Answer:
2x - 5y = 9 // standard form
y + 6 = -3 (x-1) // point slope form
y = -x + 8 // slope intercept form
Step-by-step explanation:
Two dataset in descending order (8,x,4,1) and (9,y,5,2). If the median is equal, find (y-x)
Answer:
y-x = -1
Step-by-step explanation:
Given the two dataset;
(8,x,4,1) and (9,y,5,2)
Since they are already arranged in descending order;
The median for the first dataset is;
M1 = (x+4)/2
The median for the second dataset is;
M2 = (y+5)/2
The median is equal;
M1 = M2
(x+4)/2 = (y+5)/2
x+4 = y+5
Collecting the like terms;
4-5 = y-x
y-x = -1
The value of 49% of 86 should be just a little over 43.
True
- False
Answer:
False
Step-by-step explanation:
50% of 86 would be 43, 49% would be a bit lower then that.
Answer:
False, Its 42.14
Step-by-step explanation:
What is 49 percent of 86: 49 percent *86 = (49:100)*86 = (49*86):100 = 4214:100 = 42.14. Now we have: 49 percent of 86 = 42.14
What is the answer to the series of equations
Answer:
[tex]71\frac{2}{3}[/tex]
Step-by-step explanation:
1st equation:
3 cups = 3x
3x = 75
x = 25, cup = 25
2d equation
25 + lemon* lemons= 25 + y²
25 + y² = 89
y²= 89 - 25
y²= 64
y = 8, lemon = 8
3d equation
3 circles = 3c
3c = 44
c = 44/3 = 14 2/3
4th equation
25 + 32 + 14 2/3 = 71 2/3
Answer: 427/3
Step-by-step explanation:
The 3 cups added together is equal to 75, therefore, we can establish that each cup is equal to 25.
Cup=25
With the second equation, we plug in 25 for the cup and solve for the circles.
25+ Ο×Ο= 89
Ο×Ο=64
Circle=8
For the third equation, we can find the amount for the ovals if we divide by 3.
Oval= 44/3
Now that we know the value of each picture, we can solve the fourth equation.
25+8×(44/3)=?
25+(352/3)=?
(75/3)+(352/3)=427/3
A sheriff is interested in the average speed that people drive on Highway 50. Match the vocabulary word with its corresponding example.
Answer:
1. Statistics
2. Sample
3. Population
4. Variable
5. Data
6. Parameter
Step-by-step explanation:
1. Statistics is the mean of the sample taken - The average speed that the 250 randomly selected drivers drove on Highway 50
2. Sample is the representative part of the population - The 250 randomly selected drivers who were on Highway 50
3. Population is the group of people from which the sample was taken - All people who drive on Highway 50
4. Variable is a quantity that has values which differ - The speed that a driver drives on Highway
5. Data is information obtained used for a specific purpose - The list of the 250 speeds that the drivers studied drove
6. Parameter is the mean of a population - The average speed that all drivers go on Highway 50
Please include work! :)
Answer:
m = 13.
Step-by-step explanation:
Recall that adding logarithmic equations, (ex: log a + log b) is the same as log (a·b). Therefore:
log 12 + log 5 = log (4m + 8)
log (12·5) = log (4m + 8)
log (60) = log (4m + 8) **Ignore 'Log' to solve for 'm'
60 = 4m + 8 **Subtract both sides by 8
52 = 4m **Divide both sides by 4
m = 13.
Consider reflection of JKL what line of reflection maps point L to point L at (-2,3)
It’s the y-axis for the first answer and the other one it’s a reflection of JKL what line of reflection maps point L to point L at (-2,3).
What is the line of reflection?When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a fixed-line. The fixed-line is called the line of reflection.
What reflection will produce an image of RST?RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC.
Learn more about the line of reflection at
https://brainly.com/question/8496129
#SPJ2
A county is in the shape of a rectangle that is 60 miles by 70 miles and has a population of 50,000. What is the average number of people living on each square mile of the county? Round your answer to the nearest whole number.
192
10
14
12
Answer:
The correct answer is:
12
Step-by-step explanation:
Length of county = 70 miles
breadth of county = 60 miles
area of county (rectangle) = Length × Breadth = 60 × 70 = 4,200 sqaure miles
population of county = 50,000
Therefore, to find the average number of people living on each square mile of the county, we will assume that the whole population is equally distributed in the county, hence the population per square mile is calculated thus:
Total area = 4,200 square miles
total population = 50,000
This means that:
4,200 square miles contains 50,000 people
4,200 sq. miles = 50,000 people
∴ 1 sq. mile = 50,000 ÷ 4,200 = 11.9 = 12 people (to the nearest whole number)
therefore number of people living per square mile = 12
Answer:
12
Step-by-step explanation:
Got it right on the test! <3
The telephone company charges $1.35 fir the first 3 minutes of a phone call and $0.35 for each additional minute. i talk on the phone from 4:17 pm till 4:31 pm. what will the phone call cost?
Answer:
$5.20
Step-by-step explanation:
Talked on the phone for 14 minutes .
14 - 3 = 11
11 x .35 = 3.85
3.85 + 1.35 = 5.2
Answer:
The answer is $5.20
Step-by-step explanation:
HOPE THIS HELPSSSSSS:)))))
Select the number line that matches the expression |8-1|
Answer:
B
Step-by-step explanation:
We start at point 8 and go to point 1
Solve these equations. Thanks.
Answer:
1. 3.572 x 10^(-1)
2. 3.108 x 10^(6)
3. 5.31881533 x 10^(-6)
4. 4.18676122 x 10^(-1)
Hope this helps
Explain your answer choice with sentences or record your explanation.
Which expression is equivalent to n + n - 0.18n?
A. 1.18n
B. 1.82n
C. n – 0.18
D. 2n – 0.82
Answer:
B. 1.82n
Step-by-step explanation:
Expression given: n + n - 0.18n
Adding n+n gives '2n'
then subtracting 0.18n from 2n gives= 1.82 n
Therefore,
n + n - 0.18n=0.18n
Keri deposits $100 in an account every year on the same day. She makes
no other deposits or withdrawals. The account earns an annual rate of 4%
compounded annually. How much interest does it earn on the 2nd year?*
Answer:
$20.32 or $12.16 depending on the question below!
Step-by-step explanation:
$320.32
It's a bit ambiguous, the current Principal is $100 plus 2 $ additions of $100 or the current Principal is $0 plaus 2 years of $100 contributions. In this case it's $212.16
How many terms are in the expression below?
3x + 4x - 3
In the expression, there are 3 terms.
3x and 4x are like terms because the variables are identical.
Also, we have a constant term which is -3.
Will mark BRAINLIEST thank you!
Answer:
The above mentioned answer is wrong
Correct answer is option b)14000
Step-by-step explanation:
By the rule of front-end estimation
719 is estimated as 700
And 26 is estimated as 20 .
The product of 719 and 26 is estimated by multiplying 700 and 20.
The product of 700 and 20 is 14000
Hence the correct answer is option b) 14000
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
Find the value of x.
Answer:
x=4
Step-by-step explanation:
Answer:
√21 or 4.58
Step-by-step explanation:
area of triangle can be found in different ways, and they are equal as:
1/2*x*(7+3)= 1/2*√(x²+3³)*√(x²+7²)
(10x)²= (x²+3³)*(x²+7²)
x²= y
100y= (y+9)(y+49)y²+58y+9*49-100y=0y²-42y +441=0y=21x²=21
x=√21 = 4.58
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 5 − x 2 . What are the dimensions of such a rectangle with the greatest possible area?
Answer:
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola
y=5−x^2. What are the dimensions of such a rectangle with the greatest possible area?
Width =
Height =
Width =√10 and Height [tex]= \frac{10}{4}[/tex]
Step-by-step explanation:
Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1)
are (h,k) and (-h,k).
Hence, the area of the rectangle will be (h + h) × k
Therefore, A = h²k ..... (2).
Now, from equation (1) we can write k = 5 - h² ....... (3)
So, from equation (2), we can write
[tex]A =h^{2} [5-h^{2} ]=5h^{2} -h^{4}[/tex]
For, A to be greatest ,
[tex]\frac{dA}{dh} =0 = 10h-4h^{3}[/tex]
⇒ [tex]h[10-4h^{2} ]=0[/tex]
⇒ [tex]h^{2} =\frac{10}{4} {Since, h≠ 0}[/tex]
⇒ [tex]h = ±\frac{\sqrt{10} }{2}[/tex]
Therefore, from equation (3), k = 5 - h²
⇒ [tex]k=5-\frac{10}{4} =\frac{10}{4}[/tex]
Hence,
Width = 2h =√10 and
Height = [tex]k =\frac{10}{4}.[/tex]
In an agricultural study, the average amount of corn yield is normally distributed with a mean of 189.3 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 180 bushels of corn per acre?
Answer:
About 786 would be expected to yield more than 180 bushels of corn per acre
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 189.3, \sigma = 23.5[/tex]
Proportion of acres with more than 180 bushels of corn per acre:
This is 1 subtracted by the pvalue of Z when X = 180. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 189.3}{23.5}[/tex]
[tex]Z = -0.4[/tex]
[tex]Z = -0.4[/tex] has a pvalue of 0.3446.
1 - 0.3446 = 0.6554
Out of 1200:
0.6554*1200 = 786.48
About 786 would be expected to yield more than 180 bushels of corn per acre
y = -x2 + 6x - 5 whats
the axis of symmetry.
Answer:
x=3
Step-by-step explanation:
graphed on desmos.com
Given the functions f(x) = 6x + 11 and g(x) = x^2 + 6, which of the following functions represents f[g(x)] correctly?
Answer:
6x^2+47
Step-by-step explanation:
You simple have to "plug" g(x) into f(x) for x.
f(x)=6x+11
f(g(x))=6(x^2+6)+11
f(g(x))=6x^2+36+11
f(g(x))=6x^2+47
Find the exact coordinates of point E.
Answer:
is the correct answer.
Step-by-step explanation:
We are given that co-ordinates of D is (-3,8) and F is (5,2).
For finding a point E on the line segment DF dividing it in a ratio 4:1, we can use segment formula.
[tex]x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}[/tex]
Where [tex](x,y)[/tex] is the co-ordinate of the point which
divides the line segment joining the points and in the ratio m:n.
As per the given values
[tex]x_{1} = -3\\x_{2} = 5\\y_{1} = 8\\y_{2} = 2[/tex]
Putting the given values in above formula :
x-co-ordinate of F:
[tex]x = \dfrac{5 \times 4 + (-3 \times 1)}{4+1}\\\Rightarrow \dfrac{17}{5}\\\Rightarrow x = 3.4[/tex]
y-co-ordinate of F:
[tex]y = \dfrac{4 \times 2 + 1 \times 8}{4+1}\\\Rightarrow \dfrac{16}{5}\\\Rightarrow y = 3.2[/tex]
So, answer is [tex]E(3.4,3.2)[/tex].
Which point on the number line represents the product of 4 and -2.
Answer:
A: -8
Step-by-step explanation:
4 * -2 is -8, and A is on that point.
Answer:
its a I literally just did it
Step-by-step explanation:
What is another way to write the equation StartFraction 7 over 8 EndFraction x + three-fourths = negative 6?
Answer:
1/8 x + 3/4 = -6
Step-by-step explanation:
If you want to solve this as well:
1/8 x = -5 3/4
x = -42
Answer:
B
Step-by-step explanation:
What’s the correct answer for this?
Answer
D.
Explanation
mIH = 44
mIJ = 46
mJK = 77
ADDING THEM ALL TO FIND THE MEASURE OF m<HOK
<HOK = 44+46+77
<HOK = 167°
You bought a sachet water machine from Indie Inc. The cost of the machine was GH¢35,000. At that time, you asked for the payment to be deferred, and a contract was written. Under the contract, you could delay paying for the sachet water machine if you purchased the material for packaging the water from Indie Inc. You will then pay for the machine in a lump sum at the end of 2 years, with interest at a rate of 2% per quarter-year. According to the contract, if you ceased buying the packaging material from Indie Inc. at any time prior to 2 years, the full payment due at the end of 2 years would automatically become due. One year later, you decided to buy the packaging material elsewhere and stopped buying from Indie Inc., whereupon Indie Inc., per the contract terms, asked for the full payment that is due at the end of 2 years to be paid immediately. You were unhappy about this, so Indie Inc. offered as an alternative to accept the GH¢35,000 with interest at 10% per semiannual period for the 12 months that you had been buying the packaging material from Indie Inc. Which of the alternatives should you accept? Explain.
Answer: The answer has been attached below
Step-by-step explanation:
From the attached calculation, the amount payable in the first payment is cheaper than the amount payable for the second payment.
If both alternatives were presented to me by Indie incorporation after purchasing a sachet water machine from them, I'll choose the first method of payment.
Kindly check the attached file for the calculation which prompted the decision taken.
In 2011, the industries with the most complaints to the Better Business Bureau were banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships (USA Today, April 16, 2012), The results for a sample of 200 complaints are contained in the DATAfile named B8B. Click on the datafile logo to reference the data. a. Construct a frequency distribution for the number of complaints by industry, Category Bank 26 Cable Car Cell 42 60 Collection 28 Total b. Using α = .01, conduct a hypothesis test to determine if the probability of a complaint is the same for the five industries. The test-statistic is p-value- What is your conclusion?c. Which industry has the most complaints?
Answer:
Step-by-step explanation:
Hello!
The variable of study is
X: number of complaints per industry (Categorized: Bank, Cable, Car, Cell, Collection
Considering this is a categorical variable, and the hypothesis is that all categories have the same probability, you have to apply a Chi-Square Goodness to Fit test.
Observed frequencies per category
1) Bank: 26
2) Cable: 44
3) Car: 42
4) Cell: 60
5) Collection: 28
Total= 200
Statistical hypotheses:
H₀: P₁=P₂=P₃=P₄=P₅=1/5
H₁: At least one of the proposed proportions is different.
α: 0.01
[tex]X^2= sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}[/tex]
For this test the formula for the expected frequencies is:
[tex]E_i= n * P_i[/tex]
So the expected values for each category is:
[tex]E_1= n * P_1= 200*1/5= 40[/tex]
[tex]E_2= n * P_2= 200*1/5= 40[/tex]
[tex]E_3= n * P_3= 200*1/5= 40[/tex]
[tex]E_4= n * P_4= 200*1/5= 40[/tex]
[tex]E_5= n * P_5= 200*1/5= 40[/tex]
[tex]X^2_{H_0}= \frac{(26-40)^2}{40} +\frac{(44-40)^2}{40} +\frac{(42-40)^2}{40} +\frac{(60-40)^2}{40} +\frac{(28-40)^2}{40} = 11.5[/tex]
This test is one tailed and so is its p-value, under a Chi-square with 4 degrees of freedom p-value: 0.021484.
The p-value is less than the significance level so the decision is to reject the null hypothesis.
c. The industry with most complaints is the cellular phone providers
I hope this helps!
One-fourth If a scale factor of 1/4 is used to make a reduction, what is the base of the reduced triangle? ______ cm
Answer:
8 cm
Step-by-step explanation:
1/4 of 32 cm is (32/4) cm = 8 cm
The base of the reduced triangle is 8 cm.
Answer:
8 cm
Step-by-step explanation:
I just got it right on edge :) ur welcome
Please I could really use some help on this (50 points, 5 stars and Brainliest)
Aunt Ga Ga gave you $5,500 to save for college. You deposit the money in a savings account that earns 4% annual interest, compounded quarterly. (Show your work for each question)
a. Write an exponential function to model this situation. Define your variables.
b. What will the value of the account be after 2 years?
c. how long would it take the account to be worth $10,000?
Answer:
(a)[tex]A(n)=5500(1.01)^{4n}[/tex]
(b)$5955.71
(c)15.02 years
Step-by-step explanation:
For an initial principal P deposited in an account at an annual interest r compounded for a number of period k, the amount in the account after n years is given by the model:
[tex]A(n)=P(1+\dfrac{r}{k})^{nk}[/tex]
(a)Aunt Ga Ga gave you $5,500 to save for college.
P=$5,500
Annual Interest, r=4%=0.04
Since interest is compounded quarterly, Number of Periods, k=4
Therefore, an exponential function modeling this situation is:
[tex]A(n)=5500(1+\dfrac{0.04}{4})^{4n}\\A(n)=5500(1+0.01)^{4n}\\$Simplified\\A(n)=5500(1.01)^{4n}[/tex]
(b)After 2 years, i.e. when n=2
[tex]A(2)=5500(1.01)^{4*2}\\=\$5955.71[/tex]
(c)When A(n)=$10000, we have:
[tex]10000=5500(1.01)^{4n}\\$Divide both sides by 5500\\(1.01)^{4n}=\dfrac{10000}{5500} \\$To solve for n, we change to logarithm form\\Log_{1.01}\dfrac{10000}{5500}=4n\\= \dfrac{ Log \dfrac{10000}{5500}}{Log 1.01}=4n\\4n=60.08\\n=60.08 \div 4\\n=15.02\\$Therefore, in 15.02 years, the account would be worth $10,000.[/tex]
What’s the correct answer for this question?
Answer:
C.°
Step-by-step explanation:
According to the theorem , "Angles in the same segment are congruent"
So
m<D = 55°
The driver of a car traveling along a straight, flat road applies the brakes, which produce a constant acceleration ofspace a (t )thin space equals space minus 20 space f t divided by s e c squared. If the car is traveling at 80 feet per second when the driver applies the brakes, how far does the car travel between the time the brakes are applied and the time the car comes to a stop
Answer:
x = 160 ft
Step-by-step explanation:
The distance traveled by the car between the time the brakes are applied and the time the car comes to a stop is given by:
[tex] v_{f}^{2} = v_{0}^{2} + 2ax [/tex]
Where:
[tex]v_{f}[/tex]: is the final speed of the car = 0 (since it stops)
[tex]v_{0}[/tex]: is the initial speed of the car = 80 ft/s
a: is the acceleration of the car = -20 ft/s²
x: is the distance recorred by the car
The distance traveled by the car between the time the brakes are applied and the time the car comes to a stop is:
[tex] x = \frac{v_{f}^{2} - v_{0}^{2}}{2a} = \frac{0 - (80 ft/s)^{2}}{2*(-20 ft/s^{2})} = 160 ft [/tex]
Therefore, the car travels 160 ft between the time the brakes are applied and the time the car comes to a stop.
I hope it helps you!
The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1600 and the standard deviation is $100. What is the approximate percentage of buyers who paid more than $1900? What is the approximate percentage of buyers who paid less than $1400?What is the approximate percentage of buyers who paid between $1400 and $1600?What is the approximate percentage of buyers who paid between $1500 and $1700?What is the approximate percentage of buyers who paid between $1600 and $1700?What is the approximate percentage of buyers who paid between $1600 and $1900?
Answer:
(a) 0.14%
(b) 2.28%
(c) 48%
(d) 68%
(e) 34%
(f) 50%
Step-by-step explanation:
Let X be a random variable representing the prices paid for a particular model of HD television.
It is provided that X follows a normal distribution with mean, μ = $1600 and standard deviation, σ = $100.
(a)
Compute the probability of buyers who paid more than $1900 as follows:
[tex]P(X>1900)=P(\frac{X-\mu}{\sigma}>\frac{1900-1600}{100})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid more than $1900 is 0.14%.
(b)
Compute the probability of buyers who paid less than $1400 as follows:
[tex]P(X<1400)=P(\frac{X-\mu}{\sigma}<\frac{1400-1600}{100})[/tex]
[tex]=P(Z<-2)\\=1-P(Z<2)\\=1-0.97725\\=0.02275\\\approx 0.0228[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid less than $1400 is 2.28%.
(c)
Compute the probability of buyers who paid between $1400 and $1600 as follows:
[tex]P(1400<X<1600)=P(\frac{1400-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1600-1600}{100})[/tex]
[tex]=P(-2<Z<0)\\=P(Z<0)-P(Z<-2)\\=0.50-0.0228\\=0.4772\\\approx 0.48[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1400 and $1600 is 48%.
(d)
Compute the probability of buyers who paid between $1500 and $1700 as follows:
[tex]P(1500<X<1700)=P(\frac{1500-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1700-1600}{100})[/tex]
[tex]=P(-1<Z<1)\\=P(Z<1)-P(Z<-1)\\=0.84134-0.15866\\=0.68268\\\approx 0.68[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1500 and $1700 is 68%.
(e)
Compute the probability of buyers who paid between $1600 and $1700 as follows:
[tex]P(1600<X<1700)=P(\frac{1600-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1700-1600}{100})[/tex]
[tex]=P(0<Z<1)\\=P(Z<1)-P(Z<0)\\=0.84134-0.50\\=0.34134\\\approx 0.34[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1600 and $1700 is 34%.
(f)
Compute the probability of buyers who paid between $1600 and $1900 as follows:
[tex]P(1600<X<1900)=P(\frac{1600-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1900-1600}{100})[/tex]
[tex]=P(0<Z<3)\\=P(Z<3)-P(Z<0)\\=0.99865-0.50\\=0.49865\\\approx 0.50[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1600 and $1900 is 50%.
Answer:
Step-by-step explanation: