tower is 29°. How tall is the tower?
Round your answer to 2 decimal places
The height of the tower is 600 feet
What is angle of elevation and the angle of depression?
Angle of elevation: The angle of elevation is the angle produced by the line of sight with the horizontal when the item is above the horizontal level.
Angle of depression: The angle of depression is the angle produced by the line of sight with the horizontal when the item is below the horizontal level.
Let's call the height of the tower "h".
Using trigonometry, we can set up equations based on the angles of elevation and depression:
tan 38° = h / 300
tan 29° = (h - 300) / 300
Solving for h,
h = 300 * tan 38°
h = 300 * 0.8192
h = 245.76
Now,
300 * tan 29° = (h - 300) / 300
300 * 0.5672 = (h - 300) / 300
h - 300 = 300 * 0.5672 / 0.5672
h - 300 = 300
h = 600
So, The height of the tower is 600 feet, rounded to 2 decimal places.
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If you spent $20,750 for goods, service and housing in 2000, what would the same purchase have cost in 1984?
Answer:
below
Step-by-step explanation:
20750 is to 172.2 as x is to 103.9
20750 /172.2 = x / 103.9
x = $ 12519.89
I have added a screenshot.
Answer:
44/87
Step-by-step explanation:
There are 87 fair managers. 44 of them have a college degree. Being that he is a fair manager, the chance of him having a college degree is 44 out of 87, otherwise written as 44/87.
A farmer wants to build a fence around the edge of a field shaped like a right-angled triangle, as shown below. The fence costs £1.26 per metre.
Calculate the total cost of the fence.
Give your answer to the nearest pound.
To calculate the total cost of the fence, we need to know the length of the fence.
In a right-angled triangle, the length of the fence can be calculated using the Pythagorean theorem, which states that the length of the hypotenuse (the fence) is equal to the square root of the sum of the squares of the other two sides (the base and the height of the triangle).
So, the length of the fence (C) = square root of (A^2 + B^2), where A is the base and B is the height of the triangle.
If the base of the triangle is x and the height of the triangle is y, then the cost of the fence can be calculated using the formula:
Cost = (length of fence) x (cost per meter)
Cost = (square root of (x^2 + y^2)) x 1.26
In order to calculate the cost, the farmer needs to know the values of x and y.
The total cost of the triangular shaped fence is A = £ 530
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of side AB = 145 m
Now , the measure of ∠BAC = 59°
From the trigonometric relations
tan θ = opposite / adjacent
tan 59° = BC / 145
Multiply by BC on both sides , we get
BC = 241.320524941 m
Now , the hypotenuse of the triangle is
H = √ ( 145 )² + ( 241.320524941 )²
H = √ ( 21,025 + 58,235.595757
H = √79,260.595757
H = 281.53258 m
Now , the total perimeter of triangle is P = 281.53258 + 241.320524941 + 145
P = 667.85310877 m
Now , fence costs £1.26 per meter
A = 667.85310877 m / £1.26
So , the total cost is A = £ 530
Hence , the total cost is A = £ 530
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find three different formulas or rules for the terms of a sequence {an} if the first three terms of this sequence are 1,2,4.
Three different formulas or rules for the terms of a sequence {an} if the first three terms of this sequence are 1,2,4 are as follows:
The sequence {an} is an arithmetic sequence, so the formula for the nth term is an = a1 + (n-1)d, where a1 is the first term, n is the term number, and d is the common difference. In this case, a1 = 1 and d = 1, so the formula is an = 1 + (n-1).The sequence {an} is a geometric sequence, so the formula for the nth term is an = ar^(n-1), where a1 is the first term, n is the term number, and r is the common ratio. In this case, a1 = 1 and r = 2, so the formula is an = 1*2^(n-1).The sequence {an} is a Fibonacci sequence, so the formula for the nth term is an = Fn, where F stands for the Fibonacci number and n is the term number. In this case, the Fibonacci number for the 3rd term is 2, so the formula is an = 2n.Learn more about Fibonacci sequence:
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