[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=22\\ r=4 \end{cases}\implies 22=\cfrac{\theta \pi (4)}{180}\implies 22=\cfrac{\theta \pi}{45} \\\\\\ (22)(45)=\theta \pi \implies \cfrac{(22)(45)}{\pi }=\theta \implies 315.13\approx \theta[/tex]
A population of bacteria is increasing at a rate of 7. 5% per hour. If there were originally 275 bacteria, which
of the following equations models the population of bactera h-hours after the original 275 bacteria were
measured?
The population of bacteria after h hours is 0.075.
Bacterial growth is proliferation of bacterium into two daughter cells, in a process called binary fission. Providing no event occurs, the resulting daughter cells are genetically identical to the original cell. Hence, bacterial growth occurs. Both daughter cells from the division do not necessarily survive. However, if the surviving number exceeds unity on average, the bacterial population undergoes exponential growth.
The equation that models the population of bacteria h-hours after the original 275 bacteria were measured is given by:
P(h) = 275 × [tex](1 + 0.075)^h[/tex]
p(h)=0.075
where P(h) is the population of bacteria after h hours and 0.075 is the growth rate of 7.5% per hour.
Therefore, the population of bacteria after h hours is 0.075.
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The 5th term and 8th term of an AP are 10 and 16.
Find the :
1. First Term;
2. Common Difference;
3. S10(sum of the first ten terms)
The first term is 2, the common difference is 2 and the sum of the first ten terms is 110
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
An arithmetic term is given as:
[tex]a_n=a+(n-1)d[/tex]
where a is the first term and d is the common difference.
The 5th term and 8th term of an AP are 10 and 16. Hence:
a + 4d = 10 (1)
and:
a + 7d = 16 (2)
subtract equation 1 from 2 to get d:
3d = 6
d = 2
Common difference is 2
a + 4d = 10
a + 4(2) = 10
a = 2
First term is 2
The sum of first ten terms is:
[tex]S_{10}=\frac{n}{2} (2a+(n-1)d)=\frac{10}{2}(2(2)+(10-1)2) = 110[/tex]
The sum is 110
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for students who earned a score of 20 or lower on the quiz, the cumulative frequency is and the relative cumulative frequency is . a.) 16; 32% b.) 9; 18% c.) 38; 76% d.) 29; 58%
The cumulative frequency and relative cumulative frequency for students who earned a score of 20 or lower on the quiz is 29; 58%. (option d)
Cumulative frequency refers to the running total of frequencies, or the sum of frequencies up to a certain point. In this case, the cumulative frequency is the number of students who scored 20 or lower on the quiz.
Relative cumulative frequency, on the other hand, expresses the cumulative frequency as a percentage of the total number of students in the sample. To find the relative cumulative frequency, we divide the cumulative frequency by the total number of students and multiply by 100.
Therefore, for students who scored 20 or lower on the quiz, the cumulative frequency is 29 and the relative cumulative frequency is 58% (29/50 * 100).
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Answer: 38, 76%
Step-by-step explanation:
Recall that for cumulative frequency we add up all the values that fall above or below a given bin of data. So, if we want all scores less than 20 it should be the first four bins with a total of:
8 plus 8 plus 13 plus 9 equals 38
To get the relative frequency we take the total in the bins for scores of 20 and lower divided by the total of all bins:
38 over 50 equals 0.76 equals 76 percent sign
Please solve in 20 mins
The table should be completed as follows;
Coordinate Key feature Does the coordinate Justification
make sense ___________________
(-7.565, 0) it is a key feature yes it is a zero (root).
(0, 37) it is a key feature yes it is the y-intercept.
(6, 46) it is a key feature yes it is the vertex.
A reasonable constraint for the context in set builder notation is {y|y ∈ R ≤ 46}.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph, with a maximum exponent of two (2).
What is y-intercept?In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this scenario, the y-intercept of this quadratic function can be calculated as follows;
G(x) = -1/4(x²) + 3x + 37
G(0) = -1/4(0²) + 3(0) + 37
G(0) = 37.
In conclusion, the vertex (maximum point) of this quadratic function is given by the ordered pair (6, 46).
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02: Pretest CR Algebra 2 A / 2:Equations and Functions
option B is correct, the equation or function of the graph is y≥3/4x-3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The line passing through points (4,0) and (0,3)
Slope=3/-4=-3/4
Now let us find y intercept
0=-3/4(4)+b
0=-3+b
b=3
Hence, option B is correct, the equation or function of the graph is y≥3/4x-3.
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I don't know how to solve this. Please help me.
Which expression to represents the phrase: "6 times a number plus 3."
Question 2 options:
6 x 3
6 x 3 + n
6n + 3
6n = 3
The expression to represent the phrase "6 times a number plus 3" is:
"6n + 3".
"n" represents an unknown number, and "6" and "3" are constants. The expression means that 6 is being multiplied by "n" to get an intermediate result, and then 3 is being added to that result to get the final answer.
For example, if n = 2, then the expression would evaluate to 6 * 2 + 3 = 12 + 3 = 15. So, the expression "6n + 3" represents the mathematical relationship between the unknown number "n" and the final result.
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Oleg is training for a triathlon. One day, he jogged for 2 hours at x miles per hour. Then he bicycled for 2 hours at y miles per hour. Finally, he swam a distance of 2 miles. The total number of miles did not exceed 30 miles.
What is the greatest possible speed that Oleg could have bicycled that day?
The greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.
How did we get the value?Let's call the total distance that Oleg jogged z. Then z = 2x.
The total distance that Oleg bicycled was 30 - z - 2. Let's call this distance w. Then w = 30 - 2x - 2.
Since Oleg bicycled for 2 hours, the speed that he bicycled was w / 2. So, w / 2 = y.
Substituting the expressions for z and w, we have:
y = (30 - 2x - 2) / 2.
Since y must be the greatest possible speed that Oleg could have bicycled that day, x must be the smallest possible value.
Since Oleg jogged for 2 hours, the minimum value of x is 2 / 2 = 1.
Substituting x = 1 into the expression for y, we have:
y = (30 - 2 * 1 - 2) / 2 = (26) / 2 = 13.
So, the greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.
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i need help pls rn like dang
Answer:
Step-by-step explanation:
I gotchu.
sinP = 5/14
= 0.36
P = sin^-1(5/14)
P = 20.92
what pattern would you observe if everyone in the class were to bias their results to 5 heads and 5 tails?
In a coin flip experiment, you would see a pattern of 50/50 heads and tails if every student in the class skewed their findings to show 5 heads and 5 tails.
This is due to the fact that each participant purposefully altered their results to display an equal number of heads and tails.
It is crucial to remember that this pattern does not accurately reflect the chances of either getting heads or tails in a fair coin flip. The results cannot be taken as a representative sample of a fair coin flip because everyone purposefully slanted their findings. It is crucial to conduct experiments with appropriate controls and prevent results bias in order to acquire reliable findings.
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how do we solve systems of equations by substitution
Step-by-step explanation:
Step One→ Solve one equation for either x or y.
Step Two→ Substitute the expression from step one into the 2nd equation.
Step Three→ Solve the second equation for the given variable.
Step Four→ Plug you solution back into the first equation.
Step Five→ Write your solution as a point.
Martina is solving the equation 4x-11=2x+391. Here are the first steps of her solution.
4x-11=2x+391
4x=2x+402
2x=402
What did Martina do to get 2x=402
divided both sides by 2
divided the left side by 2x
subtracted 2x from both sides
subtracted 2x from the left side and added 2x to the right side
a=1.2b
Tell whether the equation represents a direct proportion. If so, identify the constant of proportionality.
The equation represents a direct proportion
The proportionality constant is 1.2
How to determine the type of the equationFrom the question, we have the following parameters that can be used in our computation:
a=1.2b
The above equation is a proportional linear equation
A proportional linear equation is represented as
y = kx
Where
The constant of proportionality is k
Using the above as a guide, we have the following:
The equation a=1.2b is a direct proportion and the proportionality constant is 1.2
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In the interval 0° ≤ x ≤360°, find the values of x for which tan x =0. 8645 Give your answers to the nearest degree
The inverse tangent function [tex]tan^{-1}[/tex] can be used to find the values of x for which tan x = 0.8645 in the interval 0 degrees < x < 360 degrees. The inverse tangent function gives us the angle that has a tangent equal to the input value.
The function can be expressed as:
[tex]x = tan^{-1 (0.8645)}[/tex]
Using a scientific calculator or trigonometry tables, we can find that the value of [tex]tan^{-1 (0.8645)}[/tex] is approximately 47.5 degrees.
So, in the interval 0 degrees < x < 360 degrees, there is one value of x that satisfies the equation tan x = 0.8645, and it is approximately 47.5 degrees. It's important to remember that the inverse tangent function is a one-to-one function and its range is restricted to the interval -90° < x < 90°, so the value found represents the smallest angle in the interval 0° < x < 360° that has a tangent equal to 0.8645.
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2. Seth’s father is thinking of buying his son a six-month movie pass for $40. With the pass, matinees cost $1.00. If matinees are normally $3.50 each, how many times must Seth attend in order for it to benefit his father to buy the pass?
Answer: The savings per movie with the pass is $3.50 - $1.00 = $2.50. For the pass to benefit Seth's father, Seth must attend enough movies such that the total savings is equal to or greater than $40.
Let's call x the number of times Seth must attend for the pass to benefit his father. Then:
$2.50x >= $40
Solving for x:
$2.50x/$2.50 >= $40/$2.50
x >= 16
So Seth must attend at least 16 movies in order for the pass to benefit his father.
use cosine rule to find angle BAC
Answer:
where's the figure??
Step-by-step explanation:
i think this question is incomplete
PLS I NEED HELP I WILL SELL MY SOUL AND MY BODY PLS ILL DO ANYTHING!
Answer:
53 and 3/5's of a percent
Step-by-step explanation:
What is the product?
(3a^2b^7)(5a^3b^8
8a^5b^15
8a^6b^56
15a^5b^15
15a b^56
Answer/Solution:
15a^5b^15
Explanation:
First, multiply the numbers, then combine the exponents until you get the answer.
When an object is dropped vertically from a platform, its height after t
t
seconds can be estimated with the formula shown.
h=h0−16t2
h=h0-16t2
h is the height of the object in feet.
h0 is the initial height of the object in feet.
t is the time in seconds after the drop.
Which equation and solution tells how long it takes the object to reach a height of 96 feet if its initial height is 208
The quadratic equation that we need to solve is:
96 = 208 - 16t^2
And the solution is t = √7
Which equation is the correct one?
We know that the height equation is the quadratic equation below:
h = h0 - 16t^2
If the initial height is 208, then we can write:
h = 208 - 16t^2
Now we can find how long takes to reach a height of 96 feet, then we can write:
96 = 208 - 16t^2
That is the equation we need to solve.
Solving that for t we will get:
96= 208 - 16t^2
16t^2 = 208 - 96
16t^2 = 112
t^2 =112/167
t = √7
The correct option is the last one.
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what is UT? Literally can't
In a right triangle, the Pythagorean theorem states that the sum of the legs squared is equal to the hypotenuse squared.
Or that a² + b² = c²
Where and and b are the legs and c is the hypotenuse
(Note that the hypotenuse is the longest side and the legs are the two shorter sides)
Finding UTHere, we are given the length of the hypotenuse as well as the length of one of the legs. Given this we are asked to find the other leg UT.
We can find the length of UT by plugging in the given values into the Pythagorean Theorem and then solving for the missing variable.
Because the given hypotenuse is 17 we can say that c = 17 and since a leg is given we can say that a = 8
Plugging this into the formula we acquire (b is UT or the other leg)
8² + b² = 17²
==> evaluate the exponents
64 + b² = 289
==> subtract 65 from both sides
b² = 225
==> take the square root of both sides
b = 15
The length of UT is 15
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Write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. Use a graphing utility to verify your result.
Vertex:
(−4, −1);
Point:
(−2, 4)
The standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point is 1/36(x +4)² - 1.
What is Quadratic function?Equation of a quadratic function in the vertex form is given by;
f(x) = a(x - h)² + k
Here, (h, k) is the vertex of the parabola representing the quadratic function;
Given;
Vertex of the quadratic function (−4, −1);
Parabola passes through a point (−2, 4);
Substitute the vertex in the quadratic function;
f(x) = a(x +4)² - 1
Because, this parabola passes through a point (7, 0),
0 = a(-2- 4)² - 1
0 = 36a - 1
a = 1/36
Equation of the quadratic function will be;
f(x) = 1/36(x +4)² - 1
Therefore, equation of the quadratic function will be f(x) = 1/36(x +4)² - 1;
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Subtract ab-2a+3b from 5a-3ab+6b
Answer:
7a - 4ab + 3b
Step-by-step explanation:
5a - 3ab + 6b - (ab - 2a + 3b)
=5a - 3ab + 6b - ab + 2a - 3b
=7a - 4ab + 3b
pls help and give me a good answer pls
Answer:
y-intercept: 5
slope: -1
equation: y = -x + 5
Step-by-step explanation:
The y-intercept is when x is 0, and it is shown on the table as 5.
The slope can be found by doing [tex]y_1-y_2/x_1-x_2[/tex], which is 6-5/-1-0 = 1/-1 = -1.
The equation is y = mx + b, so we can write it as y = -x + 5
there exists a number , such that when is revolved abut the line , the resulting solid has the same volume as the solid in question . write but do not solve, an equation involving an integral expression that can be used to find the value of
The equation involving an integral expression that can be used to find the value of k is π integration [(k - x²)² - (k - 4)²] dx.
We need to perform integration to find the value of k which will have same volume. Thus, tos over the question the clarity of concepts of volume of any area and integration is required.
The graph representing the mentioned situation is attached in the picture. So, now, writing the expression -
π integration [(k - x²)² - (k - 4)²] dx
Remember tha the integration limit in the mentioned equation will be -2 to 2.
On solving we will get the volume 256π/5.
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The comp question is -
The shaded region, R, is bounded by the graph of y = x² and the line y = 4, as
shown in the figure.
There exists a number k, k 4 , such that when R is revolved about the line y = k , the resulting solid has the same volume as the solid in part (b).
Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.
tyler can type twice as many words wpm as kyla
define variable=
Expression to represent problem=
if kyla can type 3 wpm how many wpm can Tyler type
This means that Tyler can type 6 words in the same amount of time it takes Kyla to type 3 words. This means that Tyler is able to type twice as many words as Kyla per minute.
1. Define a variable
We define a variable called "Tyler" to represent how many words per minute Tyler can type.
2. Write the expression to represent the problem
The expression to represent the problem is "Tyler = 3 * 2", which means that Tyler can type twice as many words per minute as Kyla, who can type 3 words per minute.
The answer is that Tyler can type 6 words per minute, which is twice as many as Kyla can type.
This means that Tyler can type 6 words in the same amount of time it takes Kyla to type 3 words. This means that Tyler is able to type twice as many words as Kyla per minute.
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survey mean (miles) standard deviation (miles) a 13.9 1.5 b 15.1 1.5 the table shows the results of two surveys that asked random samples of people about the distances they commute to work each day. which statement is true based on the results of these surveys?
Answer:
Step-by-step explanation:
The mean and standard deviation of two surveys do not give enough information to determine which statement is true. To compare the two surveys and determine which is true, you would need additional information such as the sample sizes, the confidence intervals for the means, and/or a hypothesis test comparing the means of the two surveys.
Melissa bought some books for each and received a discount of off of her total purchase. She spent after the discount. How many books did she buy?
(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers , , and . Let represent the number of books.
(b) Solve the equation in part (a) to find the number of books.
The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.
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.
Melissa bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6.
Let 'x' be the number of books. Then the equation is given as,
6x - 8 = 58
Simplify the equation, then we have
6x - 8 = 58
6x = 66
x = 11
The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.
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ple Interes How much simple interest would be earned on a savings account of $4,500 at 5.5% interest per year after 24 months? I=(4,500)(055)(2)
4500(1+0.055)^24
4500(1.055)^24
= 16,265.65456755
Let $x=\frac{7}{8}$ and $y=-\frac{2}{9}$. If $x\cdot z = y$, then what is $z$?
The value of z is found by dividing y by x, which results in z =[tex]-\frac{16}{63}$[/tex]
To solve for z, we can use the equation [tex]$x\cdot z = y$[/tex]. We know that [tex]$x = \frac{7}{8}$[/tex] and [tex]$y = -\frac{2}{9}$[/tex],
Therefore, we can enter these values into the equation as substitutes:
[tex]$\frac{7}{8} \cdot z = -\frac{2}{9}$[/tex]
Next, In order to separate z, we must divide both sides of the equation by [tex]$\frac{7}{8}$[/tex]:
[tex]$z = \frac{-\frac{2}{9}}{\frac{7}{8}}$[/tex]
To divide by[tex]$\frac{7}{8}$[/tex], The fraction can be rotated, then multiplied by its reciprocal, which is [tex]$\frac{8}{7}$[/tex]
[tex]$z = \frac{-\frac{2}{9}}{\frac{7}{8}} \cdot \frac{8}{7}$[/tex]
The fraction on the right can be made simpler as follows:
[tex]$z = -\frac{2}{9} \cdot \frac{8}{7} = -\frac{16}{63}$[/tex]
So, The value of z is found by dividing y by x, which results in z =[tex]-\frac{16}{63}$[/tex]
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Audrey is getting a hoverboard, it is on sale for 35% off, it is originally $89. 95. What is the discount amount? Round to the nearest penny. Audrey is getting a hoverboard, it is on sale for 35% off, it is originally $89. 95. What is the discount amount? Round to the nearest penny
The discount amount based on 35% discount offered on $89.95 is $31.5.
The discount amount can be calculated by the formula -
Final amount = original price - discount percentage × original price
The method of solving this formula will be to first multiply followed by subtraction according to PEMDAS rule.
Now, keep the values in formula
Final amount = 89.95 - 35/100 × 89.95
Performing multiplication and division on Right Hand Side of the equation
Final amount = 89.95 - 31.48
Now performing subtraction on Right Hand Side of the equation
Final amount = $58.47
Here we see that that the discount amount is $31.48
Round to nearest penny = $31.5
Thus, the discount amount is $31.5.
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