Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below. x – y = 7 3x – 2y = 8 Step 1: x = y + 7 Step 2: 3(y + 7) – 2y = 8 Step 3: 3y + 7 – 2y = 8 Step 4: y + 7 = 8 Step 5: y = 1 In which step did Ernesto make the first error?
Answer:
answer C
Step-by-step explanation:
The table shows the estimated number of deer living in a forest over a five-year period. Which type of function best models the data? Write an equation to model the data. Year Estimated Population 0 100 1 79 2 62 3 49 4 39
We are given the following data:
Year Estimated Population
0 100
1 79
2 62
3 49
4 39
Just by looking at the data we can see that the relationship of year and estimated population is not linear. The decrease in the population does not follow a linear path, that is:
79 – 100 is not equal to 62 – 79
-21 is not equal to -17
Therefore, the relationship must be exponential. Let us find the common ratio by dividing the population in year 1 and year 0:
common ratio, r = 79 / 100 = 0.79
This means that the population decreases by 21% every year.
So the model for this data can be written as:
yn = y0 * r^n
Where,
yn = is the population after n years
y0 = initial population
r = growth rate = decreasing
n = number of years
(05.01)A company makes triangular plates for individual slices of pizza. For each plate, the base is 9 inches and the height is 14 inches. The area of the top of the plate is ____ inches squared.
Answer:
63
Step-by-step explanation:
Solve the following system. 4x2 + 9y2 =72 x2 - y2 = 5 The solutions are (), (), (), and () (remember to include the commas) there has to be 4 solutions all ordered pairs please help
Answer: The required solutions are
[tex](x,y)=(3,2),~(-3,2),~(3,-2),~(-3, -2).[/tex]
Step-by-step explanation: We are given to solve the following system of equations:
[tex]4x^2+9y^2=72~~~~~~~~~~~~~~~~~~~~(i)\\\\x^2-y^2=5~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Let us consider that
[tex]x^2=a,~~~~~y^2=b.[/tex]
So, equations (i) and (ii) becomes
[tex]4a+9b=72~~~~~~~~~~~~~~~~(iii)\\\\a-b=5~~~~~~~~~~~~~~~~~~~~(iv)[/tex]
Multiplying equation (iv) by 4 and then subtracting from equation (iii), we get
[tex](4a+9b)-(4a-4b)=72-4\times 5\\\\\Rightarrow 4a+9b-4a+4b=72-20\\\\\Rightarrow 13b=52\\\\\Rightarrow b=4.[/tex]
From equation (iv), we get
[tex]a-b=5\\\\\Rightarrow a-4=5\\\\\Rightarrow a=9.[/tex]
Therefore,
[tex]a=9~~~~~\Rightarrow x^2=9~~~~~\Rightarrow x=\pm3,\\\\b=4~~~~~\Rightarrow y^2=4~~~~~\Rightarrow y=\pm2.[/tex]
Thus, the required solutions are
[tex](x,y)=(3,2),~(-3,2),~(3, -2),~(-3, -2).[/tex]
I am a number between 30 and 50 . I am a multiple of 8. My greatest common factor with 25 is 5 what number am I ?
You invest $300 in an account at 7.5% per year simple interest. How much will you have in the account at the beginning of the 11th year
By investing $300 at a 7.5% per year simple interest rate, the accrued interest over 11 years is $247.50. Adding this to the initial investment, the total in the account at the beginning of the 11th year will be $547.50.
To determine how much you will have in an account at the beginning of the 11th year with simple interest, you can use the formula for simple interest:
Simple Interest (I) = P × r × t
Where:
P is the principal amount ($300)r is the annual interest rate (7.5% or 0.075)t is the time in years (11 years)Let's calculate the simple interest first:
I = 300 × 0.075 × 11I = 247.50So, the interest earned over 11 years is $247.50. Now, add this to the principal amount to get the total amount in the account at the beginning of the 11th year:
Total Amount = Principal + Interest
Total Amount = 300 + 247.50
Total Amount = 547.50
(Write the rate as a fraction, then find each unit rate.)
A wheel rotates through 1,800 degrees in 5 revolutions.
From the computation, the rate per revolution will be 360°.
From the information given, it was stated that the wheel rotates through 1,800 degrees in 5 revolutions.
Therefore, the rate per revolution will be:
= 1800/5
= 360°
Therefore, the rate per revolution is 360°.
Learn more about fractions on:
https://brainly.com/question/10528412
The following data points represent the number of chicken nuggets on each family member's plate. 1, 3, 0, 6? If the mean of the data set is 3 chicken nuggets, find the missing number of chicken nuggets.
The missing number of chicken nuggets will be 5.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
The following data points represent the number of chicken nuggets on each family member's plate.
1, 3, 0, 6, x
If the mean of the data set is 3 chicken nuggets. Then the missing number of chicken nuggets is calculated as,
3 = (1 + 3 + 0 + 6 + x) / 5
15 = 10 + x
x = 5
The missing number of chicken nuggets will be 5.
More about the mean link is given below.
https://brainly.com/question/521501
#SPJ2
What is the slope of a line that is perpendicular to the line whose equation is 7x−3y=107x−3y=10?
The longest straight line that can be drawn to connect two point on the circumference of a circle whose radius is 9 inches is
Answer:
18 inches.
Step-by-step explanation:
We can connect two points of a circle in many ways, as you can see in the picture below.
The longest straight line that you can draw to connect two points is the diameter, that is, the straight line that passes through the center of the circle.
If the circle has 9 inches of radius the diameter will be 9+9 = 18 inches.
which of the following describes the quotient of 2 and -12?
NEED HELP ASAP DUE TOMORROW AND ITS REALLY LATE WHERE I AM
How much is Pete's 12% commission on $50,00 in sales
Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection?
ANSWER- 0.1(175-n)+0.05n=13.30
Answer:
The equation we can use is 0.1(175-n)+0.05 n=13.30
Step-by-step explanation:
Number of Dimes= d
Number of Nickels= n
n+d=175, so d=175-n
The value of the dime is $0.10 and the value of each nickel is $0.05 and the whole collection is worth $13.30, so
0.1 d+0.05 n=13.30
Replacing
0.1(175-n)+0.05 n=13.30 this is the equation we have to use to get the number of nickels.
Question 4(Multiple Choice Worth 5 points)
(05.03 MC)A graph is shown below:
A graph is shown. The values on the x axis are 0, 3, 6, 9, 12, and 15. The values on the y axis are 0, 9, 18, 27, 36, and 45. Points are shown on ordered pairs 0, 36 and 3, 27 and 6, 18 and 9, 9 and 12, 0. These points are connected by a line
What is the equation of the line in slope-intercept form?
y = 36x − 3
y = −3x + 36
y = −3x + 12
y = −12x + 3
Answer:
y = -3x + 36
Step-by-step explanation:
first let's start with a formula.
y = mx + b
m equals the slope and b equals the y intercept.
slope can also be indetified as a rate of change.
so, looking at the graph we can see that the y intercept is (0, 36) or 36 and the rate of change is 3 subtracted.
sorry if this is wrong im not too sure myself. and sorry this is 5 years late, but alas it's too late to turn back now since i have already wrote all this.
Simplify by combining like terms: -18 + 3 (5x - 2) + 8
A television costs $270.25 including 15% tax. How much of cost is the tax
Final answer:
The tax on the television is $35.25.
Explanation:
To find the amount of tax, we first need to determine the original cost of the television. Since the total cost, including tax, is $270.25, we can set up the equation:
$270.25 = x + 0.15x
Where x is the original cost of the television. Combining like terms, we get:
$270.25 = 1.15x
To solve for x, divide both sides of the equation by 1.15:
x = $270.25 ÷ 1.15
Using a calculator, we find that x is approximately $235.00. Therefore, the tax on the television is:
$270.25 - $235.00 = $35.25
A jacket costs $35 and has an 8 percent tax rate. Which expression will find the cost of the tax on the jacket
I need help with #46!!!!
Remark
There are two formulas for doing this. I'll use the one that does not involve the slope. I think it will be easier for you to understand.
Step One
Decide which point is (x1,y1)
Since point P is 2/5 the way up from point A, we will call (x1,y1) point A
Step Two
Write the givens.
Point(A) = (-2,-3)
Point(B) = (3,2)
Step Three
Write the formula
x1 + ratio*(x2 - x1), y1 + ratio(y2 - y1)
Sub and solve.
-2 + 2/5 *(3 - - 2) , -3 + 2/5*(2 - -3)
-2 + 2/5(5) , - 3 + 2
-2 + 2 , - 1
P = (0 , - 1) <<<<<< Answer
If this turns out to be incorrect please notify me.
What is the coefficient of y in the expression 3 ⋅ 4 + 5y?
5
9
12
17
best answer will get brainiest!!!!!
According to the chart, from 1976-1986, unintentional drug overdose deaths per 100,000 population stayed relatively stable. The numbers for each year are, roughly, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2. What is the mean of these statistics?
Answer: 1.09
Step-by-step explanation:
Given that according to a chart from 1976-1986, unintentional drug overdose deaths per 100,000 population stayed relatively stable.
The numbers for each year are, roughly, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2.
We know that mean =[tex]\frac{\text{sum of all data values}}{\text{number of data values}}[/tex]
[tex]\\\Rightarrow\text{Mean}=\frac{1+1+1+1+1+1+1+1+1+1+2}{11}\\=\frac{12}{11}=1.09[/tex]
Thus the means of these statistics= 1.09
if PA=14 and PD=10 what is the length of PC
To find the length of PC when PA=14 and PD=10, apply the cosine rule formula in trigonometry.
The length of PC can be calculated using trigonometry and the given information.
Since PA=14 and PD=10, we can use the cosine rule to find the length of PC.Applying the cosine rule formula, PC = √(PA2 + PD2 - 2*PA*PD*cos(θ)).Calculate the length of PC by substituting the values: PC = √(142 + 102 - 2*14*10*cos(θ)).what is the probability of flipping a coin 10 times and getting tails8 times? Round your answer to the nearest tenth of a percent
Answer:
4.4%
Step-by-step explanation:
Walter had 2/4 yard of string. He used 3/6 of it on a school project. How much string did he use?
2/4 reduces to 1/2
3/6 reduces to 1/2
so he used 1/2 of 1/2 yard
1/2 * 1/2 = 1/4
he used 1/4 yard
How can the order of operations be used to simplify expressions?
First right answer gets brain
How to solve 19-4c=17?
True or False: Every Student's t-distribution with n < N, n the number in the sample and N the number in the population, will be less peaked and have thinner tails.
The statement is false as the Student's t-distribution is actually more peaked and has thicker tails with smaller sample sizes, and it becomes similar to the standard normal distribution as the sample size, and consequently the degrees of freedom, increase.
Explanation:The statement that every Student's t-distribution with n < N, where n is the sample size and N is the population size, will be less peaked and have thinner tails is false. In reality, the t-distribution is more peaked and has thicker tails when the sample size is smaller, which happens due to the reduced degrees of freedom (df).
The shape of the Student's t-distribution is determined by the degrees of freedom, which is n - 1 for a sample size n. As n approaches the population size N, the t-distribution approaches the standard normal distribution. This is further supported by the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample means tends to be normal. Therefore:
The statement in the question is false; the t-distribution becomes less peaked and has thicker tails as the degrees of freedom decrease.
Explanation:The Student's t-distribution is a probability distribution that is used when the sample size is small and the population standard deviation is unknown. It is similar to the standard normal distribution, but has thicker tails and less probability in the center. As the degrees of freedom increase, the t-distribution approaches the standard normal distribution. Therefore, the statement in the question is false. The t-distribution becomes less peaked and has thicker tails as the degrees of freedom decrease.
(k^3-8k^2+16k-5)/(k-5)
please use the "dividing polynomials format WILL GIVE BRAINIEST
if you do not use this format you will not become brainliest
Why do some merchants, particularly smaller businesses, set a minimum purchase of $10 for any credit card transaction, or simply refuse to take any sort of bank card from consumers?
Answer:
Just look at the one above me
Step-by-step explanation:
If x = 49 , what is the value of x(x-10)
replace 49 for x so
x(x-10) becomes 49(49-10) =
49*39 = 1911