Answer:
x = 32
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5/8*x+4-(3/8*x+12)=0
Step by step solution :
Step 1 :
3
Simplify —
8
Equation at the end of step 1 :
5 3
((—•x)+4)-((—•x)+12) = 0
8 8
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 8 as the denominator :
12 12 • 8
12 = —— = ——————
1 8
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3x + 12 • 8 3x + 96
——————————— = ———————
8 8
Equation at the end of step 2 :
5 (3x + 96)
((— • x) + 4) - ————————— = 0
8 8
Step 3 :
5
Simplify —
8
Equation at the end of step 3 :
5 (3x + 96)
((— • x) + 4) - ————————— = 0
8 8
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 8 as the denominator :
4 4 • 8
4 = — = —————
1 8
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
5x + 4 • 8 5x + 32
—————————— = ———————
8 8
Equation at the end of step 4 :
(5x + 32) (3x + 96)
————————— - ————————— = 0
8 8
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
3x + 96 = 3 • (x + 32)
Adding fractions which have a common denominator :
6.2 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(5x+32) - (3 • (x+32)) 2x - 64
—————————————————————— = ———————
8 8
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
2x - 64 = 2 • (x - 32)
Equation at the end of step 7 :
2 • (x - 32)
———————————— = 0
8
Step 8 :
When a fraction equals zero :
8.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
2•(x-32)
———————— • 8 = 0 • 8
8
Now, on the left hand side, the 8 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
2 • (x-32) = 0
Equations which are never true :
8.2 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
8.3 Solve : x-32 = 0
Add 32 to both sides of the equation :
x = 32
One solution was found :
x = 32
Step-by-step explanation:
A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t)=a(b)t.
Answer:
[tex] f(t) = 6000 (\frac{1}{2})^t^/^3 [/tex]
Step-by-step explanation:
Let's take the equation:
[tex] y = y_0 e^-^k^t[/tex]
Given the initial population of bacteria = 6000,
[tex] y = 6000e^-^k^t[/tex]
Population of bacteria after 3 hours is 3000.
y(3) = 3000
Thus,
[tex] 6000e^-^k^3 = 3000[/tex]
[tex] e^-^k^3 = \frac{3000}{6000}[/tex]
[tex] e^-^k^3 = \frac{1}{2}[/tex]
[tex] (e^-^k)^3 = \frac{1}{2}[/tex]
[tex] e^-^k= (\frac{1}{2})^1^/^3[/tex]
Let's substitute [tex] (\frac{1}{2})^1^/^3 [/tex] for [tex] e^-^k[/tex] in [tex] y = 6000e^-^k^t [/tex]
Therefore, we have:
[tex] 6000e^-^k^t [/tex]
[tex] = 6000 [(\frac{1}{2}) ^1^/^3]^t[/tex]
[tex] = 6000 [\frac{1}{2}] ^t^/^3 [/tex]
What’s the correct answer for this question?
Answer:
THE ANSWER OF THIS QUESTION IS CONE
Answer:
B. Cone
Step-by-step explanation:
The flashlight beam is of the shape of a cone
kojo had 1800 bags of rice in stock for sale. in January, he sold 2/3 of it. In February, he sold 3/4 of what was left.
a. what fraction of the stock of rice did he sell
(a) in February?
(b) in January and February ?
b. How many bags of rice were left unsold, by the end of February?
Answer:
Kojo had 1800 bags of rice in stock for sale.
In January, he sold 2/3 of it.
=> Number of bag he sold in January: 1800 x 2/3 = 1200
=> The number of bags of rice left: 1800 - 1200 = 600
In February, he sold 3/4 of what was left.
=> Number of bag he sold in February: 600 x 3/4 =450
=> Total number of bags he sold in January and February:
1200 + 450 = 1650
=> The number of bags of rice left at the end of February: 600 - 450 = 150
Hope this helps!
:)
How do you do this question
Step-by-step explanation:
use the formula in picture
00:00
Which of the following is a statistical question?
O
A.
00:00
How tall is Mr. Leung?
B.
00:00
What are the ages of all your cousins?
00:00
What is the formula for the volume of a cube?
D.
00:00
What is the school's address?
The correct answer is B. What are the ages of all your cousins?
Explanation:
Statistics focus on using numbers to analyze variables in a population or in a specific sample taken from this population. This means statistical questions can be answered by analyzing different features in a population. For example, you can wonder what is the time students on a class spend doing homework?.
According to this, the one that is a statistical question is "What are the ages of all your cousins?" because this question focuses on analyzing one variable or factor in a population; in this case, the ages of your cousins, which requires gathering information and then using numbers to represent and analyze this, which is the objective of statistics.
Find the sum of the series 0.1+0.05+0.025+… and also find the 11 term of seq 0.1,0.05,0.025,…
In recent commercials Toyota claimed that 80% of its vehicles sold in the past 20 years are still on the road. You work for an agency that wants to test this claim. You are willing to accept Toyota's claim unless there is statistically significant evidence that it is false. You have a limited budget, but you want to get the most accurate results you can. Describe, from beginning to end, how you would run your study. Use as many concepts you learned in this course as possible to get maximum credit. HTML EditorKeyboard Shortcuts
Answer:
Step-by-step explanation:
We have to perform one sample proportion test. To do so we have to proceed through following steps.
(1) We have to collect data about vehicle sales in last 20 years.
(2) Using random number table or random number generator or otherwise we have to select sample of vehicles from the list of sale. In this step, we have to keep an eye on the fact that sample is to be selected from all years (all of 20). Using stratified random sampling by dividing vehicles sold over different years is an effective way to do so. That means, we may divide vehicles sold into 20 homogeneous strata over 20 years and select sample from each strata.
(3) After selecting sample of vehicles we have to communicate to corresponding vehicle owners to gather information about that particular vehicle.
(4) We have to note number of vehicles which are still on the road.
Suppose, we have selected n vehicles as sample and after communicating we found that \tiny r of those are still on the road.
We have to test for null hypothesis [tex]H_0:p=0.80[/tex]
against the alternative hypothesis [tex]H_1 \neq 0.80[/tex]
Our test statistic is given
[tex]z=\frac{\hat p - p_0}{\sqrt{p_0(1-p_0)/n} }[/tex]
here,
[tex]\hat p =\frac{r}{n}[/tex]
[tex]p_0 =0.80[/tex]
[tex]z=\frac{r/n-0.80\sqrt{n} }{0.40} \\\\=2.5(\frac{r}{n} -0.8)\sqrt{n}[/tex]
We then calculate corresponding p-value.
We reject our null hypothesis if [tex]\text{p-value}<\alpha[/tex] , level of significance.
According to our obtained p-value and level of significance we proceed to certain conclusion.
The same Honey is sold in two different size jars. Large jar= 540g for £4.10 Small jar= 360g for £2.81. By considering the amount of honey per penny, work out which jar is the best value for money. Working must be shown.
Answer:
From our calculations the large jar is the best value for money because a penny buys more honey
Step-by-step explanation:
In this problem we are expected to determine which purchase of honey is the cheapest ? large jar or small jar ?.We will determine which has the best value for money using the quantity a pound can purchase.
firstly for the large jar.
if £4.10 will purchase 540g of honey then,
£1.00 will purchase xg
cross multiplying to find x will have
[tex]x=[/tex] [tex]\frac{1.00*540g}{4.10}[/tex]
[tex]x= 131.7grams[/tex]
Hence for the large jar a penny would buy 131.7g of honey
secondly for the small jar
if £2.81 will purchase 360g of honey then,
£1.00 will purchase xg
cross multiplying to find x will have
[tex]x=\frac{1.00*360g}{2.81}\\x= 128.1gram[/tex]
Hence for the small jar a penny would buy 128.1g of honey
What number is 144% of 5.19
Answer:
7.4736
Step-by-step explanation:
A = 144% of 5.19 means: A = (144/100) x 5.19 = 7.4736
Hope this helps!
Consider the polynomials p1(t) = 1 + t , p2(t) = 1 -t , and p3(t) = 2 (for all t). By inspection, write a linear dependence relation among p1, p2, and p3. Then find a basis for Span{ p1 , p2 , p3 }.
Answer:
[tex]\{p_1,p_2\}$ is a basis of Span\{p_1,p_2,p_3\}[/tex]
Step-by-step explanation:
Given the polynomials:
[tex]p_1(t) = 1 + t\\ p_2(t) = 1 -t\\p_3(t) = 2\\[/tex]
On Inspection
[tex](1+t)+(1-t)=1+1+t-t=2\\$Therefore:\\p_1(t)+p_2(t)=p_3(t)[/tex]
By the Spanning Theorem
If one vector in S is a linear combination of the others, we can delete it and get a subset (one vector smaller) [tex]S' \subseteq S[/tex] that has the same span.
Therefore, since [tex]p_3(t)=p_1(t)+p_2(t)[/tex]
[tex]Span\{p_1,p_2,p_3\}=Span\{p_1,p_2\}[/tex]
[tex]p_1$ and p_2[/tex] are linearly independent because [tex]p_1[/tex] cannot be written in terms of [tex]p_2[/tex].
Therefore, [tex]\{p_1,p_2\}$ is a basis of Span\{p_1,p_2,p_3\}$ as required.[/tex]
A linear dependence relation among the polynomials p₁, p₂, and p₃ is given as p₁ + p₂ = p₃
What is polynomial?Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
Consider the polynomials are
[tex]\rm p_1(t) = 1 + t\\\\ p_2(t) = 1 -t \\\\ p_3(t) = 2[/tex]
a linear dependence relation among p₁, p₂, and p₃ will be
Let add the p₁ and p₂, we have
1 + t + 1 -t = 2
We get the polynomial p₃.
Thus the linear relation is p₁ + p₂ = p₃
More about the polynomial link is given below.
https://brainly.com/question/17822016
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. f(x)= -(x-3)^(2)-2
Step-by-step explanation:
graphing the parabola, using the direction, vertex, focus, an axis of symmetry, we see that the direction it opens is down, like the picture shows. The vertex is at (3, -2), focus is (3,-9/4), axis of symmetry is x=3, and the directrix is y = -7/4 just as the picture shows. Therefore, A is the correct answer.
Hope this helps!!
Answer:
A. [tex]F(x)=-(x-3)^2-2[/tex]
Step-by-step explanation:
For the function F(x) to flip upside-down, there needs to be a negative sign in front. This eliminates answers "B," and "D." The function F(x) shifted 3 units to the right, meaning there needs to be a -3 being subtracted. The function also shifted downwards 2 units, meaning there's a -2 being subtracted.
This makes the correct answer be "A."
SOLVE THIS SUPER IMPORTANT EQUATION!!! Please
Answer:
a
Step-by-step explanation:
the slope is negative bec it's going from the top left to the bottom right corner(if I was negative the line would be going from the bottom left to the too right) then your y-intercept( the point that hits y when x is zero) is 120
Answer:
The correct answer would be A, y = -4/3x + 120
Step-by-step explanation:
Let us start with the y-intercept, the y-intercept is 120. The graph shows that the y-intercept is positive, but the slope is negative. B, C, D, and E are not correct due to the mis use of signs, a wrong slope, and a wrong y-intercept.
if u want to prove me wrong, then go ahead.
A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected.
Question:
For the following exercise, determine the range (possible values) of the random variable. A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected.
Answer:
Possible values are all integers from 1 to 491.
{1,2,...........491}
Step-by-step explanation:
Given:
Total number of machined parts = 500
Number that do not conform to customers requirements = 10
Number that conforms to customers requirements = 500 - 10 = 490
Since, parts are selected successively, without replacement, until a nonconforming part is obtained, the range of the random variable (number of parts selected) here will be all integers from 1 to 491 ie {1,2,...........,491}.
Here, we have a total of 490 conforming parts, and 10 non conforming parts, there must be a non-conforming part among 491 selections, considering the fact that total number of parts are 500
There will be one non-confirming part in the 491 selections and this can be determined by using the given data.
Given :
A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained.Given that the total number of parts is 500 that contains 10 that do not conform to customer requirements. So, the total number of parts that conform to customer requirements is (500 - 10) 490.
It is also given that parts are selected successively, without replacement, until a nonconforming part is obtained so, the range of the random variables is [1,491]
So, there will be one non-confirming part in the 491 selections.
For more information, refer to the link given below:
https://brainly.com/question/23044118
What is the system of equations in this problem
2.2.17
Given the function H(v) = 10v +9, find each of the following.
H(3) =
Answer:
H(3)=39
Step-by-step explanation:
H(3) =10 (3) + 9
=30 +9
=39
Hope this helps...
This equation shows how the total cost of visiting the art museum as a member is related to the number of visits c= v+7. The variable v represents the number of visits to the art museum and the variable c represents the total cost of those visits. For a member of the art museum, what is the total cost of 10 visits?
Answer:
17
Step-by-step explanation:
the amount of visits given by the problem is:
[tex]v=10[/tex]
and we have that the equation that relates the number of visits with the total cost is:
[tex]c=v+7[/tex]
where [tex]c[/tex] is the total cost for [tex]v[/tex] number of visits.
We plug into this equation the known value of visitors:
[tex]c=10+7[/tex]
and we solve this expression:
[tex]c=17[/tex]
the total cost for 10 visitors is 17.
2. If I paid $1.45 for an apple and an orange, and the apple cost 15 cents more than the orange, how much did the orange cost?
Answer:
0.80 + 0.65 = 1.45
Step-by-step explanation:
apple: 0.80
orange: 0.65
A particular state's license plates have 7 characters. Each character can be a capital letter, or a digit except for 0. How many license plates are there in which no two adjacent characters are the same
Answer:
N = 35 × 34^6
N = 54,068,154,560
Step-by-step explanation:
Given;
The license plate have 7 characters.
Each character can be a capital letter, or a digit except for 0.
There are 26 capital letters
And there are 9 digits excluding 0
The total number of possible entries in each character is;
26+9 = 35
The number of license plates in which no two adjacent characters are the same are;
For no two adjacent characters of the license plate not to be the same that is no two characters that follow each other can be the same, the number of possible entries in the adjacent characters apart from the first character would be reduced by one.
N = 35 × 34 ×34×34×34×34×34
N = 35 × 34^6
N = 54,068,154,560
Therefore, there are 54,068,154,560 possible license plates
Chef Gordie uses 250 ml of broccoli in his Vitafibermin loaf. How many liters is that?
Answer:
.250 L
Step-by-step explanation:
We know that 1 L = 1000 mL
250 mL * 1L /1000 mL = .250 L
Answer:
Step-by-step explanation:
its 1/25 or .25 liters. A milliliter (ml) is one thousandth of a liter, so 1000 ml would be 1 liter. Btw, why is he measuring broccoli in ml?
Suppose that, in a hypothesis test, the null hypothesis is in fact true. a. Is it possible to make a Type I error? Explain your answer. b. Is it possible to make a Type II error? Explain your answer.
Answer:
a. Yes
b. No
Step-by-step explanation:
In a hypothesis test, the null hypothesis is in fact true.
a. Is it possible to make a Type I error?
Yes, it is possible to make a type I error because a type I error typically occurs if the null is rejected when it is actually true.
b. Is it possible to make a Type II error?
It is not possible to make a type II error because the condition for a type II error is that the null is in fact not true but we fail to reject it.
The inverse of G(X) is a function.
A. True
B. False
Answer:
true its just a filp with the y and x and resolved
Step-by-step explanation:
The campus bookstore knows from the past several semesters that a certain elementary statistics book has a demand that is approximated by a normal distribution with a mean of 250 and a standard deviation of 40. They buy these books for $105 each and sell them to unsuspecting undergraduates at $222 each. All demand for this book is realized by the middle of the semester, at which point the bookstore bundles them up and sells them to a vendor in another country for $40 each. What is the marginal profit for a single elementary statistics book
Answer:
$117
Step-by-step explanation:
Given that:
They buy these books for $105 each and sell them to unsuspecting undergraduates at $222 each
Marginal Profit = Marginal Revenue – Marginal Cost.
Marginal Profit = $222 - $105
Marginal Profit = $117
the marginal profit for a single elementary statistics book $117
For the remaining unsold books in the middle of the semester he bundles them up and sells to vendor in another country for $40 each for which he suffers a marginal loss of $105 - $40 = $65 each
Listed below are the gross amounts (in millions of dollars) earned in box office receipts for a recent movie. The amounts are listed in order for the first 14 days of the movies release. Find the range, variance, and standard deviation of the data set. If you invested in this movie, what characteristic of the data set would you care about most, and is it a measure of center or variation? 60 58 55 53 47 45 44 43 25 25 20 18 7 5
Answer:
[tex] Range = 60-5=55[/tex]
In order to find the variance and deviation we need to find the mean with this formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \bar X =36.07 [/tex]
Now we can find the variance with the following formula:
[tex]s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
And replacing we got:
[tex] s^2=357.610[/tex]
And the standard deviation would be:
[tex] s = \sqrt{357.610}= 18.911[/tex]
For this case since the range observed is large is better to use a measure of variation in order to check the spread of the values and take a decision useful
Step-by-step explanation:
For this case we have the following dataset:
60 58 55 53 47 45 44 43 25 25 20 18 7 5
We can find the range with this formula:
[tex] Range = Max-Min[/tex]
And replacing we got:
[tex] Range = 60-5=55[/tex]
In order to find the variance and deviation we need to find the mean with this formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \bar X =36.07 [/tex]
Now we can find the variance with the following formula:
[tex]s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
And replacing we got:
[tex] s^2=357.610[/tex]
And the standard deviation would be:
[tex] s = \sqrt{357.610}= 18.911[/tex]
For this case since the range observed is large is better to use a measure of variation in order to check the spread of the values and take a decision useful
The ratio of the angles of a triangle is 3:8:4. What is the size of the largest angle?
Answer: 96°
Step-by-step explanation:
Sum of angles of a triangle = 180°
3 + 8 + 4 = 15
The biggest angle is 8/15 * 180 = 96°
What is the midpoint of the segment?
Answer:
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. hope that helps love!
What is the equation of a line , in general form, that passes through points (-1,2) and (5,2)
Answer:
y-2=0
Step-by-step explanation:
In y=mx+b
m=(y2-y1)/(x2-x1) [2]
Or another way of thinking about it is rise over run.
define point (-1,2) as x1,y1
define point (5,2) as x2,y2
substitute into formula [2]
m=(2-2)/(5-(-1))
We know that 2-2=0 therefore the slope (m) is 0
y=0x+b
Or simply
y=b
to solve for b we substitute into the formula any of the points
2=b for y1
or 2=b for y2
b=2
therefore y=2
to convert it into general form make the equation equal 0
y-2=0
Multiply. Write your answer in simplest form. 4/9 x 2/3
Answer:
8/27
Step-by-step explanation:
4/9 * 2/3
Multiply the numerators
4*2 = 8
Multiply the denominators
9*3 = 27
Put the numerator over the denominator
8/27
This is in simplest form
The difference between those graphs
Answer:
B
Step-by-step explanation:
the negative on the outside makes it a reflection over the x-axis
Answer:
b
Step-by-step explanation:
because if you say make up points the plot them then youll see there across from each other
Barry Beach was convicted of murder in 1983 and sentenced to life in prison without parole. In 2015, Governor Bullock commuted Beach's sentence after years of controversy surrounding Beach's confession, trial and subsequent conviction. A news program in Bozeman wanted to find out more about how people in Montana feel about Beach's release. The local program invited viewers to go their website and indicate their opinions. At the end of the show, 72% of people who voted in the poll indicated they agreed with Bullock's decision.
What is the population of interest?
1- All Montana residents
2- Viewers of this TV show
3- Residents of Bozeman, MT
4- Residents of Poplar, MT
Answer:
The correct answer to the following question will be Option 1 (All Montana residents).
Step-by-step explanation:
Barry Beach told journalists managed to gather next to the front main entrance of Montana federal penitentiary across lunchtime that perhaps the point in time seemed to be 'surreal.'A news broadcast in Bozeman was desperately trying to find out how and why individuals in Montana perceive and say about the official launch of Beach. It certainly indicates 'All Montana Residents' seems to be the group of people of benefit after that.Other choices aren't linked to just the scenario in question. Option 1 seems to be the perfect solution.
What is the value of x in the equation 3X minus 4Y equals 65, when Y equals four
Answer:
Step-by-step explanation:
3x-4y=65
3x=65+4y
x=(65+4y)/3, when y=4
x=(65+4*4)/3
x=(65+16)/3
x=81/3
x=27
