To reach the goal he student council needs to sell a minimum number of 107 tickets.
What is Sell?Sell means to gave someone something we take money from him. It is a transaction in which product is exchange with product or money. In ancient time we use barter system for transaction.
For raising $400 the student council have to sold each ticket at $4. So the number of ticket sold = $400 / $4 = 100.
They also spent $25 on decorations, so they need to recover that cost too. So, they need to sell an additional tickets = $25 / $4 = 6.25
Since we can not sell 0.25 of a ticket, So we can round the answer to 7.
So that overall total number of tickets that must be sold as 107.
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Complete question:
The student council at Deer Creek Middle School is organizing a dance to raise money for their end-of-year trip. They want to raise at least $400. Tickets are priced at $4 each and they already spent $25 on decorations. What is the minimum number of tickets they have to sell to reach their goal?
whats the value of Z
The value of Z for a score of 190 on a normal distribution with mean of 150 and standard deviation of 25 is given as follows:
Z = 1.6.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The measures for this problem are given as follows:
[tex]\mu = 150, \sigma = 25, X = 190[/tex]
Hence the z-score is given as follows:
Z = (190 - 150)/25
Z = 1.6.
Missing InformationThe problem asks for the value of Z for a score of 190 on a normal distribution with mean of 150 and standard deviation of 25.
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You toss a loaded coin twice. Suppose P( head)= 0.9.What is the
probability of tossing two heads.
Therefore , the solution of the given problem of probability comes out to be 0.81, or 81% obtaining two heads when flipping the loaded coin twice.
What precisely is probability?The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the structures with in style known as parameters. Chance can be represented by any number range 0 and 1, where 1 usually represents certainty and 0 typically represents potential. A probability diagram illustrates the likelihood that a particular occurrence will take place.
Here,
The chance of getting two heads in a succession can be calculated using the following formula given that the coin is loaded such that
the probability of getting a head is 0.9 and assuming that the coin tosses are independent:
Using the multiplication formula for independent events,
=> P(two heads) = P(head) x P(head) = 0.9 x 0.9 = 0.81
The likelihood of obtaining two heads when flipping the loaded coin twice is therefore 0.81, or 81%.
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The diameter of a circular cookie cake is 16 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14.
100.48 square inches make up half of the cookie cake. The solution has been obtained by using area of circle.
What is area of circle?
The territory that a circle's circumference encloses or includes is referred to as its area. The square is its unit of measurement.
We are given that the diameter of a circular cookie cake is 16 inches.
Area of circle = π [tex]r^{2}[/tex]
The radius (r) = 8 inches
So, from this we get
⇒ Area of circle = π [tex]8^{2}[/tex]
⇒ Area of circle = 64 * 3.14
⇒ Area of circle = 200.96 square inches
So, half cookie cake = 100.48 square inches
Hence, 100.48 square inches make up half of the cookie cake.
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A group of neighbors are working on their plans for a community garden. They started with square plots, but some of the families found that their garden was too big for them to care for, and others found that they wanted a bigger garden so they could produce more vegetables. Each family can adjust their plot as they choose. Each of the functions below represents the area of a new garden plot for one of the families. A(x) is the area of the new garden in square feet and represents the previous length of their garden in feet.
Original garden A: f(x)=x^2
Garden B: A(x)= x^2 +8x+7
Garden C: A(x)= x^2-9
Garden D: A(x)= x^2-13x+36
The interpretations of the functions for the new garden plots are as follows:
A(x) = x^2 represents the area of the original garden plot. Now, let's take a look at the other three functions:
What do other functions mean?Garden B: A(x) = x^2 + 8x + 7
This function adds 8x and 7 to the original garden plot area. This means that the garden will be wider and longer than the original plot. The 8x term indicates that the garden will be extended by 8 feet in length, and the constant term 7 indicates that the garden will be extended by 7 feet in width. Therefore, Garden B will be bigger than the original garden.
Garden C: A(x) = x^2 - 9
This function subtracts 9 from the original garden plot area. This means that the garden will be shorter and narrower than the original plot. The -9 term indicates that the garden will be reduced by 9 feet in width. Therefore, Garden C will be smaller than the original garden.
Garden D: A(x) = x^2 - 13x + 36
This function subtracts 13x and adds 36 to the original garden plot area. This means that the garden will be shorter and wider than the original plot. The -13x term indicates that the garden will be reduced by 13 feet in length, and the constant term 36 indicates that the garden will be extended by 36 feet in width. Therefore, Garden D may be bigger or smaller than the original garden, depending on the specific value of x used in the function.
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The complete question goes thus:
A group of neighbors are working on their plans for a community garden. They started with square plots, but some of the families found that their garden was too big for them to care for, and others found that they wanted a bigger garden so they could produce more vegetables. Each family can adjust their plot as they choose. Each of the functions below represents the area of a new garden plot for one of the families. A(x) is the area of the new garden in square feet and represents the previous length of their garden in feet.
Original garden A: f(x)=x^2
Garden B: A(x)= x^2 +8x+7
Garden C: A(x)= x^2-9
Garden D: A(x)= x^2-13x+36
Analyze each of the given function above.
Miller’s Hardware store was having a sale on pints and gallons of paint. There were 107 people who bought pints of paint and 132 people who boight gallons of paint. 92 customers bought only pints. Some people bought both pints and gallons, and 48 customers did not buy any pints or gallons of paint. How many customers shopped during the sale?
There were 302 customers who shopped during the sale at Miller's Hardware store.
Let's first define the variables:
x: the number of customers who bought both pints and gallons of paint
y: the number of customers who only bought gallons of paint
Using this information, we can create a Venn diagram to represent the situation:
GALLONS
/ \
/ \
/ \
PINTS --------------
\ /
\ /
\ /
\ /
NEITHER
We know that there were 107 people who bought pints of paint and 92 customers bought only pints. Therefore, the number of customers who bought both pints and gallons is:
107 - 92 = 15
We also know that 48 customers did not buy any pints or gallons of paint. Therefore, the total number of customers who bought either pints or gallons of paint is:
107 + 132 - 15 + y = 224 + y
We can now use the fact that the total number of customers who shopped during the sale is equal to the sum of the customers who bought either pints or gallons of paint and those who did not buy any paint:
224 + y + 48 = x + y + 107 + 92
Simplifying the equation, we get:
y + 272 = x + 199
x - y = 73
Finally, we can add up all the customers who shopped during the sale:
107 + 132 + 15 + 48 = 302
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If a man stands 6ft tall and stands 30 ft from a tree of unknown height and also 5 ft away from a steak in the ground tied to the top of the tree how tall is the tree ?
Using the concept of similar triangles, we were able to find the height of the tree given the man's height, distance from the tree, and distance from the steak. The tree is approximately 6.25 feet tall.
We can use similar triangles to find the height of the tree. Let x be the height of the tree in feet. Then, we have:
x / (x+5) = 6 / 30
Cross-multiplying, we get:
30x = 6(x+5)
Expanding and simplifying, we get:
30x = 6x + 30
24x = 30
x = 1.25
Therefore, the tree is 1.25 + 5 = 6.25 feet tall.
In conclusion, the height of a tree can be determined using similar triangles. By setting up the proportion of the tree's height to its distance from a person, and using cross-multiplication, the height can be solved for. The tree is 6.25 feet tall.
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A group of 8 friends each buy 1 ticket and 1 small popcorn
at the movie theater. Each ticket costs $7.50. The group of
friends spends a total of $83.60.
Enter the cost of 1 small popcorn.
Answer:
$2.95
Step-by-step explanation:
8x+8y=83.60
8 is the amount of friends/amount of tickets/amount of small popcorn
x is the cost 1 ticket
y is the cost 1 small popcorn
We know that the price of a ticket is 7.50 so we replace "x" with 7.50
8(7.5)+8y=83.60
Simplify
60+8y=83.60
Now subtract 60 from both sides
8y=23.60
Now divided both sides by 8
y=2.95
the cost of 1 small popcorn is $2.95
Find the arc length of the semicircle
if anyone could help, would be much appreciated
The variation model can be used to find the value of f = 42(m/p) for any given values of m and p.
What is the variation model?
The variation model is a mathematical model that describes the relationship between two or more variables. It is used to represent how the value of one variable changes in response to changes in another variable. The variation model can be direct or inverse, depending on whether the two variables change in the same direction or in opposite directions. In a direct variation model, two variables are directly proportional to each other, meaning that when one variable increases, the other variable also increases in the same proportion. This can be represented mathematically as y = kx. In an inverse variation model, two variables are inversely proportional to each other, meaning that when one variable increases, the other variable decreases in the same proportion. This can be represented mathematically as y = k/x.
If f varies directly with m and inversely with p, we can write:
f ∝ m/p
Using the constant of proportionality k, we can write:
f = k(m/p)
To find the value of k, we can use the given information that f=36 when m=6 and p=7:
36 = k(6/7)
Solving for k, we get:
k = 36(7/6) = 42
Now that we have the value of k, we can use the variation model to find the value of f for any given values of m and p:
f = 42(m/p)
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A boat can be hired for children's parties. The
cost of hiring the boat can be worked out using
the formula below.
The cost of a party was £314.50. How many
children were at the party?
Cost (£) £12.50 × the number of children + £27
=
After answering the presented question, we can conclude that As a result, the party had 23 children.
What is equation?In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.
We may begin by constructing an equation using the supplied formula and the party cost:
£12.50 multiplied by the number of children Equals £314.50
The equation can then be simplified by removing £27 from both sides:
£12.50 multiplied by the number of children Equals £287.50
Lastly, we can figure out how many children there are by dividing both sides by £12.50:
£287.50 x number of children = £12.50
total number of children = 23
As a result, the party had 23 children.
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The temperature in Austria one morning was _5at 08:00and increased by 2every hour until 12:00. What will be the temperature be at 11:30
The temperature will rise by 7° till 11:30 as 11:30 is 3.5 hours from 8:00 and 2° rise every year. This is a simple concept of the unitary method.
In order to solve a problem, the unitary method involves first figuring out the value of a single unit, then multiplying that value to get the answer.
In mathematics, multiplying the numbers is used to find the product of two or more numbers. It is a basic mathematical operation that we carry out on a regular basis. The most obvious application is multiplication tables.
Mathematicians use the multiplication of two numbers to represent the repeated addition of one number to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.
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How to generate Pythagorean triples using an odd number
To construct a Pythagorean triple using an odd number, an odd number must first be chosen. Here 5, 12, and 13 form a Pythagorean triple.
To generate Pythagorean triples using an odd number, follow these steps:
Choose any odd number, say n.
Calculate (n^2-1)/2 and n. These two numbers will form a Pythagorean triple.
Check if the numbers obtained in step 2 are indeed a Pythagorean triple. The two numbers should satisfy the Pythagorean theorem, i.e., a^2 + b^2 = c^2, where a and b are the smaller numbers, and c is the largest number.
If the numbers in step 2 do not form a Pythagorean triple, choose a different odd number and repeat the process.
For example, let's choose the odd number 5:
(n^2-1)/2 = (5^2-1)/2 = 12
n = 5
Now, we can check if 5, 12, and 13 form a Pythagorean triple:
5^2 + 12^2 = 13^2
25 + 144 = 169
Therefore, 5, 12, and 13 form a Pythagorean triple.
We can repeat this process with different odd numbers to generate more Pythagorean triples.
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The outstanding balance on Bill's credit card account is $3400. The bank issuing the credit card is charging 9.7%/year compounded monthly. If Bill decides to pay off his balance in equal monthly installments at the end of each month for the next 18 months, how much will be his monthly payment? (Round your answer to the nearest cent.)
What is the effective rate of interest the bank is charging Bill? (Round your answer to three decimal places.)
Bill needs to make monthly payments of approximately $206.81 in order to pay off his balance in 18 months.
The effective rate of interest the bank is charging Bill is approximately 10.4%
Calculating the monthly payment and effective rate of interestFrom the question, we are to calculate how much Bill's monthly payment will be
To find the monthly payment Bill needs to make in order to pay off his balance in 18 months, we can use the formula for the present value of an annuity:
PMT = PV / ((1 - (1 + r)^(-n)) / r)
Where PMT is the monthly payment
PV is the present value of the outstanding balance
r is the monthly interest rate
and n is the number of payments (in this case, 18).
First, we need to calculate the monthly interest rate. Since the annual interest rate is 9.7%, the monthly interest rate is:
r = 0.097 / 12 = 0.0080833
Next, we can plug in the values for PV, r, and n:
PMT = 3400 / ((1 - (1 + 0.0080833)^(-18)) / 0.0080833)
PMT ≈ $206.81
Hence, Bill needs to make monthly payments of $206.81
To find the effective rate of interest the bank is charging Bill, we can use the formula:
(1 + r)^12 - 1
Where r is the monthly interest rate.
Plugging in the value for r, we get:
(1 + 0.0080833)^12 - 1 ≈ 0.104
Hence, the effective rate of interest is approximately 10.4%.
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Which angles are congruent? ∠edh and ∠fdg ∠fde and ∠gdh ∠gdh and ∠edh ∠gdf and ∠hdg
Based οn the central angle theοrem, the angles that are cοngruent are: C.) GDH and EDH.
What is Angle?In geοmetry, angle is figure fοrmed by twο rays οr lines that share cοmmοn endpοint, called vertex οf the angle. The rays οr lines that fοrm the angle are called sides οr legs οf angle.
Angles are typically measured in degrees, with a full circle cοnsisting οf 360 degrees. Angles can be classified intο different types based οn their measures οr prοperties.
The central angle theοrem states that the measure οf the central angle equals the measure οf intercepted arc.
Thus:
m∠GDH = 63°
m∠EDH = 63°
Therefοre, based οn the central angle theοrem, the angles that are cοngruent are: C.) GDH and EDH.
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Complete question:
Circle D is shown with the measures of the minor arcs. Which angles are congruent?
A.) EDH and FDG
B.) FDE and GDH
C.) GDH and EDH
D.) GDF and HDG
Travis is at a basketball practice and is practicing his free throws his coach told him that he could go home when his free throw percentage is 85% Or higher
Travis is practicing his free throws at a basketball practice, and his coach set a goal for him to achieve an 85% or higher free throw percentage before he can go home.
A free throw is a type of shot made in basketball from the free-throw line, usually given to a player after a foul has been committed by the opposing team. To calculate Travis's free throw percentage, the number of successful free throws he makes must be divided by the total number of free throws he attempted, then multiplied by 100 to get a percentage.
If his free throw percentage is 85% or higher, he can go home from the basketball practice.
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minimum and maximum error possibilities
The minimum possible area of this rectangle is 78.75 yd².
The maximum possible area of this rectangle is 101.75 yd².
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length or height of a rectangle.In order to determine the minimum possible area of this rectangle, we would subtract the greatest possible error from each measurement and then multiply as follows:
Amin = (18 - 0.5) × (5 - 0.5)
Amin = 78.75 yd²
For the maximum possible area of this rectangle, we would add the greatest possible error to each measurement and then multiply as follows:
Amin = (18 + 0.5) × (5 + 0.5)
Amin = 101.75 yd²
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Which question is best given in a multiple-choice format?
O A What is your favorite television show?
OB. Where are you from?
O C. In what range is your grade point average?
o D. Where do you see yourself in five years?
The best question to give in a multiple-choice format is Question C: In what range is your grade point average?
A multiple-choice question is a type of question that provides a list of pre-defined answer options from which one or more can be chosen as the correct answer. The formula used to calculate the total number of answer options available in a multiple-choice question is: Total Number of Answer Options = n + 1, where n is the number of answer choices given.
For example, if a multiple-choice question provided three answer choices (A, B, and C), then the total number of answer options would be 4 (A, B, C, and none of the above), since there is also the option of not selecting any of the provided answers. Similarly, for a multiple-choice question with five answer choices (A, B, C, D, and E), the total number of answer options would be 6 (A, B, C, D, E, and none of the above).
Thus, the best question to give in a multiple-choice format is Question C: In what range is your grade point average? Since there are several possible ranges that a grade point average can fall into (e.g. A, B, C, D, F, etc.), this question allows for the selection of one or more of the given answer options, as well as the possibility of not selecting any of them.
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The standard deviation of the lifespan of a certain brand of LED light bulbs is 13 months. The quality
control department at this company takes a random sample of 55 LED light bulbs and finds the mean
lifespan of sample is 156 months. What is the probability that this sample mean is within 1 months of the
mean of all light bulbs produced by the company? Round the solution to four decimal places, if necessary.
The probability that the sample mean is within 1 month of the population mean is 0.7794, which is equivalent to a 77.94% chance.
The standard deviation of the lifespan of a certain brand of LED light bulbs is 13 months. The mean lifespan of all light bulbs produced by the company is 156 months. We want to find the probability that the sample mean is within 1 month of the population mean. To solve this problem, we need to use the z-score. The z-score is calculated as (sample mean - population mean) / standard deviation. In this case, the z-score is (156 - 155) / 13 = 0.077. We can then use a z-score table to find the probability. Using the table, we find that the probability is 0.7794. This means that there is a 77.94% chance that the sample mean is within 1 month of the population mean.
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the sum of three squared and two to the fourth power, divided by the difference of eleven and six
Step-by-step explanation:
the sum of three squared and two to the fourth power : 3^2 + 2^4
divided by the difference of eleven and six ( 11-6 )
= (3^2 + 2^4 ) / (11-6) = (9+16) / 5 = 25/5 = 5
Solve two steps equations
Answer:
21 hazardous state waste sites in State Y.
Step-by-step explanation:
x=2n-8
x=34
2n-8=34
2n=42
n=21
Substitute for the variable and evaluate the algebraic expression 3t-13 when t=4
Answer:
-1
Step-by-step explanation:
3t - 13 t = 4
= 3(4) - 13
= 12 - 13
= -1
So, the answer is -1
Answer:
your equation would be 3(4)-13 which would equal 12-13=-1
Step-by-step explanation:
What is the equation of the line that passes through the point (-6, -4) and has a
slope of
Answer:
y = 1/3x - 2
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
We know
m = 1/3
Y-intercept is located at (0, -2)
So, the equation is y = 1/3x - 2
ALL YOU AMAZING MATHEMATICIANS I NEED YOUR HELP!!!!!!!!
Answer:
Step-by-step explanation:
40x + 35x-28 = 75x - 28
40x+35x + -32x - 28 = 84xx - 28
40x - 28
40x + 35x + 32+ 28 = 75x + 60
8x X 5x=40x
8x X -4 = -32x
35x= 7x X5x
7 X -4 = -28
40x - 32x + 35x - 28
75x- 32x = 43x-28
I am pretty sure its the 3rd 1
T= paintings from the 20th centuary B=British paintings a painting is chosen at random it is from the 20th century workout the probability that it is British
The probability that a randomly chosen painting from the 20th century is British is B/T.
It is determined by the ratio of British paintings to total paintings from the 20th century. If we assume that the total number of 20th century paintings is represented by T and the number of British paintings is represented by B, then the probability of a randomly chosen painting from the 20th century being British is B/T.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
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you can rent a ski boat for $20 plus $35 per hour. If you want to spend no more than $150, how many hours can you rent a ski boat?
Answer: 3 hours
Step-by-step explanation:
Answer:
you can only rent the ski boat for about 3 hours.
Step-by-step explanation:
if you cant spend no more than $150
you need to see how much u can spend within hours.
so you would have to see what 35 can be multiplied to get to 150.
obviously no number multiplied by 35 will get you 150, but if you multiply 35 x 4, you will get 140, which is close enough, yet still you don't have enough for a full 4 hours.
Then you have to consider that you still need to pay $20 just to rent the ski boat alone.
So that will take away from the money you have.
when you subtract 20 from 140, you will still not have enough money for 4 whole hours, therefore you will only have enough for 3 hours with the $ 120 you have left.
lmk if it was right. hope this helps.
help please :((
....................................................
The probability that both her selections are vegetarian is 1/14.
What is probability?
Probability is a branch of mathematics that deals with the study of random events or processes. It is the measure of the likelihood or chance of an event or outcome occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
There are 15 toppings in total, so there are 15 ways for the customer to choose her first topping.
If the first topping is vegetarian, there are 8 vegetarian toppings left out of 14 total toppings, so there are 8 ways for the customer to choose a second vegetarian topping.
If the first topping is non-vegetarian, there are 7 vegetarian toppings left out of 14 total toppings, so there are 7 ways for the customer to choose a second vegetarian topping.
Therefore, the total number of ways for the customer to choose two vegetarian toppings is 8 + 7 = 15.
The total number of ways for the customer to choose two toppings is the number of ways to choose the first topping (15) multiplied by the number of ways to choose the second topping after the first topping has been chosen (14).
Therefore, the total number of ways for the customer to choose two toppings is 15 x 14 = 210.
The probability of choosing two vegetarian toppings is the number of ways to choose two vegetarian toppings (15) divided by the total number of ways to choose two toppings (210):
P(choosing two vegetarian toppings) = 15/210
Simplifying the fraction by dividing the numerator and denominator by 15, we get:
P(choosing two vegetarian toppings) = 1/14
Therefore, the probability that both her selections are vegetarian is 1/14.
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If cot x = 8 & csc < 0 Find sin x & cos x
well, csc(x) < 0, is just another way of saying csc(x) is negative, now, we know that csc(x) is the reciprocal of sin(x), so if the cosecant is negative, the sine is also negative.
[tex]\cot(x)=8\implies \cot(\theta )=\cfrac{\stackrel{adjacent}{8}}{\underset{opposite}{1}}\hspace{5em} \textit{let's find the \underline{hypotenuse}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ c=\sqrt{ 8^2 + 1^2}\implies c=\sqrt{ 64 + 1 } \implies c=\sqrt{ 65 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cos(x )=\cfrac{\stackrel{adjacent}{8}}{\underset{hypotenuse}{\sqrt{65}}}\implies \cos(x )=\cfrac{8\sqrt{65}}{65} \\\\\\ \sin(x )=\cfrac{\stackrel{opposite}{-1}}{\underset{hypotenuse}{\sqrt{65}}}\implies \sin(x )=-\cfrac{\sqrt{65}}{65}[/tex]
Which equation accurately represents this statement? Select three options. Negative 3 less than 4. 9 times a number, x, is the same as 12. 8. Negative 3 minus 4. 9 x = 12. 8 4. 9 x minus (negative 3) = 12. 8 3 + 4. 9 x = 12. 8 (4. 9 minus 3) x = 12. 8
There are three equations that accurately represent the statement "Negative 3 less than 4": 4. 9 minus (negative 3) = 12. 8, 3 + 4. 9 x = 12. 8, and 9 x minus (negative 3) = 12. 8.
There are three equations that accurately represent the statement "Negative 3 less than 4": 4. 9 minus (negative 3) = 12. 8, 3 + 4. 9 x = 12. 8 and 9 x minus (negative 3) = 12. 8.
The first equation, 4. 9 minus (negative 3) = 12. 8, states that if you subtract negative 3 from 4. 9, the result is 12. 8. This equation is useful for understanding the relationship between 4. 9 and 12. 8.
The second equation, 3 + 4. 9 x = 12. 8, states that if you add 3 to 4. 9 times a number (x), the result is 12. 8. This equation is useful for finding out what number (x) is needed to reach 12. 8 when added to 3.
The third equation, 9 x minus (negative 3) = 12. 8, states that if you subtract negative 3 . This equation is useful for finding out what number (x) is needed to reach 12. 8 when subtracted from 9.
These three equations accurately represent the statement "Negative 3 less than 4" and can be used to understand the relationship between 4. 9 and 12. 8 or to find out what number (x) is needed to reach 12. 8.
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Given G(t) = 2 − 3t, write G(−3 + h) − G(−3) in simplest form
given G(t) = 2 − 3t, G(-3 + h) - G(-3) simplifies to 3h.
To evaluate G(-3 + h) - G(-3), we need to substitute -3 + h and -3 for t in the expression for G(t) and then simplify:
G(-3 + h) - G(-3) = (2 - 3(-3 + h)) - (2 - 3(-3))
= (2 + 3h + 9) - (2 + 9)
= 3h
So, G(-3 + h) - G(-3) simplifies to 3h.
In mathematics, the term "simplest form" refers to the expression of a mathematical term or equation in its most basic or minimal form, typically by simplifying or reducing it as much as possible using mathematical operations or techniques.
if we have an algebraic expression with multiple terms, we can simplify it by combining like terms, expanding brackets, or using other algebraic techniques to reduce the expression to its most basic or minimal form.
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in the same bottle of ethanol starts at 10C and absorbs 2500 J of heat, what is its final temperature
When a same bottle of ethanol starts at 10°C and absorbs 2500 J of heat, its final temperature is 45°C.
This problem can be solved using the specific heat capacity formula, which is expressed as
Q= mc ∆T
where Q is the amount of heat absorbed, m is the mass, c is the specific heat capacity and ∆T is the change in temperature.
The initial temperature of ethanol = 10°C
The amount of heat absorbed = 2500 J
We need to find the final temperature of ethanol. Let's use the specific heat formula to solve for the final temperature.
Q=mc∆T
where, Q = amount of heat absorbed = 2500 J
c = specific heat of ethanol = 2.44 J/g°C
∆T = change in temperature = final
temperature - initial temperature m = mass of ethanol
We need to calculate the mass of ethanol to use this formula.
Let's assume that the mass of ethanol is
100 g.m = 100 gQ = mc∆T2500 = 100 × 2.44 × ∆T ∆T = 10.25°C
Now, let's add this change in temperature to the initial temperature to find the final temperature.
Final temperature = Initial temperature + ∆T Final temperature = 10°C + 10.25°C
Final temperature = 20.25°C + 24.75°C
Final temperature = 45°C
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