For a project in her Geometry class, Morgan uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 13.85 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. She then walks 4.25 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Let's call the height of the goalpost "h". We can use similar triangles to solve for h. Morgan walks a total of 13.85 and placed the mirror and walk 4.25 more, let d = 13.85.
The mirror forms a right triangle with the height of the goalpost, the distance from her eyes to the ground, and the distance d.
So, we have:
h / d = 1.15 / 4.25
Solving for h:
h = (1.15 ×13.85 ) / 4.25
h = 6371 / 1700
Rounding to the nearest hundredth of a meter, the height of the goalpost is 3.74 meters.
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The mass of a radioactive substance follows a continuous exponential decay model, with the decay rate parameter 4% per day. A sample of this radioactive substance has an initial mass of 2.05 kg. Find the mass of the sample after four days. Round your answer to two decimal places.
The mass of the sample after 4 days is 1.54 kg.
What is exponential decay?Exponential decay can be defined as the process in which a quantity decreases over time with the rate of decrease becoming proportionally smaller as the quantity gets smaller.
The formula for exponential decay is given by:
m(t) = m0 * e^(-kt)
where m(t) is the mass of the substance after time t
M0 is the initial mass
k is the decay rate parameter
E is the base of natural logarithms
Plugging in the values:
m(4) = 2.05 * e^(-0.04 * 4)
m(4) = 1.54 kg
Therefore, The mass of the sample after 4 days is 1.54 kg.
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36 x 5 +59 x(234)(51)
the simplified Answer to the given expression 36 x 5 +59 x(234)(51) will be 7,04,286.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given, an expression 36 x 5 +59 x(234)(51)
Simplifying using PEMDAS
=> 36 x 5 +59 x(234)(51)
First, we will open a bracket
=> 36 * 5 + 59 * 11934
Now multiple of the given terms:
=> 180 + 704106
Addition of the last two-term
=> 7,04,286
Therefore, the simplified Answer to the given expression will be 7,04,286.
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5. Find (a) the discount and (b) the proceeds for the following simple discount note. Use 360 days for a
full year.
Face Value: $9700 Discount Rate: 9.5% Time (Days): 135
The discount is $278.59 and the proceeds for the following simple discount note, using 360 days for a year is $9421.41
What do you mean by discount?Discount refers to a reduction in the price of an item or service. It can be expressed as a percentage or an absolute value, and it is usually calculated as a difference between the original price and the reduced price. In finance, discount is often used to refer to the reduction in the face value of a financial instrument, such as a bond or a bill, before it matures. The amount of the discount is usually based on the interest rate and the time to maturity. The term "discount" is also used in various other contexts, such as in retail sales, where items are sold at a lower price than their regular price to encourage customers to buy.
(a) The discount is calculated by multiplying the face value of the note by the discount rate and then dividing by the number of days in a year (360).
Discount = $9700 * 9.5% * 135/360
Discount = $9700 * 0.095 * 3/10
Discount = $9700 * 0.285/10
Discount = $278.59
(b) The proceeds are calculated by subtracting the discount from the face value of the note.
Proceeds = Face Value - Discount
Proceeds = $9700 - $278.59
Proceeds = $9421.41
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d) y=4+x
6) Find the constant of proportionality for the table below then write an equation
Hours (x)
2
4
6
Tickets Sold (y)
24
48
72
Answer: For each hour worked, the number of tickets sold increases by 12.
Step-by-step explanation:
The constant of proportionality for the table can be found by dividing the value of y by the value of x for one of the data points. For example, when x = 2, y = 24, so the constant of proportionality k can be found as follows:
k = y/x = 24/2 = 12
So, the equation relating the number of hours worked, x, to the number of tickets sold, y, can be written as y = kx, where k is the constant of proportionality, which we found to be 12.
Thus, the equation relating the number of hours worked, x, to the number of tickets sold, y, can be written as:
y = 12x
This equation states that for each hour worked, the number of tickets sold increases by 12.
solve step by step:
3x - 2y = -22
2x + y = -3
the answer is -13. And this is why, because the negative sign is bigger so same sign add keep the same sign that’s why I got -13
Can you help me? I need to do this IXL ASAP
Answer:
u=20
Step-by-step explanation:
How does rewriting radicals in different forms help you communicate your answer?
We can write radicals [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] forms to help us communicate our answers.
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Suppose, We have a radical [tex]16^{\frac{1}{4}[/tex].
Now, We know 2⁴ = 16.
So, We can rewrite [tex]16^{\frac{1}{4}[/tex] as [tex](2^4)^{\frac{1}{4}[/tex] and multiply the exponents which
results to 1.
Again say we have [tex]9^{\frac{3}{2}[/tex] and we know 3² = 9, Se we can rewrite [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] , and the exponent multiplies to 3 so it is now 3³ which is 27.
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Please help me answer this 20 POINTS!!!
THEORY
1 a. In a class of 58 students, 35 offer Biology, 28 offer Economics and 15 offer Physics. Each student offers at least one of the three subjects. If 12 students offer both Biology and Economics , 7 students offer both Biology and Physics and 5 students offer both Economics and Physics, how many students offer all three subjects?
b. A regular polygon with (2m+1) sides has each interior angle equal to 1440 . Find the value of m.
don't spam.
Answer:
a. In a class of 58 students, 35 students offer Biology, 28 students offer Economics and 15 students offer Physics.
Using the Principle of Inclusion-Exclusion, we can calculate the number of students who offer all three subjects as follows:
The total number of students who offer at least one subject is 35 + 28 + 15 = 78
The number of students who offer Biology and Economics is 12
The number of students who offer Biology and Physics is 7
The number of students who offer Economics and Physics is 5
So the number of students who offer all three subjects is given by:
35 + 28 + 15 - (12 + 7 + 5) = 58 - 24 = 34
Therefore, 34 students offer all three subjects.
b. A regular polygon with (2m + 1) sides has each interior angle equal to 1440.
Each interior angle of a regular polygon with n sides is given by:
angle = (n-2) * 180 / n
So for a regular polygon with (2m + 1) sides, we have:
1440 = (2m + 1 - 2) * 180 / (2m + 1)
Expanding and simplifying:
1440 = 360m / (2m + 1)
Multiplying both sides by (2m + 1):
1440 * (2m + 1) = 360m
Expanding the left side:
2880 + 1440 = 360m
4320 = 360m
Finally, dividing both sides by 360:
m = 12
Therefore, the value of m is 12.
solving joint variation
Th equaton of d in terms of W and L is d = W/LK
How to determine the joint variationFrom the information given, we have that;
The weight of the metal varies jointly as its LengthIt also varies jointly as the square of its diameterGiven that the parameters are;
Weight of the metal in kilogram is WThe length of the metal in meters is LThe diameter of the metal in mm is dThis is represented as;
W ∝ Ld
Find the constant value
W/Ld = K
Substitute the values
K = 140/4×54
find the value
k = 35/54
To determine , d, we have;
d = W/LK
Hence, the expression is d = W/LK
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Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 13 centimeters and a height of 15 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
A. 531 cm2
B. 612 cm2
C. 1,755 cm2
D. 2,286 cm2
The number of square centimeters of icing that would be needed for one cake is equal to: C. 1,755 cm².
How to determine the surface area of the cylindrical round cakes?Since everything but the circular bottom of the cake was iced, the number of square centimeters of icing that would be needed for one cake can be calculated by using this mathematical expression:
Total surface area of cake = Curved surface area of cake + area of the top
Total surface area of cake = 2πrh + πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the total surface area of cake formula, we have;
Total surface area of cake = (2 × 3.14 × 13 × 15) + (3.14 × 13²)
Total surface area of cake = 1224.6 + 530.66
Total surface area of cake = 1755.26 ≈ 1755 square centimeter.
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Answer: C. 1,755 cm2
Hope this helps
BRAINLIST FOR THE RIGHT ANSWER PLEASE ANSWER THE RIGHT ANSWER also let me know how you got the answer please because I have more questions
Answer:
C
Step-by-step explanation:
when multiplying 2 matrices:
a11 a12 a13 ... a1n
a21 a22 a23 ... a2n
...
am1 am2 am3 ... amn
X
b11 b12 b13 ... b1m
b21 b22 b23 ... b2m
...
bn1 bn2 bn3 ... bnm
you have to consider that this is only possible, when A has m rows and n columns, and B has n rows and m columns.
because the rows of A are multiplied by the columns of B.
the resulting matrix C is a square matrix and looks like
c11 c12 c13 ... c1m
c21 c22 c23 ... c2m
...
cm1 cm2 cm3 ... cmm
the different terms are created
cxy = ax1×b1y + ax2×b2y + ax3×b3y ... + axn×bny
so, in our case, we have m=n=2.
therefore, we get also C as 2×2 matrix :
2×3 + 8×2 2×0 + 8×-1
0.6×3 + 3×2 0.6×0 + 3×-1
=
6 + 16 -8
1.8 + 6 -3
=
22 -8
7.8 -3
FYI
as rule of thumb always remember :
first line first column
first line second column
...
first line last column
...
second line first column
second line second column
...
second line last column
...
last line first column
last line second column
...
last line last column
The number of people who were expected to go for the first show of a movie was 600. But due to rain the number of people who had been to the movie was 540. What is the percentage decrease in the number of people?
Answer:
10%
Step-by-step explanation:
540/600 = 90%
so 10% decrease
Carlito is competitive, though, and his best friend at school brags that he manages to save $250 every month to put toward college. How would you recommend Carlito adjust his budget in order to out-save his friend?
Does anyone know how to do this
well, the line y = -5 is simply a horizontal line, a perpendicular line to that will simply be a vertical one, Check the picture below.
Does 4/2750 reduce into a smaller fraction
A survey was carried out to find the favorite beverage of a particular telemarketing company having 2,000 employees. To carry out this survey, two groups of 100 employees each were randomly selected and asked to vote for their favorite beverage. The results obtained are given in the table shown below.
Beverage Group A Group B
Coffee 42 44
Green Tea 9 11
Soft Drinks 28 22
Energy Drinks 21 23
Which of the following statements about the data above is true?
A.
The estimated number of employees who would have voted for coffee is higher when based on the results of Group A rather than Group B.
B.
The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.
C.
The estimated number of employees who would have voted for green tea is higher when based on the results of Group A rather than Group B.
D.
The estimates for both groups show an equal number of employees would have voted for coffee.
If a survey was carried out to find the favorite beverage of a particular telemarketing company having 2,000 employees. The statement that is true about the data: B. The estimated number of employees who would have voted for coffee is higher when based on the results of Group B rather than Group A.
How to know the correct statement?The estimated number of employees who voted for coffee from Group A is 42 out of 100 (42%).
The estimated number of employees who voted for coffee from Group B is 44 out of 100 (44%).
The higher percentage of employees who voted for coffee in Group B (44%) suggests that a higher number of employees would have voted for coffee if the entire population of 2,000 employees had been surveyed.
Therefore the correct option is B.
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Answer:b
Step-by-step explanation:
in order to be approved for a home loan a lending institution uses the standard 28/36 ratio. Jared's loan application is for $180,000. Jared has an annual salary of $56,400, a car
mayment of $270 per month and he has a monthly student loan payment of $90. How likely is Jared to be approved for the home loan?
O Very likely, recurring debt is considerably less than what is allowed.
O Somewhat likely, recurring debt is very close to what is allowed.
O Not likely, recurring debt is higher than what is allowed.
O There is not enough information given to determine the answer.
The likelihood of getting the loan cannot be ascertained. Hence the answer is D. There is not enough information given to determine the answer.
What is the information aboutTo determine whether Jared is likely to be approved for the home loan, it would be necessary to calculate his debt-to-income ratio, which is one of the main factors that lenders consider when evaluating loan applications. This ratio is calculated by dividing a person's total recurring monthly debt payments by their gross monthly income. If the debt-to-income ratio is higher than 28% or 36% (depending on the lender), the loan application may be declined.
Based on the information provided, it is not possible to determine Jared's debt-to-income ratio. In order to determine the ratio, it would be necessary to know Jared's gross monthly income, which is not provided. Therefore, it is not possible to say whether Jared is very likely, somewhat likely, or not likely to be approved for the home loan.
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Select the correct answer from each drop-down menu. The number - 7/5 is
We can conclude, the number -7/5 is less than the number 1 1/5.
How to know whether a fraction is greater or less than other?One of the ways to know how a fraction compares to another is by simplifying the fraction, which can be done by dividing the numerator by the denominator.
Let's simplify the fractions given:
-7/5 = -1.4
-1 1/5 = 1 + 0.2 = -1.2
Moreover, in the case of negative numbers those that are closer to 0 are greater. Based on this, -1.2 is greater than -1.4, which means -7/5 is less than the number 1 1/5.
Note: This question is incomplete; here is the missing section:
The number -7/5 is less or greater than the number 1 1/5.
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A bicycle manufacturer currently produces 256,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $1.80 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in-house production costs are estimated to be only $1.50 per chain. The necessary machinery would cost $206,000 and would be obsolete after 10 years. This investment could be depreciated to zero for tax purposes using a 10-year straight-line depreciation schedule. The plant manager estimates that the operation would require $51,000 of inventory and other working capital upfront (year 0), but argues that this sum can be ignored since it is recoverable at the end of the 10 years. Expected proceeds from scrapping the machinery after 10 years are $15,450. If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, what is the net present value of the decision to produce the chains in-house instead of purchasing them from the supplier?
Answer:
NPV = -$57,937
Step-by-step explanation:
NPV = ($1.50 - $1.80) * 256,000 - $206,000 - $51,000 + $15,450 / (1 + 0.15)^10 - ($206,000 + $51,000) * 0.35
What are two numbers that when multiplied equal 5/9 and when added together equal -2?
The two numbers that when multiplied equal 5/9 and when added together equal -2 will be - 1/3 and - 5/3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let the two numbers be 'x' and 'y'. Then the equations are given as,
xy = 5/9 ...1
x + y = - 2 ...2
From equations 1 and 2, then we have
x + 5 / (9x) = -2
9x² + 5 = - 18x
9x² + 18x + 5 = 0
9x² + 15x + 3x + 5 = 0
3x(3x + 5) + 1(3x + 5) = 0
(3x + 1)(3x + 5) = 0
x = -1/3, -5/3
At x = - 1/3, the value of y is given as,
- 1/3 + y = -2
y = - 5/3
At x = - 5/3, the value of y is given as,
- 5/3 + y = -2
y = - 1/3
The two numbers that when multiplied equal 5/9 and when added together equal -2 will be - 1/3 and - 5/3.
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Martina and her roommate are renting furniture for their apartment. The delivery and set up charge is $75. There is a monthly rental fee of $90. Which expression can be used to calculate their total cost for m months?
expression : 75+90m
the 75 is the base payment, plus 90 per month, and the variable m symbolizes the amount of months.
Hope this helped =)
-YinAhara
PLEASE HELP!!
the variables x and y have a proportional relationship and y=40 when x=30 what is the value of x when y=50
Refer to the given image
Swimming Pool On a certain hot summer's day, 364 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $707.50. How many children and how many adults swam at the public pool that day?
1. There were _ children at the public pool.
2. There were _ adults at the public pool.
Step-by-step explanation:
x = number of children
y = number of adults
x + y = 364
x = 364 - y
1.75x + 2.25y = 707.5
using the first equation in the second :
1.75(364 - y) + 2.25y = 707.5
637 - 1.75y + 2.25y = 707.5
637 + 0.5y = 707.5
0.5y = 70.5
y = 70.5/0.5 = 141
x = 364 - y = 364 - 141 = 223
there were 223 children at the public pool.
there were 141 adults at the public pool.
In the latest published financial statements, an amount of $42,000 appears against accounts payable. During the year, goods worth $150,000 were purchased on credit.
Assuming 365 days in a year, what is the approximate accounts payable payment period (in days)?
Answer:in the latest published financial statements,an amount of $42000 appears against accounts payable.During the year,goods worthy $150000 were purchased on credit .assuming 365 days in a year ,what is the approximate accounts payable payment period.
Step-by-step explanation:
Suppose you deposit $1000 in a college fund that pays 7.2% interest compounded annually. Find the account balance after 5 years.
Answer:
To find the account balance after 5 years, we need to calculate the compound interest earned during this period. The formula for compound interest is:
A = P × (1 + r/n)^(nt)
where:
A = the final amount of the investment
P = the principal investment amount ($1000)
r = the annual interest rate (7.2%)
n = the number of times that interest is compounded per year (1)
t = the number of years the investment is held (5)
So, plugging in the values into the formula, we get:
A = 1000 * (1 + 0.072/1)^(1 * 5)
A = 1000 * (1.072)^5
A = 1000 * 1.44444444
A = $1444.44
So, the account balance after 5 years would be $1444.44.
Answer:
Step-by-step explanation: I could mostly say $36,000. How I did it was:
1000x7.2x5=36,000
Could you find this helpful???
How much money is 1 quarter, 6 dimes, and 7 Pennies?
Answer: $0.92
Step-by-step explanation:
Answer:
92 cents = $0.92 = 0.92 dollars
Step-by-step explanation:
1 quarter = 25 cents
1 dime = 10 cents
6 dimes = 6 × 10 cents = 60 cents
1 penny = 1 cent
7 pennies = 7 cents
1 quarter + 6 dimes + 7 pennies =
= 25 cents + 60 cents + 7 cents
= 92 cents = $0.92 = 0.92 dollars
Help
__________________
The minimum = (-11, -2)
And the maximum = (2, 5).
What is differentiation?Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.
Given:
The function,
f(x) = ∛(x + 3).
The graph of the function is given in the attached image.
f'(x) = d/dx{∛(x + 3)}
= 1/{3(x + 3[tex])^{2/3}[/tex]}
The critical point = (-3, 0)
The minimum = (-11, -2)
And the maximum = (2, 5).
Therefore, all the required values are given above.
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A local hamburger shop sold a combined total of 553 hamburgers and cheeseburgers on Wednesday. There were 53 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?
hamburgers
Answer: Let's call the number of hamburgers sold "x". Then the number of cheeseburgers sold would be x + 53. The total number of hamburgers and cheeseburgers sold is 553, so we can set up the equation:
x + (x + 53) = 553
Expanding the left side:
2x + 53 = 553
Subtracting 53 from both sides:
2x = 500
Finally, dividing both sides by 2:
x = 250
So on Wednesday, 250 hamburgers were sold.
Step-by-step explanation: