Answers
The form of the exponential growth/decay function is
[tex]f(x)=a(1\pm r)^x[/tex]a is the initial amount
r is the rate of growth/decay per x years
We use + with growth and - with decay
Since the given function is
[tex]f(t)=2700(1.6)^{7t}[/tex]Where t is time per week
Compare the two functions
[tex]\begin{gathered} a=2700 \\ (1+r)=1.6 \\ x=7t \end{gathered}[/tex]Since 1.6 is greater than 1, then
The function is growth
Equate 1.6 by (1 + r) to find r
[tex]\begin{gathered} 1+r=1.6 \\ \\ 1-1+r=1.6-1 \\ \\ r=0.6 \end{gathered}[/tex]Change it to percent by multiplying it by 100%
[tex]\begin{gathered} r=0.6\times100\text{ \%} \\ \\ r=60\text{ \%} \end{gathered}[/tex]Since x = 7t then the time is every 7 weeks
The answer is
The function is growing exponentially at a rate of 60% every 7 weeks
Related Questions
Turn into an inequality A speed limit of 65 mph
Answers
The question says we should turn into an inequality a speed limit of 65 miles per hour.
This means the speed should'nt be more than 65 miles per hour. In other words the speed shouldn't exceed 65 miles per hour.
Let represent the speed with a. Therefore,
a < 65 miles per hour
a < 65
i need help with math
Answers
∠1 and ∠2 are on same side exterior angles. FALSE
∠3 and ∠12 are alternate interior angles. FALSE
∠2 and ∠10 are corresponding angles. TRUE
∠6 and ∠11 are alternate exterior angles. TRUE
What are the different types of angles?Corresponding angles ; Angles that are present in similar locations are said to be in correspondence with one another. The dimensions of both angles are equal
Alternate Interior Angle: This term refers to the angles that are present on the opposing sides of the transversal. They can be found on the inside of the Z that the figure's Z has produced. The angles are both equal to one another.
Alternative Exterior Angle: The alternative exterior angles are those that are externally located and present on the opposing sides of the transversal. Both angles measure the same and they may be seen on the exterior.
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What is the value of the expression below? If entering the value as fraction or mixed number, give the answer in lowest term.-0.2 + (-¾) + 2.15 - (-⅖)
Answers
Explanation:
-0.2 + (-¾) + 2.15 - (-⅖)
let's convert the decimal to fractions:
-0.2 = -2/10 = -1/5
2.15 = 215/100 = 43/20
-0.2 + (-¾) + 2.15 - (-⅖) = -1/5 + (-¾) + 43/20 - (-⅖)
Expanading the bracket:
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
= -1/5 -3/4 + 43/20 + 2/5
[tex]\begin{gathered} \text{The LCM = 20} \\ =\frac{-1(4)-3(5)+43+2(4)}{20} \\ \end{gathered}[/tex][tex]\begin{gathered} =\frac{-4-15+43+8}{20}=\frac{32}{20} \\ =\frac{8}{5} \\ =1\frac{3}{5} \end{gathered}[/tex]the square practice x² + 6x + 9 = 0
Answers
x = -3 twice
Explanation:x² + 6x + 9 = 0
Since the method for solving the question isn't specified, we will be using factorisation method to solve for x.
factors of 9 = 1, 3, 9
The two numbers when multiplied gives 9 and when added gives 6 are +3 and + 3.
using factorisation method:
x² + 3x + 3x + 9 = 0
x(x + 3) + 3(x + 3) = 0
(x + 3)(x + 3) = 0
(x+3) = 0 or (x+3) = 0
x = -3 or x = -3
x = -3 twice
The second method is because of the square practice in the question.
Using complete the square:
x² + 6x + 9 = 0
x² + 6x = -9
we half the coefficient of x and the square the result
coefficient of x = 6
1/2 of coefficient of x = 6/2
square of the result = (6/2)² = 3² = 9
Add the above result from both sides of the equation:
x² + 6x + 9 = -9 + 9
(x + 3)² = 0
square root both sides:
x + 3 = +/- √0
subtract 3 from both sides:
x +3 -3 = -3 +/-√0
x = -3 + 0 or -3 - 0
x = -3 twice
how to solve the volume of sphere and the area of a cylinder.
Answers
Consider a sphere of radius r, then the volume of the sphere is given by,
[tex]V=\frac{4}{3}\pi\times r^3[/tex]Here
[tex]\pi=3.14[/tex]Now let us consider a cylinder of with base radius r and height h, as in the figure,
The area is the total area of the base surface and the niddle surface.
This can be written as,
[tex]A=2\pi(h+r)[/tex]Consider a sphere of radius 2 cm, the volume can be calculated as,
[tex]v=\frac{4}{3}\times3.14\times2^3=\frac{4}{3}\times3.14\times2\times2\times2=33.49cm^3[/tex]Use the Pythagorean Theorem to find the missi romanille 1 1 point a = 3 and b = 7. Round to two decimal places. Type your answer... 2. 1 point a = 3 and c = 23. Round to two decimal places. Type your answerExercise number 1
Answers
The formula of the Pythagorean Theorem is
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where c is the hypotenuse and} \\ a,b\text{ are the sides of the triangle} \end{gathered}[/tex]Graphically,
So, in this case, you have
[tex]\begin{gathered} a=3 \\ b=7 \\ c=\text{?} \\ a^2+b^2=c^2 \\ \text{ Replacing} \\ (3)^2+(7)^2=c^2 \\ 9+49=c^2 \\ 58=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{58}=\sqrt[]{c^2} \\ 7.62=c \end{gathered}[/tex]Therefore, the missing side measurement is 7.62 units.
Jay Field's bank granted him a single-payment loan of $6,800. He agreed to repay the loan in 91 days at an ordinary interest rate of 4.25 percent. What is the maturity value of the loan?
Answers
Answer:
$6,872.05
Explanation:
The maturity value of the loan can be calculated as:
[tex]V=P(1+r\cdot t_{})[/tex]Where P is the initial amount, r is the interest rate as a decimal and t is the time in years.
4.25% is equivalent to: 4.25/100 = 0.0425
91 days are equivalent to 91/365 = 0.25 years
Then, the maturity value is equal to:
[tex]\begin{gathered} V=6800(1+0.0425\cdot0.25) \\ V=6800(1+0.011) \\ V=6800(1.011) \\ V=\text{ \$6,872.05} \end{gathered}[/tex]So, the maturity value of the loan is $6,872.05
Given the following expressions, you will identify the followingslope, y- intercept , x intercept, domain range , and is the function increasing or decreasing
Answers
Given the following function:
[tex]\text{ 3x - 2y = 16}[/tex]A.) SLOPE
Let's first transform the given equation into the standard slope-intercept form: y = mx + b
Because the m in the equation represents the value of the slope.
We get,
[tex]\begin{gathered} \text{ 3x - 2y = 16} \\ \text{ (3x - 2y = 16)( -}\frac{\text{ 1}}{\text{ 2}}) \\ \text{ -}\frac{3}{2}x\text{ + y = -}\frac{16}{2} \\ \text{ -}\frac{3}{2}x\text{ + y = -}8 \\ \text{ y = }\frac{3}{2}x\text{ - 8} \end{gathered}[/tex]The slope-intercept form of 3x - 2y = 16 is y = (3/2)x - 8. Where m = 3/2.
Therefore, the slope of the function is 3/2.
B.) Y - INTERCEPT
In the standard slope-intercept form : y = mx + b, b represents the y - intercept.
Therefore, in the converted form of the function y = (3/2)x - 8. b is equals to -8.
The y-intercept is 0, -8.
C.) X - INTERCEPT
The x - intercept is the point at y = 0.
We get,
[tex]\text{ 3x - 2y = 16}[/tex][tex]\text{ 3x - 2(0) = 16}[/tex][tex]\text{ 3x = 16}[/tex][tex]\text{ }\frac{\text{3x}}{3}\text{ = }\frac{\text{16}}{3}[/tex][tex]\text{ x = }\frac{\text{ 16}}{\text{ 3}}[/tex]Therefore, the x - intercept is 16/3, 0
D.) DOMAIN RANGE
The function has no undefined points nor domain constraints. Therefore, the domain is
[tex]-\infty\: We usually encounter undefined points when a given value of x will make the denominator equal to zero (0).Example: 2/(3 - x) at x = 3 is undefined.
E.) INCREASING OR DECREASING
The easiest way to determine if the function is decreasing or increasing is by looking at the slope (m). If the slope is greater than 0 (m > 0) or a positive, the function is increasing. If the slope is less than 0 (m < 0) or a negative, the function is decreasing.
Here, the slope is 3/2 which we first solved. Since the slope is greater than zero or a positive, the function is, therefore, increasing.
The answer is increasing.
The value V of an item after t years is given by the following formula, assuming linear depreciation,V = C - Crt.where C is the original cost and r is the rate of depreciation expressed as a decimal.If you buy a car for $7191 and it depreciates linearly at a rate of 5% per year, what will be its value after 9 months? Round youranswer to the nearest cent.
Answers
Here C=$7191
r=0.05
t=9 months=0.75 years
The value of the car will be
[tex]V=7191-7191\times0.05\times0.75\Rightarrow V=7191-269.6625\Rightarrow V=6921.34[/tex]Hence the value of the car will be $6921.34.
Find the least-squares regression line y = bo + b₁x through the points
(-2,0), (0,7), (4, 15), (8, 18), (9,24),
and then use it to find point estimates y corresponding to x = 1 and x = 8.
For this problem and to give you practice for the test, use the shortcut method to find bo given that b₁ = 1.9051724137931.
For x = 1, y =
For x = 8, y^=
Answers
The values for x = 1, then y = 38.23 and for x = 8, then y^ = 55.375.
Given that, [tex]y = b_{0}+ b_{1}x[/tex]
x y xy xx yy
-2 0 0 4 0
0 7 0 0 49
4 15 60 16 225
8 18 144 64 324
9 24 216 81 576
19 64 420 165 1174 - Total(T)
n = 5
Given line is [tex]y = b_{0}+ b_{1}x[/tex]
Solve for the value of [tex]b_{0}[/tex]
[tex]b_{0} = \frac{Ty*Txx-Tx*Txy}{nTx^{2} -(Tx)^{2} }[/tex]
[tex]= \frac{64*165-19*420}{5*165-(19)^{2} }\\ \\= \frac{10560-7980}{825-361}\\ \\= \frac{2580}{64} = 40.135[/tex]
Solve for the value of [tex]b_{1}[/tex]
[tex]b_{1} = \frac{nTxy-Tx*Ty}{nTx^{2} -(Tx)^{2} }\\ \\= \frac{5*420-19*64}{5*165 - (19)^{2} }\\ \\= \frac{2100-1216}{464}\\ \\= \frac{884}{464} = 1.905[/tex]
Therefore, y = 40.135 + 1.905x
To solve for x = 1
y = 40.135 + 1.905(1)
= 38.23
To solve for x = 8
y^ = 40.135 + 1.905(8)
= 55.375
Hence the answer is the values for x = 1, then y = 38.23 and for x = 8, then y^ = 55.375.
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The 5 participants in a 200-meter dash had the following finishing times in seconds)24, 28, 26, 30, 32Send data to calculatorAssuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places,
Answers
Given:
Data x: 24, 28, 26, 30, 32
n = 5
Asked: What is the standard deviation of the population?
Formula:
[tex]\text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}}[/tex]Solution:
Step 1: We will get the average of the data given.
NOTE: Bar x is also the mean or the average.
[tex]\begin{gathered} \bar{x}\text{ = }\frac{24+28+26+30+32}{5}\text{ } \\ \bar{x}=\text{ 28} \end{gathered}[/tex]Step 2: We will subtract the mean from each number.
Step 3: We will square the differences and get the summation.
Step 4: We will substitute the acquired values to find the standard deviation using the formula above.
[tex]\begin{gathered} \text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}} \\ \text{standard deviation = }\sqrt[]{\frac{40^{}}{5}}\text{ } \\ \text{standard deviation = 2}\sqrt[]{2}\text{ = }2.828427125 \end{gathered}[/tex]ANSWER: standard deviation = 2.83 (Rounded off to 2 decimal places)
A sample of 26 customers was taken at a computer store. Each customer was asked the price of the computer she bought. Here is a summary Number of computers 7, 10,9 Price paid for each (in dollars) 900, 800, 1200 Find the mean price for this sample. Round your answer to the nearest dollar.
Answers
formula for the mean
[tex]\bar{x}=\frac{\sum ^{\infty}_{n\mathop=0}x_i}{n}[/tex]for this exercise n=26
replace data on the formula
[tex]\begin{gathered} \bar{x}=\frac{(7\cdot900)+(10\cdot800)+(9\cdot1200)}{26} \\ \bar{x}=965.385 \end{gathered}[/tex]- Graph the function f (x) = x - 4. Use the line tool and select two points to graph. Line * Move Undo Redo x Reset 10 9 8 7 6 5 4 3 N 1 1 2. 3 4 6 7 8 9 10 10 9 8 7 6 5 4 3 2 -19 -2
Answers
we have the function
f(x)=x-4
That is the equation of a line
to graph a line we need at least two points
so
Find out the intercepts
step 1
Find out the y-intercept (value of y when the value of x is zero)
For x=0
f(x)=0-4
f(x)=-4
the y-intercept is the point (0,-4)
step 2
Find out the x-intercept (value of x when the value of y is zero)
For y=0
0=x-4
x=4
the x-intercept is the point (4,0)
step 3
Plot the points (0,-4) and (4,0), join them, to graph the line
see the attached figure to better understand the problem
Teresa is riding in a bike race that goes through a valley and a nearby mountain range.The table gives the altitude (in feet above sea level) for the five checkpoints in the race.Use the table to answer the questions.Checkpoint,Altitude(feet above sea level)1, -1152, 2,1663, 1,1854, -1685, -32(a)The top of a hill rises 530 feet above Checkpoint 4.What is the altitude of the top of the hill?(b)How much lower is Checkpoint 4 than Checkpoint 1?
Answers
a)
Checkpoint 4 = -168 ft
Add 530
-168 + 530 = 362 ft
b) Compare checkpoint 1 to checkpoint 4
1 = -115 ft
4 = -168
-168 -(-115) = -53
Checkpoint 4 is 53ft lower than checkpoint 1
Answers : • center c and scale factor 2• center a and scale factor 5• center c and scale factor 1• center a and scale factor 2
Answers
In order to find the scale factor of the dilation of ΔABC, we just need to divide any pair of the corresponding sides of both triangles. We have that the division of the corresponding sides will be always the same:
[tex]\frac{A^{\prime}C^{\prime}}{AC}=\frac{B^{\prime}C^{\prime}}{BC}=\frac{A^{\prime}B^{\prime}}{AB}=\text{scale factor}[/tex]We are going to choose the first division:
[tex]\frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor}[/tex]Finding the scale factorWe have that AC = 5 and A'C' = 10:
Then:
[tex]\begin{gathered} \frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor} \\ \downarrow \\ \frac{10}{5}=2 \end{gathered}[/tex]The scale factor is 2.
And since the point C and C' are the same, the center is C.
Answer- A. center C and scale factor 2
4:58 PM 16 AA.18 Area of compound figures... < Surina Silva's prac... 38 What is the area of this figure? 3 mi 14 mi 5 mi 9 mi 10 mi 5 mi 4 mi 10 mi Write your answer using decimals, if necessary. square miles.
Answers
ANSWER
230 square miles
EXPLANATION
We can divide this figure as shown in the picture: 2 rectangles and a right triangle. We find the area of each figure and then we add them up.
One of the rectangles's length is 5 mi and its width is 14 mi. Its area is:
[tex]A_{\text{rectangle}1}=5mi\times14mi=70mi^2[/tex]The other rectangle's lenght is 10mi and its width is 5mi. Its area is:
[tex]A_{\text{rectangle}2}=10mi\times5mi=50mi^2[/tex]The triangle height is:
[tex]3mi+5mi+10mi+4mi=22mi[/tex]And its base is 10mi. Its area is:
[tex]A_{\text{triangle}}=\frac{22mi\times10mi}{2}=\frac{220mi^2}{2}=110mi^2[/tex]The area of the figure is:
[tex]\begin{gathered} A=A_{\text{rectangle}1}+A_{\text{rectangle}2}+A_{\text{triangle}} \\ A=70mi^2+50mi^2+110mi^2 \\ A=230mi^2 \end{gathered}[/tex]Question AA baseball is hit, following a path represented by x = 135t and y = 3.3 + 38t − 16t 2 for 0 ≤ t ≤ 3.Part A: Find the ordered pairs, (x, y) when t = 0.2, 1.2, and 2.2.Part B: The fence, which is 10 feet tall, lies 320 feet away from home plate. Does the baseball travel over the fence? Justify your answer mathematically.Part C: Write a rectangular equation to represent the plane curve.
Answers
Explanation
For the given question, we have the following
[tex]\begin{gathered} x=135t \\ y=3.3+38t-16t^2 \end{gathered}[/tex]Part A
find the ordered pairs (x,)
[tex]\begin{gathered} when \\ t=0.2 \\ \\ x=135(0.2)=27 \\ y=3.3+38(0.2)-16(0.2)^2=10.26 \\ \\ when\text{ t=0.2} \\ (x,y)=(27,10.26) \\ \end{gathered}[/tex][tex]\begin{gathered} when \\ t=1.2 \\ x=135(1.2)=162 \\ y=3.3+38(1.2)−16(1.2)^2=25.86 \\ \\ (x,y)=(162,25.86) \end{gathered}[/tex][tex]\begin{gathered} when \\ t=2.2 \\ x=135(2.2)=297 \\ y=3.3+38(2.2)−16(2.2)^2=9.46 \\ \\ (x,y)=(297,9.46) \end{gathered}[/tex]Can help me:coin is flipped 6 times. What is the probability that heads and tails occur an equal number times?
Answers
The probability that heads and tails occur an equal number times is 5/16.
From the question, we have
The number of permutations =HHHTTT
The total number of permutations = 6!=720.
Since, there are two groups comprising 3 identical objects, the number of permutations = 720/3!3!=20.
total number of possibilities in the event space= 2^6=64
the required probability = 20/64=5/16.
Probability:
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
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11. The trigonometric ratio of cos B isPYTHAGOREAN TRIPLE PROBLEMB13590°A125/1212/135/1313/5
Answers
From the given right-angled triangle, we have the following:
Hypothenuse side = 13
Opposite side = 12
Adjacent side = 5
Solution
The trigonometric ratio of cos B can be found using the relationship:
[tex]\cos \text{ B = }\frac{Adjacent}{Hypothenus}[/tex]By substituting, we have:
[tex]cos\text{ B = }\frac{5}{13}[/tex]Hence, the answer is 5/13 (option C)
At a fundraiser , a sorority is able to raise $5 less than four times the amount of money a fraternity raises
All together they raised $115
First question what is known is the situation?
Second question what is unknown in the situation
Third question how do I write an equation that represents the situation use at to represent the fraternity
NEED HELP ASAP I WILL MARK YOU BRAINLIEST NO LINKS PLEASE AND THANK YOU
Answers
An equation that represents the situation used to represent the amount that the fraternity raises is; x + (4x - 5) = 115
How to solve Algebra Word Problems?Let the amount of money raised by the fraternity be x.
Now, we are told that the sorority raises $5 less than four times the amount that a fraternity raises. Thus;
Amount raised by Sorority = $(4x - 5)
Together, we are told that they raised $115. Thus, the equation will be;
x + (4x - 5) = 115
5x - 5 = 115
5x = 115 + 5
5x = 120
x = 120/5
x = $24
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I'll send the question 2-x>8
Answers
The given inequality is
[tex]2-x>8[/tex]We subtract 2 from each side.
[tex]\begin{gathered} 2-2-x>8-2 \\ -x>6 \end{gathered}[/tex]Then, we multiply the inequality by -1.
[tex]\begin{gathered} -x\cdot-1<6\cdot-1 \\ x<-6 \end{gathered}[/tex]Hence, the answer is b.if you could please try to answer quickly my brainly keeps crashing
Answers
The lateral area of a cylinder is given by:
[tex]L=2\pi rh[/tex]where r represents the radius and h represents the height.
Then,
h=13m
In this case, we have the diameter. However, the radius is the half value of the diameter.
Then,
r=d/2=6m/2=3m
Replacing:
[tex]\begin{gathered} L=2\pi(3m)(13) \\ L=245m^2 \end{gathered}[/tex]Hence, the lateral area is 245m².
Find the surface area of a sphere with a radius of 1 cm to the nearest tenth. (Do NOTtypeinany units in your answer.)
Answers
The area of the sphere is 12.6
Here, we want to find the area of the sphere given the radius
Mathematically, we can calculate the area of the sphere using the formula below;
[tex]\begin{gathered} A\text{ = 4}\times\pi\times r^2 \\ r\text{ = 1 cm} \\ \pi\text{ = 3.142} \\ \text{Area of sphere = 4}\times3.142\times1^2=12.6cm^2 \end{gathered}[/tex]enter an equation that describes the propitiatial relationship between the number of days and the number of weeks in a giving length of time
Answers
We need to find an equation that describes the relationship between days and week.
We know that one week has 7 days:
So, to find the number of days for a given number of weeks, what we need to do is multiply the number of weeks by 7.
If we call the number of weeks "w" and the number of days "d", the equation that describes the proportional relationship is:
[tex]d=7w[/tex]The number of days is equal to the number of weeks multiplied by 7.
Now with this, we can complete the table of values. For 4 weeks, the number of days is:
[tex]\begin{gathered} d=7(4) \\ d=28 \end{gathered}[/tex]For 5 weeks, the number of days is:
[tex]\begin{gathered} d=7(5) \\ d=35 \end{gathered}[/tex]To complete the next row, we don't need the days, we need the number of weeks. For that, we take our equation and substitute the number of days:
[tex]\begin{gathered} d=7w \\ 42=7w \end{gathered}[/tex]And we solve for "w" by dividing both sides by 7:
[tex]\begin{gathered} \frac{42}{7}=w \\ 6=w \end{gathered}[/tex]Finally, for the last row, we find the number of days in 13 weeks using our equation:
[tex]\begin{gathered} d=7(13) \\ d=91 \end{gathered}[/tex]complete the square with the following equation of a circle so that you can convert the equation into standard form.
Answers
Equation of a Circle
We are given the equation:
[tex]x^2+y^2+10x+12y+12=0[/tex]The equation of a circle of radius r and center (h,k) is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]To convert the given equation into the standard form, we need to complete squares as follows.
First, rearrange terms:
[tex]x^2+10x+y^2+12y+12=0[/tex]The term 10x is divided by 2x to find the correct number to complete:
10x/(2x) = 5
Similarly, dividing 12y/(2y) = 6
Now we complete both squares by adding (and subtracting) 25 and 36:
[tex]x^2+10x+25+y^2+12y+36+12-25-36=0[/tex]Operating:
[tex](x+5)^2+(y+6)^2=49[/tex]Second choice
Write the following decimal numbers as a fraction: • One hundred and twenty four hundredths • Five tenths 5/10 Twenty seven thousandths Fifty two and nine hundredths
Answers
ANSWER:
10024/100
5/10
27/1000
5209/100
STEP-BY-STEP EXPLANATION:
The first thing is to convert the writing into a decimal number and then convert it into a fraction, just like this:
One hundred and twenty four hundredths:
100.24 = 10024/100
Five tenths
0.5 = 5/10
Twenty seven thousandths
0.027 = 27/1000
Fifty two and nine hundredths
52.09 = 5209/100
Solve the following equation for X 5x+7y=19 X= ?
Answers
1) We can solve this equation for x, by doing the following algebraic manipulation:
[tex]\begin{gathered} 5x+7y=19 \\ \\ 5x+7y-7y=19-7y \\ \\ 5x=19-7y \\ \\ \frac{5x}{5}=\frac{19}{5}-\frac{7y}{5} \\ \\ x=-\frac{7}{5}y+\frac{19}{5} \\ \\ x=\frac{19-7y}{5} \end{gathered}[/tex]2) In this problem, we can't go any further than that. So, that is the answer.
At his job, Tomas earns a commission plus an hourly wage. The function below describes the total dollar amount Tomas earns, based on the number of hours he works,f(h) = 250 +8.5hWhat represents the hourly rate Tomas earns
Answers
f(h) = 250 +8.5h
The function is on slope-intercept form:
y(x)= mx +b
Where m is the slope.
Rearranging the function given:
f(h) = 8.5h +250
Where:
250 is the fixed commission since it doesn't have a variable next to it.
8.5 is the hourly wage.
We can see that the hourly rate (8.5 per hour) is the slope of the function.
A box contains letters, shown as MARCHING. What is the probability of the outcome in that order if letters are drawn one by one (a) with replacement? (b) without replacement?
Answers
There are 8 letters in the word MARCHING.
So, the number of letters in the box, N=8
b)
The probabilty of drawing the first letter M is,
[tex]P(M)=\frac{1}{N}=\frac{1}{8}[/tex]If the letter is not replaced, the number of remaining letters in the box is 7.
So, the probabilty of drawing the second letter A is,
[tex]P(A)=\frac{1}{7}[/tex]Similarly, the probabilities of drawing letters R,C,H,I, N and G respectively is,
[tex]\begin{gathered} P(R)=\frac{1}{6} \\ P(C)=\frac{1}{5} \\ P(H)=\frac{1}{4} \\ P(I)=\frac{1}{3} \\ P(N)=\frac{1}{2} \\ P(G)=1 \end{gathered}[/tex]So, the probability of of the outcome in that order if letters are drawn one by one without replacement is,
[tex]undefined[/tex]I’m trying to figure out how to do this one ! It’s kind of got me stuck
Answers
ANSWER :
The answer is Option 3.
EXPLANATION :
From the problem, we have the equation of the line :
[tex]y=x+3[/tex]First thing to do is check the correctness of the table.
The given values in the table must satisfy the equation.
For Option 1.
Let's check the point (2, 3)
[tex]\begin{gathered} y=x+3 \\ 3=2+3 \\ 3=5 \\ \text{ False!} \end{gathered}[/tex]For Option 2.
Let's check the point (-2, 1)
[tex]\begin{gathered} y=x+3 \\ 1=-2+3 \\ 1=1 \\ \text{ True!} \end{gathered}[/tex]But the point (-2, 1) is not in the graph, so this is false!
For Option 3.
The points are the same with Option 2, so we need to check the graph.
(-2, 1) is on the graph.
(-1, 2) is on the graph.
(0, 3) is on the graph.
(1, 4) is on the graph.
(2, 5) is on the graph.
So this must be the correct table and graph.