Answer:
[tex]y=\frac{6}{5}(x-5)[/tex]
Step-by-step explanation:
Use point-slope form.
A cell of some bacteria divides into two cells every 30 minutes. The initial population is 3 bacteria.
(a) Find the size of the population after t hours
y(t)
(function of t)
=
(b) Find the size of the population after 7 hours.
y(7)=
=
(c) When will the population reach 21?
T =
After t hours, the population is 3(2^2t).
After 7 hours, the population is 3(2^14).
In 2.33 minutes, the population would be 21.
What is the function representing bacterial growth?The following formula is used to calculate the bacteria population:
The formula for calculating future value is as follows:
FV = P (1 + r)^n
Where:
FV stands for Future Value.
P = Present value of three
R = growth rate = 100%
(hours x 60 minutes) / 30 = 2t = time
3(2^2t) = population in t hours
3(2 ^14) = population in 7 hours
The population of time would be 21 =[( FV /PV) / r] X 30.
2.33 minutes = ( 21 / 3) / 3.
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6 singles, 7 fives, 3 twenties, and 2 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?
Fair price to play this game is $16.72
Explanation:[tex]\begin{gathered} \text{Given:} \\ 6\text{ singles, 7 fives, 3 twenties and 2 hundred dollar bills in a hat} \\ \end{gathered}[/tex]To find the fair price, we divide the total amount by the number of bill denominations given
[tex]\text{fair price = }\frac{total\text{ amount in the hat}}{nu\text{mber of bills in the hat}}[/tex][tex]\begin{gathered} nu\text{mber of bills = }6\text{ + 7 + 3 + 2 = 18} \\ \\ \text{singles = 1} \\ 6\text{ singles = 6 }\times\text{ 1} \\ 7\text{ fives = 7}\times\text{ 5} \\ 3\text{ twenties = 3}\times20 \\ 2\text{ hundred = 2 }\times\text{ 100} \\ \\ \text{Total amount in the hat = 6 }\times\text{ 1 + 7}\times\text{ 5 + 3}\times20\text{ + 2 }\times\text{ 100} \\ \text{Total amount = 6 + 35 + 60 + 200 = 301} \end{gathered}[/tex][tex]\begin{gathered} \text{fair price = }\frac{301}{18} \\ \text{fair price = 16.72} \end{gathered}[/tex]Fair price to play this game is $16.72
Round your answer to two
decimal places.
7X = 77
Answer:
x = 11
Step-by-step explanation:
7X = 77
divide both sides by 7
x = 11
3 1 1 1 Evaluate 2 when n = 10 5 1 3 3 2 10 10 1 3 3 + + 2 10 10 (Type integers or fractions.)
The given expression is
[tex]\frac{1}{2}n+\frac{3}{10}[/tex]Where n = 1/5.
Let's replace the variable for its value.
[tex]\frac{1}{2}(\frac{1}{5})+\frac{3}{10}[/tex]First, we solve the product.
[tex]\frac{1}{10}+\frac{3}{10}[/tex]Then, we sum fractions. Notice that we just have to sum numerators because the denominators are equal.
[tex]\frac{1+3}{10}=\frac{4}{10}=\frac{2}{5}[/tex]Therefore, the answer is 2/5.can someone help please.(the part cut out says" Slope intercept form)
we have that
the equation of the line in slope intercept form is
y-=mx+b
we have
m=2
b=3/2
substitute
y=2x+3/2
answer is option C
The sides of a square are represented by 3x-9. If the perimeter is 216, what's the
value of X?
The value of X = 21 .
What is perimeter?The length of every closed shape's perimeter is its whole perimeter. This rectangular farm has two sides, with l being the bigger side and b being the smaller side. His farm's circumference may be calculated by adding the lengths of its four sides. Total distance = 2l + 2b (l + b + l + b). In light of this, a rectangle's perimeter is equal to 2 (l + b) units. The complete distance around a shape is referred to as its perimeter. It is any two-dimensional geometric shape's perimeter or outline length. Depending on the measurements, the perimeter of multiple figures may be equivalent. Consider a triangle that is constructed from an L-length wire as an example.
Permitter of square= 4(x)
y = side
y = 3x -9
4(3x -9) = 216
x = 21
Each side = 54
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In 2016, there were 34,602 burger restaurants worldwide, with 12,994 of them located in a country. Determine the percent of burger restaurants in that country in 2016Approximately % of the burger restaurants worldwide were in that country in 2016.
% of the burger restaurants worldwide were in that country in 2016 =
= 12994/ 34602 X 100
= 37.55 %
Enter your answer as an integer or as a reduced fraction in the form A/B.
From the given graph, let's find the slope of the line.
To find the slope of the line, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Take two points on the line:
(x1, y1) ==> (-6, 4)
(x2, y2) ==> (3, -2)
To find the slope, we have:
[tex]\begin{gathered} m=\frac{-2-4}{3-(-6)} \\ \\ m=\frac{-6}{3+6} \\ \\ m=\frac{-6}{9} \\ \\ m=-\frac{2}{3} \end{gathered}[/tex]Therefore, the slope of the line is:
[tex]-\frac{2}{3}[/tex]
ANSWER:
[tex]-\frac{2}{3}[/tex]
5 MATH QUESTIONS WILL MARK BRAINLIEST PLS HELP
The correct options regarding the functions are given as follows:
1. C. y = -2x - 7/9, m = -2, b = -7/9.
2. A. y = 1400x + 5000, 10,600 lbs.
3. A. t = 0.75m + 12, $23.25.
4. A. y = (x - 2) - 3.
5. B. 302.5 miles.
Item 1In slope-intercept formula, a linear function is given as follows:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For this problem, the equation is:
-18x - 9y = 7.
Then:
9y = -18x - 7
y = -2x - 7/9, which slope -2 and intercept -7/9.
Thus option C is correct.
Item 2The table represents a linear function, in which:
The initial value is the intercept of b = 5000.Each week, the amount increases by 1400, hence the slope is of m = 1400.Thus the function is:
y = 1400x + 5000.
In four weeks, x = 4, hence the amount is of:
y = 1400(4) + 5000 = 10600.
Which means that option A is correct.
Item 3Also a linear function, in which:
The intercept is the flat fee of $12.The slope is the cost per mile of $0.75.Hence the function is:
t = 0.75m + 12.
For 15 miles, the cost is given as follows:
t = 0.75(15) + 12 = $23.25.
Which means that option A is correct.
Item 4In this graph, we have a concave up parabola with vertex at (2,-3), hence the rule is:
y = (x - 2) - 3.
Which means that option A is correct.
Item 5The distance function after t hours is given by:
d = 45t + 100.
Hence, after 4.5 hours, as 1/2 = 0.5, the distance is of:
d = 45(4.5) + 100 = 302.5 miles.
Which means that option B is correct.
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Henry is shipping a package that weighs 7 7/8 lbs. What is the weight of the package expressed as a decimal?
Answer:
7.875
Step-by-step explanation:
A local hamburger shop sold a combined total of 632 hamburgers and cheeseburgers on Saturday. There were 68 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
The number of hamburger is 350 and the number of cheeseburger is 282.
How to illustrate the information?It should be noted that an expression is simply used to show the relationship between the variables.
In this case, the local hamburger shop sold a combined total of 632 hamburgers and cheeseburgers on Saturday and there were 68 fewer cheeseburgers sold than hamburgers.
Let Cheeseburger = x
Hamburger = x + 68
This will be:
x + x + 68 = 632
2x + 68 = 632
2x = 632 - 68
2x = 564
x = 564/2
x = 282
Cheeseburger = 282
Hamburger = x + 68 = 282 + 68 = 350
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4
An ice cream shop has a sign in the shape
of an ice cream cone. The sign is made
using a semicircle and a triangle, as
modeled below.
The base of the
triangle is the
6 in.
diameter of the
semicircle.
12 in.
Which is the best estimate of the area of
the sign in square inches?
F 150 in.2
F
G 14 in.2
H 36 in.2
J 50 in.2
In order to determine the total area of the sign, we need to calculate the area of the triangle, and the area of the semicircle. The expressions we need to use are described below:
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\cdot r^2}{2} \\ A_{\text{triangle}}=\frac{b\cdot h}{2} \end{gathered}[/tex]We were given the diameter of the semicircle, it's radius is half of the diameter, therefore:
[tex]r=\frac{6}{2}=3\text{ in}[/tex]The base of the triangle is equal to the diameter of the semicircle. With this we can calculate both areas:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{6\cdot12}{2}=36\text{ square inches} \\ A_{\text{semicircle}}=\frac{\pi\cdot3^2}{2}=14.13\text{ square inches} \end{gathered}[/tex]The total area of the figure is the sum of the above, therefore:
[tex]\begin{gathered} A=A_{\text{triangle}}+A_{\text{semicircle}} \\ A=36+14.13=50.13 \end{gathered}[/tex]The area is approximately 50 in². The correct option is J.
Use the formula n+1/2 to find the median in the list of numbers. 1, 2, 2, 3, 3, 3, 3, 5, 6, 8, 9, 10, 13, 18, 18, 19, 21
The median is 6 in the given list of numbers
The list of numbers is 1, 2, 2, 3, 3, 3, 3, 5, 6, 8, 9, 10, 13, 18, 18, 19, 21
Formula: (n+1)/2th term
Median: The median of the data is the value of the middle observation found after sorting the data in ascending order. In many cases, it is challenging to evaluate the entire set of data for representation, and in these cases, the median is helpful.
where n is the number of items in the list of numbers
n = 17
Substituting the value in the formula we get:
(17+1)/2th term
= 9th term
9th term in the list is 6
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hii i have a question on the question below . in the photo
Solution
For this case we need to sort the values and we have:
Studied
79, 83, 84, 88, 89, 89, 91, 92, 93, 94, 95, 95, 96, 99, 100, 100, 100, 100
Q3= 98.25
Q1= 89
Therefore IQR = 98.25-89= 9.25
Not Studied
45, 58, 65, 72, 73, 77, 82, 83, 87, 89, 90, 91
Q3= 87.5
Q1= 70.25
Therefore IQR = 87.5-70.25= 17.25
From the results obtained we can conclude that the students who not studied havve larger variability compared to those who studied
Determine the slope given two points (-2,3) (6,-7)
Answer: m = -3/5
Step-by-step explanation:
The average teachers' salary in a certain state is $57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7500. Assume that the sample is taken from a large population and the correction factor can be ignored. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places.What is the probability that a randomly selected teacher makes less than $50,000 per year?
Normal distribution of salaries
d = Standard dev = $7500 =
Correction factor= 0
Di
f(x) = (1/ d•√2π )• e ^- ((s- s')^2/2d^2)
Average value = u = 57337
Now calculate f(x)
Difference of salaries ,with respect to average
S^ 2= 57337 - 50000= = 7337
Now squared = (7337^2) = 53831569
d = 7500
2•d^2= 112500000
Then
S^2/ (2•d^2) = 53831569/112500000= 0.4785
Then now calculate
f(x) = (1/ d•√2π )•e^- (0.4785)
f(x)= 0.619/ (2•d^2)
Answer is
Probability of 61.9%
find the length of the base if the area of the trapezoid is 198 M2.
The area of a trapezoid is given by:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]where b1 and b2 are the bases of the trapezois and h is the height. In this case we have that A=198, b1=15 and h=12, plugging this values into the equation above and solving for b2 we have:
[tex]\begin{gathered} 198=\frac{1}{2}(b_2+15)12 \\ 2\cdot198=12(b_2+15) \\ 396=12(b_2+15) \\ \frac{396}{12}=b_2+15 \\ 33=b_2+15 \\ b_2=33-15 \\ b_2=18 \end{gathered}[/tex]Therefore b2 is equal to 18 m
Nancy is a high scorer on her basketball team. she made 24 free throws out of 32 free throws attempted. what was her percentage of free throw shots made?
32 ------------------ 100
24 -------------------- x
x = (24 x 100) / 32
x = 2400/32
x = 75%
To solve this problem use a rule of three
8x^2+8x-22 In (x-p)^2=q
The given function 8x^2+8x-22 rewritten using the completing the square method is (x+1/2)^2 = 3
Completing the square methodBy altering the equation's form so that the left side is a perfect square trinomial, a quadratic equation can be solved using the "Completing the Square" approach.
Given the quadratic equation below;
8x^2+8x-22 = 0
This can be simplified into the equation below;
8x^2+8x-22 = 0
4x^2+4x-11 = 0
Add 11 to both sides of the equation
4x^2+4x-11 + 11= 0 + 11
4x^2+4x = 11
Factor out 4x from the expression;
4(x^2+1) = 11
(x+1/2)^2 = 11/4 + 1/4
(x+1/2)^2 = 12/4
(x+1/2)^2 = 3
Hence the expression in the form of (x-p)^2=q is (x+1/2)^2 = 3
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A basketball player had scored 879 points in 34 games. a) At this rate, how many games will it take him to score 1500 points? b) There are 82 games in an entire season. At this rate, how many points would he score in the entire season? a) It will take him approximately games to score 1500 points . (Round up to the next whole number of games.) b) At this rate, he would score approximately (Round to the nearest one if necessary.) points in the entire season. Enter your answer in each of the answer boxes.
We know that he scored 879 points in 34 games, so we can calculate the average rate as:
[tex]r=\frac{879\text{ points}}{34\text{ games}}=25.85\text{ points/game}\approx26\text{ points/game}[/tex]At this rate, we can calculate the total points P by multiplying the rate r by the number of games n:
[tex]P=r\cdot n=25.85\cdot n[/tex]We can calculate how many games are needed for P=1500 as:
[tex]\begin{gathered} P=26\cdot n=1500 \\ n=\frac{1500}{25.85}\approx58.02\approx58\text{ games} \end{gathered}[/tex]For n=82 games, the expected number of points P is:
[tex]P=25.85\cdot n=25.85\cdot82=2119.7\approx2120\text{ points}[/tex]Answer:
a) It will take him approximately 58 games to score 1500 points.
b) At this rate, he would score approximately 2120 points in the the entire season.
A chord of a circle is 56cm long. The distance of the chord to the centre of the circle is 20cm. a) calculate the radius of the circle b) calculate the length of a chord which is 24cm from the center of the circle.
Answer:
a) 34.4 cm,b) 49.4 cmStep-by-step explanation:
The distance from the center to the chord is the perpendicular bisector of the chord.
The three segments form a right triangle:
The radius - hypotenuse,The half-length of the chord - leg,The distance to the chord - another leg.a) Use Pythagorean to find the radius:
r² = (56/2)² + 20²r² = 28² + 20²r² = 1184r = √1184r = 34.4 cm (rounded)b) Let the half-chord is x cm long. Use Pythagorean to find the missing leg:
34.4² = x² + 24²1184 = x² + 576x² = 1184 - 576x² = 608x = √608x = 24.7 cm (rounded)The length of the chord is:
24.7*2 = 49.4 cm3x+7x-28+31-8x for x=2043
The value of the function when x is equivalent to 2043 is 4089.
Solving linear equationLinear equations are equation that has a leading degree of 1. Given the linear equation;
3x+7x-28+31-8x
Collect the like terms
3x+7x-28+31-8x
3x+7x-8x-28+31
10x-8x-28+31
2x+3
If the value of x is 2043, substitute;
2x+3 = 2(2043) + 3
2x + 3 = 4086 + 3
2x + 3 = 4089
Hence the value of the function when x is equivalent to 2043 is 4089.
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Please show work as if you didn’t have a calculator
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given function.
[tex]f(x)=\frac{1}{(x+3)}-2[/tex]STEP 2: Explain the means to use to find the required values
Since we were given a graph and can not use a caculator, we will be using the graph to get the values.
STEP 3: Plot the given function on a graph
STEP 4: Get the domain of the function
Domain: The domain is all x-values or inputs of a function. The domain of a graph consists of all the input values shown on the x-axis.
[tex]\begin{gathered} The\text{ domain from the graph is given as:} \\ x<-3\text{ or }x>-3 \\ \text{The interval notation is given as:} \\ (-\infty,-3)\cup(-3,\infty) \end{gathered}[/tex]STEP 5: Get the Range of the function
The range is all y-values or outputs of a function.
[tex]\begin{gathered} \mathrm{The\: set\: of\: values\: of\: the\: dependent\: variable\: for\: which\: a\: function\: is\: defined} \\ \text{The range of the graph is given as:} \\ f(x)<-2\text{ or }f(x)>-2 \\ \text{The interval notation is given as:} \\ (-\infty,-2)\cup(-2,\infty) \end{gathered}[/tex]STEP 6: Get the value on which the function is increasing on
[tex]\begin{gathered} \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)>0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: increasing.} \\ \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)<0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: decreasing.} \end{gathered}[/tex]STEP 7: Get the value on which the function is decreasing on
[tex]\begin{gathered} \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)<0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: decreasing.} \\ It\text{ can be s}een\text{ that the function on the graph decreases on the point betw}een\text{ negative infinity} \\ \text{and -3 and the point betw}een\text{ -3 and infinity. }\therefore This\text{ can be written as:} \\ \: \\ \mathrm{Decreasing}\colon-\infty\:STEP 8: Get the values of the asymptotes
An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.
[tex]\mathrm{Vertical}\colon\: x=-3,\: \mathrm{Horizontal}\colon\: y=-2[/tex]
Find the surface area for the triangular prism below if AB = 16 m, AC = 33 m, AD = 12 m, and DP = 9 m. (Note: the bases are isosceles triangles.)
INFORMATION:
We have the following figure
And we must find its surface area
STEP BY STEP EXPLANATION:
To find the surface area of the triangular prism, we can divide the figure in:
- The two triangle bases:
We have the next triangle in the two bases:
We can calculate the area of the triangle
[tex]A=\frac{16\times9}{2}=72m^2[/tex]Since we have the same triangle in the two bases, the total area of the two triangles would be
[tex]72m^2\cdot2=144m^2[/tex]-
What is 3m+n evaluate the expression. I’m confused on how to solve this this is what my teacher gave me that’s it
Explanation:
The expression is given below as
[tex]3m+n[/tex]Concept:
The sum of two or more like terms is a single like term; but the two unlike terms cannot be added together to get a single term. Suppose, to find the sum of two unlike terms x and y, we need to connect both the terms by using an addition symbol and express the result in the form of x + y.
In this case,
The terms given ( 3m and n ) are unlike terms and as such the expression cannot be simplified further
Hence,
The final answer is
[tex]3m+n[/tex]such
NEEEEEEEEDDDDDD HELPPPPP ASAPPPPPPP
Matching the specific Polygons with their descriptions, we have;
15-gon → An exterior angle measures 24°
16-gon → The Sum of interior angles is 2520°
12-gon → An interior angle measures 150°
18-gon → An interior angle measures 160°
What is the sum of interior angles of a Polygon?The formula for sum of interior angles of a Polygon is;
S = (n - 2) * 180
where n is number of sides of polygon. Thus;
1) For a 15 sided polygon;
Sum = (15 - 2) * 180
Sum = 13 * 180
Sum = 2340
Sum of exterior angles of a polygon is; 360°
Thus, external angles = 360/15 = 24°
2) For a 16 sided polygon;
Sum of interior angles = (16 - 2) * 180 = 2520°
3) The value of the interior angles of a polygon with 12 sides is;
(12 -2) * 180/12 = 150°
4) The value of the interior angles of a polygon with 18 sides is;
(18 - 2) * 180/18 = 160°
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5 · 4 -3 + 10 ÷ 2 A. -65 B. -55 C. -35 D. -25
we have
5 · 4 · -3 + 10 ÷ 2
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
step 1
Multiplication
5.4.-3=-60
substitute
-60+10÷ 2
step 2
Division
10÷ 2=5
substitute
-60+5
step 3
Addition
-55
therefore
option B
Aaliyah needs to bake 42 servings of treats. She has cooked 20 servings of treats already. She has bars left to
make and each bar is 2 servings. How many bars does she need to make?
Answer:
she needs to make 11 bars
Step-by-step explanation:
42-20
22
each bar is 2 servings so
22÷2
11 bars
for each equation give for solution. Then, graph the solution set on the graph provided.
Given the equation x+2y=8
[tex]\begin{gathered} \text{When x=-4} \\ x+2y=8 \\ -4+2y=8 \\ 2y=8+4 \\ 2y=12 \\ y=6 \\ (-4,\text{ 6)} \end{gathered}[/tex]When x = -2
[tex]\begin{gathered} \\ x+2y=8 \\ -2+2y=8 \\ 2y=8+2 \\ 2y=10 \\ y=5 \\ (-2,\text{ 5)} \end{gathered}[/tex]When x=0
[tex]\begin{gathered} \\ x+2y=8 \\ 0+2y=8 \\ 2y=8 \\ y=4 \\ (0,\text{ 4)} \\ \end{gathered}[/tex]When x=2
[tex]\begin{gathered} \\ x+2y=8 \\ 2+2y=8 \\ 2y=8-2 \\ 2y=6 \\ (2,\text{ 3)} \end{gathered}[/tex]We then plot these points.
Which statement is true regarding the functions on the graph? 6 9) O f2) = g(2) O fO) = g(0) O f2) = g(0) Of(0) = g(2) 2 5 6 -421
F(x) is blue and G(x) is red
Have to find at which point both functions have the same value, or the same in which point both lines intercept
and looking at the graph ,theres only one point where both are equal. Its the point x= 2 y=0.
so the correct answer is f(2) = g(2)