[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2 \implies A = 2121.8[/tex]
Research shows that approximately 18 out of every 100 people have blue eyes and there are 50 people in a room what is the fraction of them having blue eyes make sure you leave the total other denominator
the fraction of people in the room with blue eyes is 9/50.
If approximately 18 out of every 100 people have blue eyes, then the fraction of people with blue eyes can be expressed as 18/100 or 0.18. To find the fraction of people with blue eyes in a room of 50 people, we need to multiply this fraction by the total number of people:
(0.18) x 50 = 9
So, there are approximately 9 people in the room with blue eyes. To express this as a fraction with a denominator of 50, we can write:
9/50
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Si la suma de las razones de una igualdad de 3 razones geométricas continuas es 3/4,
calcule la suma de antecedentes. Considere que la diferencia entre el mayor
y menor consecuente es 120
Note that where the above conditions exists with regard to the geometric ratios, the sum of the antecedents is approximately 445.31.
What is the explanation for the above response?Let the three continuous geometric ratios be a, ar, and ar^2, where a is the first term and r is the common ratio. Then the equality can be written as:
a/ar + ar/ar² + ar² = 3/4
Simplifying this equation, we get:
1/r + r + r² = 3/4
Multiplying both sides by 4r², we get:
4r + 4r³ + 4r⁴ = 3r²
Rearranging, we get:
4r⁴ + 3r² - 4r = 0
We can factor this equation as:
r(4r³ - 4r² + 3) = 0
Since r cannot be zero, we must solve the cubic equation:
4r³ - 4r² + 3 = 0
Using a numerical method or a computer program, we can find that one real root of this equation is approximately 0.8202.
Now that we know the value of r, we can use the difference between the largest and minor consequent to find the value of a. The largest consequent is ar², and the minor consequent is a, so we have:
ar² - a = 120
Substituting r = 0.8202, we get:
a(0.8202)² - a = 120
Simplifying, we get:
a = 120 / (0.6721)
a ≈ 178.63
Finally, we can calculate the sum of the antecedents:
a + ar + ar² = 178.63 + (178.63)(0.8202) + (178.63)(0.8202)²
Summing these terms, we get:
a + ar + ar² ≈ 445.31
Therefore, the sum of the antecedents is approximately 445.31
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Translation:
If the sum of the ratios of an equality of 3 continuous geometric ratios is 3/4, calculate the sum of antecedents. Consider that the difference between the largest and minor consequent is 120
M7 App P2of2B. Suppose that you are working for a chain restaurant and wish to design a promotion to disabuse the public of notions that the service is slow. You decide to institute a policy that any customer that waits too long will receive their meal for free. You know that the wait times for customers are normally distributed with a mean of 20 minutes and a standard deviation of 4 minutes. Use statistics to decide the maximum wait time you would advertise to customers so that you only give away free meals to at most 1% of the customers.a. Determine an estimate of an advertised maximum wait time so that 1% of the customers would receive a free meal. Round to one decimal place. __________ minutesb. Include a graph illustrating the solution. For the graph do NOT make an empirical rule graph, just include the mean and the mark off the area that corresponds to the 1% who would receive the refund. There is a Normal Distribution Graph generator linked in the resources area. Combine the above into as single file and upload using the link below. Choose Filec. Write a response to the vice president explaining your prescribed maximum wait time. Structure your essay as follows:An advanced explanation of the normal distributionWhy the normal distribution might apply to this situationDescribe the specific normal distribution for this situation (give the mean and standard deviation)Explain how the graph created in part b. represents the waiting times of the customers.Explain the answer to part a. in terms of both the customers who get a free meal and those who do not. Feel free to use the accurate answer in part a to determine a "nice" wait time to be used in the actual advertising campaign.Use the answers to parts a. and b. to explain how the proposal will not result in a loss of profit for the company.
The normal distribution is a mathematical model used to describe real-world data that occurs in many scenarios, including restaurant wait times. The normal distribution is characterized by a mean and a standard deviation; in this case, the mean wait time is 20 minutes, and the standard deviation is 4 minutes.
In order to find the maximum wait time for customers so that at most 1% of them would receive their meals for free, we can use the normal distribution graph.
The graph shows the probability of a customer waiting any given amount of time. The mean is the highest point on the graph, while the standard deviation can be seen as two "bumps" on either side of the mean. For this scenario, any customer who waits more than 25.5 minutes will be in the top 1% of wait times, and therefore, should receive their meal for free.
This provides a reasonable time limit for customers to expect their meal, while also helping to dispel any negative perceptions about the speed of service.
In terms of the company's profitability, offering free meals to the top 1% of customers does not present any significant risk. The 25.5 minute wait time is well above the average wait time of 20 minutes, so it's unlikely that the company will incur a significant loss due to this promotion.
To sum up, the maximum wait time to be advertised to customers so that 1% of them will receive their meals for free is 25.5 minutes. The normal distribution graph shows how this wait time is chosen, as it corresponds to the top 1% of wait times.
As the average wait time is much lower than this maximum wait time, this promotion is unlikely to cause the company any significant loss in profit.
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hii, I need help please !
Answer:
∠ 6 = 59°
Step-by-step explanation:
∠ 3 and ∠ 8 are same- side interior angles and sum to 180° , that is
∠ 3 + ∠ 8 = 180°
121° + ∠ 8 = 180° ( subtract 121° from both sides )
∠ 8 = 59°
∠ 8 and ∠ 6 are vertically opposite angles and are congruent , then
∠ 6 = 59°
b. What is the probability of the event of getting 2 socks of the same color? The probability is (Type an integer or a simplified fraction.) c. What is the probability of the event of getting two gray
Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.
What is prοbability?The chance that a particular event will οccur is quantified by prοbability. It is a number between 0 and 1, where 0 denοtes that the event is hypοthetical and 1 denοtes that it will undοubtedly οccur. The number οf successful results multiplied by the entire number οf pοssible οutcοmes is used tο calculate an event's prοbability. Tο put it anοther way, prοbability is a way tο express the likelihοοd οf an event οccurring and tο quantify uncertainty.
given:
we can determine the likelihοοd οf receiving twο sοcks οf the same cοlοr.
We can select twο sοcks οf the same hue in any οf the fοllοwing ways:
In ₃C₂ = 3 οptiοns, we can select οur 2 gray sοcks.
There are ₃C₂ = 3 different methοds tο select 2 black sοcks.
Therefοre, there are a tοtal οf 3+3=6 methοds in which we can select 2 sοcks οf the same cοlοr.
There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.
The likelihοοd οf receiving twο sοcks οf the same cοlοr is as fοllοws:
6/15 = 2/5
Thus, the respοnse is c) 2/5.
b) The likelihοοd οf receiving twο pairs οf gray hοsiery is:
There are 3 οptiοns tο chοοse 2 pairs οf gray sοcks (₃C₂ = 3).
There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.
Cοnsequently, the likelihοοd οf receiving twο pairs οf gray hοsiery is:
3/15 = 1/5
Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.
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What is the volume of the triangular prism? A) 57. 75 m3 B) 115. 5 m3 C) 231. 0 m3 D) 462. 0 m3
The volume of the triangular prism is 115.5m³.
Given that,
Base = 7m.
Height = 3m.
Length = 11m.
Therefore, The area of the triangle on one side = [tex]\frac{1}{2} bh[/tex]
= [tex]\frac{1}{2}[/tex] × 7 × 3
= 21/2
= 10.5 m².
The volume of the prism = area of the triangle × height
= 10.5 × 11
= 115.5 m³.
Therefore, the volume of the triangular prism is 115.5m³.
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The question is incomplete, the complete question would be
What is the volume of the triangular prism? A) 57. 75 m3 B) 115. 5 m3 C) 231. 0 m3 D) 462. 0 m3
if anyone could help, would be much appreciated
The numeric value of the expression is given as follows:
[f(x + h) - f(x)]/h = 5h + 10x + 6.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is given as follows:
f(x) = 5x² - 6x + 1.
The numeric value at x = x + h is given as follows:
f(x + h) = 5(x + h)² - 6(x + h) + 1
f(x + h) = 5(x² + 2xh + h²) - 6x + 6h + 1
f(x + h) = 5x² + 10xh + 5h² - 6x + 6h + 1
Hence:
f(x + h) - f(x) = 5x² + 10xh + 5h² - 6x + 6h + 1 - 5x² + 6x + 1
f(x + h) - f(x) = 10xh + 5h² + 6h
f(x + h) - f(x) = h(5h + 10x + 6).
Simplifying by h, we have that:
[f(x + h) - f(x)]/h = 5h + 10x + 6.
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Find the gradient of the line passing through (-2, 5) and (5, -5)
work out the value of
7 squared + \sqrt{25 }
Answer:54
Step-by-step explanation:
7 squared + \sqrt{25 }
[tex]7^{2}=49\\and \ \\\sqrt{25}=5[/tex]
49+5=54
Answer:
54
Step-by-step explanation:
[tex]7 ^2 + \sqrt{25} \\= 49 + 5\\= 54[/tex]
Hope this helps!
Brainliest and a like is much appreciated!
the function f(x)=6x^2-180x=1000 represents the profit f(x) in thousands of dollars of selling x items. what is the meaning of the extreme value?
The extreme value of the function f(x) is the minimum value of the profit, which occurs when x = 15.
How to Determine the Extreme Value?The given function f(x) represents the profit in thousands of dollars of selling x items. To find the meaning of the extreme value, we need to find the critical points of the function, which are the values of x where the derivative of the function is equal to zero or undefined.
The derivative of the given function is:
f'(x) = 12x - 180
Setting f'(x) = 0 to find critical points:
12x - 180 = 0
Solving for x, we get:
x = 15
So, x = 15 is the critical point of the function.
Now, we need to determine whether this critical point is a maximum or a minimum.
To do so, we can use the second derivative test. The second derivative of the given function is:
f''(x) = 12
Since f''(15) = 12 > 0, the critical point x = 15 is a minimum.
Therefore, the extreme value of the function f(x) is the minimum value of the profit, which occurs when x = 15. This minimum value represents the least amount of profit that can be earned by selling the items.
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Determine how many solutions the following systems have
Y=2x-4
-2x+y=-4
There are 5,642 fans at a concert. If there are 6 seats in each row, how many rows will be needed to seat all the fans?
There are 5,642 fans at a concert. If there are 6 seats in each row, the there are 940 rows each.
Numbers are mathematical objects used for counting, measuring and marking. The original examples are the natural numbers 1, 2, 3, 4, etc. Numbers can be represented by number words. More generally, individual numbers can be represented by symbols, called numerals; for example, "5" is the number representing the number five. Since only relatively few symbols can be memorized, base numbers are usually organized into a number system, which is an organized way of representing any number.
The most common numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of ten basic numeral symbols, called numerals. In addition to being used for counting and measuring, numbers are often used for labels (like phone numbers), orders (like serial numbers), and codes (like ISBNs) . In common usage, a number is not clearly distinguishable from the number it represents.
According to the question:
Number of chairs = 6 and
Number of rows =x
capacity of auditorium = Number of chairs × Number of rows
⇒ 5642 = 6 × x
⇒ 6x = 5642
⇒ x = 5642/6
⇒ x = 940
round term = 940
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Below, there is a pattern with its first 5 terms listed. Describe a way to produce each tern from the previous term.
5,8,11,14,17..
Answer:
Add 3
Step-by-step explanation:
The pattern provided can be obtained by adding a constant number to the previous term. The common number is 3 because each term is 3 more than the previous term.
[tex]5^{+3} =8^{+3} =11^{+3} ...[/tex]and so onTherefore, you can add 3 to the previous term to get the next term.
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Answer:
3rd and 5th options (check below)
Step-by-step explanation:
The gift card has $22.20
After payment he had $1.90 left
What was charged for the 4 tire patches? $22.90 - $1.90
How many tire patches did he pay for? 4
Let the patch be X, 4 patches will be 4X
4X = 22.20 - 1.90
The cost of the patches + the balance on the gift card is also 22.20
4x + 1.90 =22.20
If you Subract the cost of 4tire patches from 22.20, you will have 1.90 on the gift card
22.2 - 4X = 1.9
These are the three right equations
Use the Remainder Theorem to determine whether x = 2 is a root
of ????(x) =3x^3−4x^2−8.
x = 2 is not a root of the given function.
We are required to use the Remainder Theorem to determine whether x = 2 is a root of the given function:????(x) = 3x³ − 4x² − 8.Remainder Theorem The Remainder Theorem states that when a polynomial function f(x) is divided by (x - a), the remainder equals f(a).In order to find whether x = 2 is a root of the function or not, we have to apply the Remainder Theorem. We can perform the division in the following manner: Solution The given polynomial function is: ????(x) = 3x³ − 4x² − 8.So, we can perform the division as shown below: On dividing f(x) by (x - a), the remainder is f(a). Hence, the remainder when the given function is divided by (x - 2) is -14.Therefore, x = 2 is not a root of the given function.
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John has pens that come in packages of 15 and crayons that come in packages of 20. What is least number of packages of pens and pack; crayons he will need in order to have the same total number of pens and crayons?
Answer:
15 packs of crayons and 20 packs of pens
Step-by-step explanation:
you have to the multiply the amount that comes in each pack together
What point on the coordinate plane is halfway between (–0. 75, –1. 25) and (–0. 75, –0. 25)?
The point halfway between (–0.75, –1.25) and (–0.75, –0.25) is (–0.75, –0.75).To find the point halfway between (–0.75, –1.25) and (–0.75, –0.25), we will use the midpoint formula.
To find the point halfway between (–0.75, –1.25) and (–0.75, –0.25), we will use the midpoint formula. The midpoint formula is (x1 + x2) / 2, (y1 + y2) / 2. In this case, x1 and x2 are both –0.75, and y1 is –1.25 and y2 is –0.25. Plugging in the values and doing the math, we get (–0.75 + –0.75) / 2 = –0.75, and (–1.25 + –0.25) / 2 = –0.75. Therefore, the point halfway between (–0.75, –1.25) and (–0.75, –0.25) is (–0.75, –0.75).
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There are 8 circles and 4 squares. What is the simplest ratio of squares to total
shapes?
Answer: 4:12
Step-by-step explanation: Since it is squares to total you have to put the amount of squares first. That would be 4. Then, you have to figure out the total which is just adding 4+8=12. That would be the total. Therefore, the answer would be 4 to 12.
The given equation has been solved in the table.
Answer option for step 2
Addition
Subtraction
multiplication
Division
Answer option for step 4
Addition
Subtraction
multiplication
Division
The operations used here are as follows:
Addition.
Division.
What are operations?The order of operations is a collection of rules that must be followed in a particular order while solving an equation.
The evaluation of any mathematical expression, which includes arithmetic operations like addition, subtraction, multiplication, and division, is what we mean when we say "operations" in mathematics.
Here in the question,
For the 2nd step,
10 was added on both the sides of the equation.
So, addition was the property used.
For the 4th step,
3 was divided from both the sides of the equation.
So, division was the property used.
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The diameter of a circle is 18 millimeters. What is the circle's circumference?
Use 3.14 for .
= millimeters
Answer:
56.52mm
Step-by-step explanation:
If the diameter is 18, the radius is 9.
The formula for circumference is c=2πr
so, 2*3.14*9=56.52
56.52mm
I NEED HELP ON THIS ASAP!
A graph of each inequality is shown in the grid below.
A shape which the solution region represent is a rectangle.
How to graph this system of inequalities?In order to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;
0.4r ≤ 120 .....equation 1.
r ≥ 4(360/5) .....equation 2.
By evaluating the given system of inequalities, we have;
r ≤ 120/0.4
r ≤ 300
r ≥ 4(360/5)
r ≥ 4(72)
r ≥ 288
By combining the system of inequalities, we have:
288 ≤ r ≤ 300
Based on the graph shown in the image attached below, we can logically deduce that the solution to the given system of inequalities is within the shaded region between the solid lines, and the point of intersection of these solid lines on the graph.
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please guys ano toh answer this
Answer: 15, 18, 21 (next three terms), Rule: Skip counting by 3
What is the rule to finding nth term?First calculate the common difference between the terms, If [tex]a_{1}, a_{2}, a_{3}, a_{4}.....[/tex] are in sequence, the common difference is calculated by [tex](a_{2} -a_{1}), (a_{3} -a_{2}), (a_{4} -a_{3}) .......[/tex]
Since, the common difference are equal so its clear that the given sequence is an Arithmetic Expression.
The nth term of the AP is an = a + (n-1)*d
1. Given: 3, 6, 9, 12, .....
Answer: 15, 18, 21 (next three terms)
Rule: Skip counting by 3
2. Given: 3, 5, 7, 9, .....
Answer: 11, 13, 15 (next three terms)
Rule: Skip counting by 1
3. Given: a, (a+b), (a+2b),.....
Answer: (a+3b), (a+4b), (a+5b) (next three terms)
Rule: nth term = a+(n-1)*b = a+nb-b
if we need 4th term, put n=4 so that 4th term= a+4b-b = (a+3b)
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Given matrix A, find -2A.
To find -2A, we simply multiply every element of A by -2. Therefore,
6 -10 0
-2A = -6 4 -2
2 -8 -14
What is matrix?A matrix is a rectangular array of numbers, arranged in rows and columns. Matrices are used in many areas of mathematics, science, and engineering to represent and manipulate data.
Matrices can have any number of rows and columns, but are typically denoted by the letter A with a subscript indicating the number of rows and columns. For example, a matrix with 2 rows and 3 columns might be denoted as [tex]A_{2x3}[/tex].
To find -2A, we need to multiply every element of matrix A by -2. In other words, we need to apply the scalar multiplication operation to every element in the matrix.
Scalar multiplication is a simple operation where we multiply each element in a matrix by a scalar, which is just a regular number. In this case, our scalar is -2.
To perform scalar multiplication on a matrix, we simply multiply each element of the matrix by the scalar. So, for each element in matrix A, we can write:
(-2) * aij
where i is the row number and j is the column number of the element.
We can use this formula to find each element of -2A. Let's look at the first element, a11:
(-2) * a11 = (-2) * 5 = -10
So the first element of -2A is -10. We can repeat this process for each element in the matrix to get the following result:
6 -10 0
-2A = -6 4 -2
2 -8 -14
And that's it! We have successfully found -2A by applying scalar multiplication to every element of matrix A.
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A quantity p varies jointly with r and s. Which expression represents the constant of variation, k?
prs
StartFraction p Over r s EndFraction
StartFraction r s Over p EndFraction
p + r + s
Answer:
[tex]\boxed{k=\frac{p}{r \ s} }[/tex]
Second option is correct.
Step-by-step explanation:
We have been given that p varies jointly with r and s.
Thus, we can write it mathematically as
[tex]p=krs[/tex]
Here, k is the constant of variation.
Now, we have to find the value of k.
Divide the above equation by rs
[tex]\dfrac{p}{r \ s}=\dfrac{kr\ s}{rs}[/tex]
[tex]k=\dfrac{p}{r s}[/tex]
Hence, the value of k is [tex]k=\dfrac{p}{r s}[/tex]
Second option is correct.
Answer:
B
Step-by-step explanation:
edge 23
Angles Q and R form a right angle. Angle Q is twice as large as angle R. What is the measure of angle Q?
Answer:
60°
Step-by-step explanation:
Let m<R = x.
Let m<Q = 2x.
m<Q + m<R = 90
2x + x = 90
3x = 90
x = 30
m<Q = 2x = 2(30) = 60
Answer: 60°
Solve the formula for r.
The solution for the formula V = πr² is A. r = √(V/(π)).
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To solve for r in the formula V = πr², we need to isolate r on one side of the equation.
We can do this by dividing both sides of the equation by π and then taking the square root of both sides:
V/π = r²
√(V/π) = r
Therefore, the solution is A. r = √(V/(π)).
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Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value ta/2, (b) find the critical value za/2, or (c) state that neither the normal distribution nor the t distribution applies.
Here are the summary statistics for randomly selected weights of newborn girls: n=180, x=28. 1 hg, s=6. 2 hg. The confidence level is 90%
The confidence interval then takes the form of x ± margin of error, which in this example is 28 ± 1.9, or (26.1, 29.9). This means that we are 90% confident that the true population mean of newborn girl's weights lies between 26.1 and 29.9 hg. the critical value t0.05/2, which is 1.699.
To construct a confidence interval with a 90% confidence level, we need to find the critical value t0.05/2. This critical value is found by using the t-distribution with a confidence level of 90% (0.90) and degrees of freedom equal to the sample size minus 1 (180 - 1 = 179). We can then use this critical value to calculate the margin of error of the confidence interval, which is equal to the critical value multiplied by the standard error (s/√n). In this example, that results in a margin of error of 1.699*(6.2/√180) = 1.9.
To construct a confidence interval with a 90% confidence level, we need to find the critical value t0.05/2. This critical value is found by using the t-distribution with a confidence level of 90% (0.90) and degrees of freedom equal to the sample size minus 1 (180 - 1 = 179). The t-distribution is used instead of the normal distribution because it is better suited to smaller sample sizes. We can then use this critical value to calculate the margin of error of the confidence interval, which is equal to the critical value multiplied by the standard error (s/√n). In this example, that results in a margin of error of 1.699*(6.2/√180) = 1.9. The confidence interval then takes the form of x ± margin of error, which in this example is 28 ± 1.9, or (26.1, 29.9). This means that we are 90% confident that the true population mean of newborn girl's weights lies between 26.1 and 29.9 hg.
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i need help with a. b. and c.
Check the picture below.
so if we just find the vertex of that parabolic path, we'd get how far up it went and how long it took
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+16}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 16}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (16)^2}{4(-16)}\right) \implies \left( - \cfrac{ 16 }{ -32 }~~,~~0 - \cfrac{ 256 }{ -64 } \right) \\\\\\ \left( \cfrac{ -1 }{ -2 } ~~~~ ,~~~~ 0 +4 \right)\implies \stackrel{seconds ~~ feet }{\left(0.5~~,~~4 \right)}[/tex]
well, as you see in the picture, the horse hits the ground again when h(t) = 0
[tex]\stackrel{h(t)}{0}=-16t^2+16t\implies 0=-16t(t-1)\implies t= \begin{cases} 0\\ 1 \end{cases}[/tex]
so at t=0 and t=1 it's touching the ground, at t=0 when it begins to jump at t=1 when it thumps back down, took that long.
At a football game, a vender sold a combined total of 118 sodas and hot dogs. The number of sodas sold was 50 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold
By making linear equations for given situation, the vendor sold 34 hot dogs and 84 sodas at the football game.
What is a linear equation, exactly?
A linear equation is an algebraic equation in which each term a constant or variable. In other words, a linear equation is an equation of the form:
y = mx + b
where y and x are variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).
Now,
Let x be the variable or number of hot dogs sold.
Then, according to the problem, the number of sodas sold is 50 more than the number of hot dogs sold. Therefore, the number of sodas sold can be represented as (x + 50).
We know that the total number of sodas and hot dogs sold is 118, so we can write an equation:
x + (x + 50) = 118
Simplifying and solving for x:
2x + 50 = 118
2x = 68
x = 34
Therefore, the number of hot dogs sold is 34, and the number of sodas sold is (x + 50) = 84.
So, the vendor sold 34 hot dogs and 84 sodas at the football game.
To know about linear equations visit the link
brainly.com/question/29739212
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What is the answer for this questions?
Answer:
A. Corresponding angles
B. Vertically opposite angles
C. Alternate angles
Step-by-step explanation:
Alternate angles are two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines. If the original two lines are parallel, the alternate angles are equal.
Vertically Opposite Angles are the angles opposite each other when two lines cross "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down. Example: a° and b° are vertically opposite angles.
Corresponding angles are the angles which occupy the same relative position at each intersection where a straight-line crosses two others. If the two lines are parallel, the corresponding angles are equal.