The value of the variable a in the equation is 5 from the calculation here.
How to determine the value?We need to square of a number is described as a number that when multiplied by itself give the original number.
Also, index forms are described as those mathematical forms that are used to represent numbers that are too large or small.
From the information given, we have the equation;[tex]a^2[/tex]=25
find the square root of value of 25,
We have;25 = [tex]5^2[/tex]
Substitute the value, we get;[tex]a^2[/tex] = [tex]5^2[/tex]
Take out the similar factor, this is their exponents.
We then have;
a = 5
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Complete question;
Find the value of a in the equation;a² = 25
Time (minutes) Jumping Jacks
1 50
2 100
3 150
4 200
Considering the jumping jacks: 50, 100, 150, 200, what is the common difference?
50
Now, think of this table as a set of ordered pairs. This means that the first row can be placed in an ordered pair as (1, 50). The second row can be written as (2, 100). Using this, what is the slope of the line that connects the first two points?
50
What is the slope of the line that connects the 3rd and 4th point?
50
What is the slope of the line that connects the 1st and the 4th point?
150
Is the common difference (aka slope aka rate of change) constant?
Yes
Why is it or is it not constant?
It is constant because it is a linear function.
Answer:
Step-by-step explanation:
The common difference between the number of jumping jacks is 50, as you correctly stated. This means that the number of jumping jacks increases by 50 for each additional minute.
The slope of the line that connects any two points on this table represents the rate of change of the number of jumping jacks with respect to time. Since the common difference is constant, the slope of the line that connects any two points on this table will be the same. In this case, the slope is 50.
The slope of the line that connects the first and fourth points is calculated as (200 - 50) / (4 - 1) = 150 / 3 = 50, not 150.
The common difference (aka slope aka rate of change) is constant because the number of jumping jacks increases by the same amount for each additional minute. This means that the relationship between time and the number of jumping jacks is linear.
The nine members of a coed intramural volleyball team are to be randomly selected from nine college men and ten college women. To be classified as coed the team must include at least one player of each gender. What is the probability the selected team includes more women than men?
The probability that selected team includes more women then men is [tex]\frac{Σ^{8} _{n=5} (^{10} _{n} )(^{9} _{9-n} )}{(^{19} _{9} ) - (^{10} _{9} ) - (^{9} _{9} )}[/tex]
The likelihood that the selected team contains more women than males matches the probability that the team contains 5, 6, 7, or 8 women (there would therefore be 4, 3, 2, or 1 man in the squad, respectively).
The likelihood of there being 5 women on the team is equal to
[tex]\frac{(^{10} _{5} )(^{9} _{4} )}{(^{19} _{9} ) - (^{10} _{9} ) - (^{9} _{9} )}[/tex]
Since, we can choose 5 women out of 10 in [tex](^{10} _{5} )[/tex] ways, 4 men out of 9 in [tex](^{9} _{4} )[/tex] ways, and 9 persons out of 19 in [tex](^{19} _{9})[/tex] - [tex](^{10} _{9})[/tex] - [tex](^{9} _{9})[/tex] ways (we must reject the possibility of having all men ( [tex](^{9} _{9})[/tex] ways) or all women ( [tex](^{10} _{9})[/tex] ways) because it is a must).
Similarly, we compute the odds of having 6, 7, or 8 women on the team, and because these are disjoint alternatives, the final result is the total of their probabilities, which is
[tex]\frac{Σ^{8} _{n=5} (^{10} _{n} )(^{9} _{9-n} )}{(^{19} _{9} ) - (^{10} _{9} ) - (^{9} _{9} )}[/tex]
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PLEASE HELP SO CONFUSING PLEASE HELP WITH THE WHOLE PROBLEM THOUGH‼️‼️
When a student is chosen at random, the student is more likely to be from Mrs Johnson's class.
The probability that the student got A in the first semester will be 0.15.
How to calculate the probabilityWhen a student is chosen at random, the student is more likely to be from Mrs Johnson's class. It should be noted that this is because 152 students out of 300 are from her class compared to Dixon who has 148 students.
The probability that the student got A in the first semester will be:
= 46 / 300
= 0.15
The probability for the last question will be:
= 14 / 148
= 0.095.
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A diamond ring was bought a number of years ago for R3 180,00. The value of the ring increases by 4% per year. Answer the following questions: a. Determine the exponential function that describes the value of the ring after t years. b. Determine the value of the ring nine years after it was bought Choose the correct answers. Select one: a. C. a. V(t) = 3 180,00(1,4)* b. a. V(t) = 3 180,00 × (1+0,04)* b. R4 352,04 d. a. V(t) = (3180,00 × 1,04)* b. R4 526,13 a. V(t) = 3 180,00 x 1,04 b. R4184,66 b. R4526,13
Select the incorrect phrases in the paragraph.
Given:
is a right angle
is a right angle
Prove:
Four lines M A, M B, M C, and M D that starts from point M are drawn such that angle A M C equals 90 degrees, and angle B M D equals 90 degrees.
1. Angle A M C is a right angle. It leads to angle A M B and angle B M C are complementary 2. Angle B M D is a right angle. It leads to angle B M C and angle C M D are complementary. 1 and 2 lead to Angle A M B which approximately equals angle C M D.
The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
is a right angleis given.
is a right angleis also given.Since
is a right angle,
and
are complementary.Since
is a right angle,
and
are complementary.By the Congruent Complements Theorem,
.
Note that in the proof stated above, there is no incorrect statement.
How is this so?The evidence is that when four lines are drawn starting from a point and making two right angles, the two angles between those lines are equal.
The proof begins by stating that when you have a right angle, the two angles that add up to produce the correct angle are referred to as complementary angles.
The Congruent Complements Theorem is then used to demonstrate that the two angles in the centre are equal.
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PLEASE HELP ILL GIVE BRAINLIEST
What is the difference in what you have as a balance in your check register versus your online statement by 11/18?
your answer goes here
Answered
What is the combined total of the two translation they have in common
The difference in what you have as a balance in your check register versus your online statment by 11/18 is $34.78.
The combined total of the 2 transactions they have in common is $206.99.
How to calculate the valueUse the amount in 11/1 as your balance, then compute by deducting the checks (chk) and debit purchases and adding the deposits. Then get the difference.
Check Register:
Total = 397.45 - 50.32 - 16.32 + 190.67
Total = 521.48
Online Statement:
Total = 486.44 - 84.80 - 19.73 - 16.32 + 190.67
Total = 556.26
Difference = online - check register
Difference = 34.78
On 11/10 and 11/18, check and online have the same transactions (same date, same amount) which are 16.32 and 190.67. Add them together to get 206.99
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Which of the following values are solutions to the inequality -8- 4x > 1?
4
I. - 10 II. - 1
O None
O II only
O I and II
O II and III
O I only
O III only
○ I and III
O I, II and III
III. 6
Submit Answer
Answer:
the answer is:l only
because -10 only states the true statement while -1 and 6 gave False Staments...
to help open up a restaurant Alonzo borrowed money from his Credit Union.
he took out a personal amortized loan for $49,000 at an interest rate of 6.55% with monthly payments for a term of 6 years. is Alonso pays the monthly payment each month for the full term find his total amount to repay the loan
If Alonso pays the monthly payment each month for the full term. Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.
How to find the total amount?To calculate the total amount that Alonzo will repay over the 6-year term of the loan, we need to use the formula for the monthly payment on an amortized loan:
M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)
where:
M is the monthly payment
P is the principal amount
r is the monthly interest rate (which is the annual interest rate divided by 12)
n is the total number of payments (which is the number of years multiplied by 12).
Using the values given in the problem, we have:
P = $49,000
r = 6.55% / 12 = 0.005458333 (monthly interest rate)
n = 6 years * 12 months/year = 72
Substituting these values into the formula, we get:
M = $49,000 * 0.005458333 * (1 + 0.005458333)^72 / ((1 + 0.005458333)^72 - 1)
= $824.85 (rounded to the nearest cent)
To find the total amount he will repay, we can simply multiply the monthly payment by the number of payments:
Total amount =$824.85 * 72
Total amount = $59,389.2
Therefore, Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.
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HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
Answer:
Step-by-step explanation:
To determine which flight will have the most no-shows, we need to compare the probabilities of no-shows for each flight.
The probability of a no-show for the afternoon flight is 1/10, which means that on average, 1 out of every 10 passengers on the afternoon flight will not show up.
The probability of a no-show for the morning flight is 1/20, which means that on average, 1 out of every 20 passengers on the morning flight will not show up.
Since 1/10 is greater than 1/20, the afternoon flight will have a higher number of no-shows, on average. Therefore, the afternoon flight is more likely to have the most no-shows.
he table of values represents a quadratic function.
Write an equation of the function in standard form.
The equation of the quadratic function in standard form is f(x) = 5x² - 3x - 7
To write an equation for a quadratic function in standard form, we need to use the general form of the equation, which is: f(x) = ax² + bx + c where a, b, and c are constants that determine the shape and position of the graph of the function.
Let's choose the points (-2, -16), (-1, -15), and (0, -12) from the table. Substituting these values into the equation above, we get:
-16 = 4a - 2b + c -15 = a - b + c -12 = c
We can use the third equation to solve for c, which is -12 in this case. Substituting this value into the first two equations, we get:
-16 = 4a - 2b - 12 => 4a - 2b = 4 -15 = a - b - 12 => a - b = 3
Now we have two equations in two unknowns, which we can solve by substitution or elimination. Let's use substitution to solve for b first:
a - b = 3 => b = a - 3
Substituting this into the first equation, we get:
4a - 2(a - 3) = 4 => 2a = 10 => a = 5
Now we can substitute the values of a and b into one of the original equations to find c:
-15 = 5 - b + c => -15 = 5 - (5 - 3) + c => c = -7
Therefore, the equation of the quadratic function in standard form is:
f(x) = 5x² - 3x - 7
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The times to run a mile are 7,
9, 10, 11, 11, and 12.
What is the mean?
Answer:
10
Step-by-step explanation:
When you think of the mean of a data set, think of the word average. 'Mean' and 'average' are the same thing when you're talking about a set of data.
To find the mean, you have to divide the sum of all values in your data set, by the number of values.
7 + 9 + 10 + 11 + 11 + 12 = 60
60/6 = 10
Therefore, the mean of this data set would be 10.
If Duane's income tax bill was $1000, what was his taxable income?
To determine Duane's taxable income, we need to know his tax rate. Let's assume that his tax rate is a flat 20%.
We can use the formula:
taxable income = tax bill / tax rate
Plugging in the values given, we get:
taxable income = $1000 / 0.20
taxable income = $5000
Therefore, Duane's taxable income was $5000.
Answer:
Without more information, it is not possible to determine Duane's taxable income.
The ratio of children: teenagers: adults in a survey sample are 2: 11:17. a) Which is the largest group represented? b) If there are 180 people surveyed how many are:
The solution is,
there are children = 12, teenagers= 66, adults = 102,
so, adults = 102 is the largest group represented
Here, we have,
given that,
The ratio of children: teenagers: adults in a survey sample are 2: 11:17.
now, we have,
If there are 180 people surveyed
now, let , we have,
children = 2x
teenagers= 11x
adults = 17x
now, we have,
2x + 11x + 17x = 180
or, 30x = 180
or. x = 6
Hence, The solution is,
there are children = 12, teenagers= 66, adults = 102,
so, adults = 102 is the largest group represented.
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The Blue Whale is the largest animal to have ever lived. As an adult it is as long as three school buses added together. A 170,000 kg Blue Whale cruises along at a modest pace. If it has 890,000 Joules of kinetic energy, what is its cruising speed?
the cruising speed of the blue whale is approximately 3.16 meters per second.
What are velocity?
a velocity is a unit of measurement for the Distance an object travels in a
the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by
dividing the total Distance traveled by the journey time.
In this case, we know the mass of the blue whale (m = 170,000 kg) and its kinetic energy (KE = 890,000 J), but we need to solve for its velocity (v).
Rearranging the formula, we get:
v = √(2 * KE / m)
Plugging in the values we know, we get:
v = √(2 * 890000 J / 170000 kg)
Simplifying this expression, we get:
v = √10 = 3.16 m/s
Therefore, the cruising speed of the blue whale is approximately 3.16 meters per second.
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The coordinates of the midpoints of the four sides of a square are S(-4, 11), Q(2, 5), U(-4, -1), and A(-10, 5).
Determine the perimeter and area of the square.
5
O perimeter is 144 units; area is 48 square units
O perimeter is 48 units; area is 144 square units
O perimeter is 24√/2 units; area is 72 square units
O perimeter is 72 units; area is 24√/2 square units
The perimeter and area of the square are 24√2 units and 12 units² respectively
What is the perimeter and area of the square?
To determine the perimeter and area of the square, we have to find the lengths of the sides.
But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.
SQ = √(x₂ - x₁)² + (y₂ - y₁)²
SQ = √(2 - (-4)² + (5 - 11)²
SQ = 6√2
Let's find for QU
QU = √(-4 - 2)² + (-1 - 5)²
QU = 6√2
Let's find for UA ;
UA = √(-10 - (-4))² - (5 - (-1)²
UA = 6√2
And the distance from AS = 6√2
The perimeter of the square = 4 * (6√2)
Perimeter = 24√2 units
The area of the square is l²
Area of the square = (6√2)²
Area of square = 12 units²
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What is the surface area of a rectangular prism that has a length of 4 cm, a height of 14 cm, and a width of 15 cm?
Answer:
the surface area of the rectangular prism is 572cm².
Step-by-step explanation:
The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:
2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²
So the surface area of the rectangular prism is 572 square centimeters.
The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on date from the College Board). If a college includes a minimum score of 1025 among its requirements, what percentage of females do not satisfy that requirement?
I have already tried 64.8% as my answer!!
The percentage of females that do not satisfy the requirement is given as follows:
55.17%.
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 mean and the standard deviation are given as follows:
[tex]\mu = 998, \sigma = 202[/tex]
The proportion that does not satisfy the requirement is the p-value of Z when X = 1025, hence:
Z = (1025 - 998)/202
Z = 0.13
Z = 0.13 has a p-value of 0.5517.
Hence the percentage is given as follows:
0.5517 x 100% = 55.17%.
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Which function equation is represented by the graph?
ANSWER: f(x)=40(2.25)x
just took the test
40(2.25)ˣ function equation is represented by the graph transformation.
What do graph transformations mean?
Changes to the graph of a parent function are referred to as transformations. Transformations may be divided into three categories: translations, reflections, and dilations. There are two types of transformations that may be done to a function: vertical (which affects the y-values) and horizontal.
(affects the x-values). The following guidelines apply to the function translation and transformation: The function is moved up b units by f (x) + b. The function is moved downward by the notation f (x) b. The function is moved left by the value of f (x + b).
Let the function be of the form
f(X ) = a(b)ˣ
Then the point (0,40) lies on the graph of this function. This point must satisfy the equation of the function.
We substitute the point to get,
40 = a(b)⁰
This implies that,
40 = a(1)
40 = a
We substitute a=40 into the function equation to get,
f(x) = 40(b)ˣ
The point (1,90) also lies on the graph of the function. This gives us,
90 = 40(b)¹
90 = 40b
b = 90/40
b = 2.25
We substitute the value of b also into function to get,
f(X) = 40(2.25)ˣ
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The speed limit on the Princes Highway in Victoria is 100km/hour.
What is this speed limit, rounded to the nearest whole number, in m/s?
The speed limit for the highway in rounded to the nearest whole is 33 mi/h.
Unit ConversionThe speed is the ratio of the distance in a given time interval. The distance is represented by a unit of length and the time is represented by a unit of time.
There are different units for the length or distance. In the International System Units (SI), the standard unit of distance is the meter (m) and the standard unit of time is the second (s). Nonetheless, there are others units, for example: inches (in), miles (mi) and yards (yd).
For solving this exercise, you need to know the relation between the given units for distance and time.
The question gives - 100 km/h. The kilometer (km) is a multiple of the standard unit of distance - the meter (m) and the hour is a submultiple of the standard unit of time - the second (s)
For solving this question, it is necessary that you know the relation between km/h and mi/h. See below.
[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]
Now you can solve the question from a math tool - Rule of three. Thus,
[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]
[tex]100 \ \text{km/h}= \text{x mi/h}[/tex]
[tex]\text{x}= 100 \times 0.6[/tex]
[tex]\text{x}=33 \ \text{mi/h}[/tex]
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help please The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?
A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.
The conjecture that can be made about the other number is option A: the other number is odd.
Let's assume that the two even numbers are x and y. Then, we can write their sum as x + y = 2a, where a is some even number.
Now, let's consider the sum of 6 and another number, which we can represent as 6 + z, where z is some unknown number. If this sum is even, then we can write it as 2b, where b is some even number.
So, we have the equations:
x + y = 2a (since the sum of two even numbers is even)
6 + z = 2b (since the sum of 6 and another number is even)
We can subtract 6 from both sides of the second equation to get:
z = 2b - 6
Now, we can substitute this expression for z into the first equation:
x + y = 2a
And we get:
x + y + z - 2z = 2a
x + (y + z) - 2z = 2a
x + (2b - 6) - 2z = 2a
x + 2b - 2z - 6 = 2a
This equation tells us that x + 2b - 2z - 6 is an even number (since 2a is even). Since x and 2b are even, the expression -2z - 6 must also be even. Therefore, -2z must be even. This means that z is odd (since an even number minus an even number is even, and -6 is even).
So, we can conclude that the other number (z) is odd. Option A is the correct answer.
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11. Higher Order Thinking Gabriela lives.
2 miles from school. On her way home,
she runs of the way and walks the rest.
How far does she walk? Explain.
Gabriela walks 1 mile distance on her way home from school as she is running part of the way.
What is distance?The distance between two things is measured in distance units like miles, kilometres, or metres. Given that it only possesses magnitude and not direction, distance is a scalar number.
We must ascertain Gabriela's total trip distance before we can respond to this query.
We can get the overall distance by adding the distance she runs to the distance she walks because she runs a portion of the route and walks the other.
Gabriela commutes two miles to school, so
She needs to travel a total of 2 miles.
We need to figure out how far she runs because she is running a portion of the way.
Since running is typically faster than walking, we can infer that she covers the distance in one mile by running half of it.
She will therefore need to walk the additional mile.
Gabriela walks a mile on her way home from school, which is the answer to the question.
This is because she walks the remaining mile and runs the first mile.
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What is the base pic attached below
Answer: 2.5
Step-by-step explanation:
the base is always positive, and it says f(x)= 1/2*5^x
1/2*5 is 2.5, so I think the base is 2.5
hope it helped:)
Prove the following this : Let H be a subgroup of a group G . The left cosets of H constitute a partition of G ; the right cosets of H constitute a partition of G ?
To prove that the left cosets of H constitute a partition of G, we need to show that they satisfy two conditions:
1) Each element of G belongs to some left coset of H.
2) Any two distinct left cosets of H are disjoint.
Let g be any element of G. Then, by definition of a left coset, there exists an element h of H such that g = h·x for some x in G. Therefore, g belongs to the left coset H·x. Since this holds for any element g of G, we have shown that the left cosets of H cover all of G, satisfying the first condition.
Now, let H·x and H·y be two distinct left cosets of H. Suppose there exists an element z in both H·x and H·y.
Then, z = [tex]h_{1}[/tex]·x = [tex]h_{2}[/tex]·y for some [tex]h_{1}[/tex], [tex]h_{2}[/tex] in H.
Solving for x,
x = [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] · y.
Since H is a subgroup, [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] is also in H, and therefore x belongs to H·y.
Thus, H·x is contained entirely in H·y, and the two cosets cannot intersect.
This satisfies the second condition, and hence the left cosets of H constitute a partition of G.
A similar argument can be used to show that the right cosets of H also constitute a partition of G. This completes the proof.
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What is the equation through the points: (6, 10), (5, -6)
ASAP please
Answer: y=16x - 86
Step-by-step explanation:
A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.8 in. The slant height of the pyramid is 89.8 in. What is the height of the pyramid?
The height of the pyramid formed by the patio heater is 89.07 inches
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
Pythagoras theorem shows the relationship between the sides of a right angled triangle.
To find the height (h) of the pyramid. A right angled is form with base (b) = side of square / 2 = 22.8 / 2 = 11.4 in
Slant height (S) = 89.8 in
Using Pythagoras:
S² = h² + b²
89.8² = h² + 11.4²
h = 89.07 inches
The height of the pyramid is 89.07 inches
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collect data on the OBSERVATION table in ANNEXURE A to record 30 days of the minimum and maximum temperature in your community
Here, We provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.
To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:
25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22
The sum of the values is:
25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813
Dividing by the number of values (30), we get:
Mean = 813/30 = 27.1
To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.
To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:
20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34
There are 30 values, so the median is the 15th value, which is 28.
To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:
Range = 34 - 20 = 14
To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:
20-24, 25-29, 30-34
The frequency table would look like this:
Interval | Frequency
20-24 | 4
25-29 | 18
30-34 | 8
To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:
Proportion = Frequency/Total frequency = 18/30 = 0.6
Angle = Proportion x 360° = 0.6 x 360° = 216°
We can repeat this calculation for each interval to obtain the angles for the pie chart.
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Tyler, just letting you can do and then let it burn all the way down to nothing the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h right in equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit.
The equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit is 15 in - (1.25 in/hr)t
Given the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h
L(t) is a function of time, t:
L(t) = 15 in - (1.25 in/hr)t
Note that when the candle has burned down to nothing, L(t) = 0.
Set 15 in - (1.25 in/hr)t equal to zero and solve for t:
(1.25 in/hr)t = 15 in, or
t = 15/ 1.25 in/hr
t = 12 hrs
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Help asap!! Please help I don’t get this
The value of arc CD is 110⁰.
The value of arc AD is 120⁰.
What is the measure of the angle?The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
angle DEC = ¹/₂ (360 - 2x100) (sum of angle at a point)
angle DEC = ¹/₂ (360 - 200)
angle DEC = 80⁰
The value of arc CD is calculated as follows;
80 = ¹/₂ (CD + 50) (intersecting chord theorem)
2 x 80 = CD + 50
160 = CD + 50
CD = 110⁰
Arc AD = 360 - (50 + 80 + 110) (sum of angles in a circle)
arc AD = 120⁰
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What integer is closest to the radius of a circle with a circumference of 50.27?
The integer which is closest to the radius of a circle with a circumference of 50.27 as required is; Choice A; 8.
Which answer choice is closest to the radius of the circle?It follows from the task content that the integer which is closest to the radius of the circle whose circumference is; 50.27 is to be determined.
Recall; Circumference, C = 2πr
r = C / 2π
r = 50.27 / 2π
r = 8.000718989
Ultimately, the integer which is closest to the radius is; Choice A; 8.
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Polynomial Functions
a) Yes, the function is in standard form.
Degree = 2
Exponent = 2
Constant term = -1
b) No, the function is not in standard form.
And it doesn't have the degree, exponent and constant term.
Firstly, let's consider the function f(x) = x(x-1). To determine if it is a polynomial function, we need to check if all of its terms have non-negative integer exponents. In this case, we see that f(x) can be written as x² - x, which has only two terms, and each term has a non-negative integer exponent. Therefore, f(x) is a polynomial function.
In this case, the degree of f(x) is 2 because the highest exponent of x is 2.
In this case, the leading term of f(x) is x², and its leading coefficient is 1.
Finally, the constant term is the term that does not have the variable in it. Here, the constant term of f(x) is -1.
Next, let's consider the function f(x) = 3 - 1/2 x. We can see that f(x) is not a polynomial function because it has a term with a negative exponent.
Polynomial functions must have non-negative integer exponents on all terms.
Therefore, the answer to the first question is 'no.'
Since f(x) is not a polynomial function, it does not have a degree, leading term, or constant term.
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