Answer:
3000 gallons of gasoline and 2000 gallons of kerosene
Step-by-step explanation:
The first thing is that 16 ¢ and 15 ¢ are 16 and 15 cents, therefore we can express it as $ 0.16 and $ 0.15 respectively.
Now, we can solve by means of a 2x2 system of equations, we have to:
"x" is the number of gallons of gasoline
"y" be the number of gallons of kerosene
x + y = 5000 => x = 5000 - y
0.16 * x + 0.15 * y = 780
replacing
0.16 * (5000 - y) + 0.15 * y = 780
800 - 0.16 * y + 0.15 * y = 780
-0.01 * y = 780 - 800
y = -20 / -0.01
y = 2000
Therefore x:
x = 5000 - 2000
x = 3000
which means 3000 gallons of gasoline and 2000 gallons of kerosene
Write the slope-Intercept form of the equation for the line
Answer:
Equation : y = -0.9x − 1.5
Step-by-step explanation:
Slope is rise over run, 7 over 8
-7/8 = -0.875, round to nearest tenth
-0.875 = -0.9
y- intercept is the point that crosses the y-axis,
the line crosses the y-axis at -1.5
Two angles of a triangle measure 78 and 24
Answer: 78
Step-by-step explanation: Remember every triangle ads up to a total of 180 degrees. You just have to make sure that it adds up to 180
In a lottery​ game, the jackpot is won by selecting five different whole numbers from 1 through 37 and getting the same five numbers​ (in any​ order) that are later drawn. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. Complete parts​ (a) through​ (c) below:a. What is the probability of winning a jackpot in this​ game? ​P(winning a jackpot in this ​game)= ________b. In the Pick 5 ​game, you win a straight bet by selecting five digits​ (with repetition​ allowed), each one from 0 to​ 9, and getting the same five digits in the exact order they are later drawn. What is the probability of winning this​ game? ​P(winning the Pick 55​game)= ______________c. The Pick 5 game returns ​$50,000 for a winning​ $1 ticket. What should be the return if the lottery organization were to run this game for no​ profit? ​
Answer:
The probability of winning a jackpot is [tex]P = 0.000003[/tex]
The probability of winning the pick 5 game is [tex]P_a = 0.00001[/tex]
The earning of the lottery organisation if the game were to be runed for no profit is [tex]x =[/tex]$10 000
Step-by-step explanation:
From the question
The sample size is n= 37
The number of selection is [tex]r = 5[/tex]
Now the number of way by which these five selection can be made is mathematically represented as
[tex]\left n} \atop {}} \right.C_r = \frac{n!}{(n-r)!r! }[/tex]
Now substituting values
[tex]\left n} \atop {}} \right.C_r = \frac{37!}{(37-5)!5! }[/tex]
[tex]\left n} \atop {}} \right.C_r = 333333.3[/tex]
Now the probability of winning a jackpot from any of the way of selecting 5 whole number from 37 is mathematically evaluated as
[tex]P = \frac{1}{333333.3}[/tex]
[tex]P = 0.000003[/tex]
Now the number of ways of selecting 5 whole number from 0 to 9 with repetition is mathematically evaluated as
[tex]k = 10^5[/tex]
Now the probability of winning the game is
[tex]P_a = \frac{1}{10^5}[/tex]
[tex]P_a = 0.00001[/tex]
We are told that for a $1 ticket that the pick 5 game returns $50 , 000
Generally the expected value is mathematically represented as
[tex]E(X) = x * P(X =x )[/tex]
In this question the expected value is $1
So
[tex]1 = x * 0.00001[/tex]
So [tex]x = \frac{1}{0.00001}[/tex]
[tex]x =[/tex]$10 000
What is 100 times 10
Answer:
Central graph
Step-by-step explanation:
When a function has a negative rate of change, it means that as the x value increases, the y value decreases. The only graph that does this continuously is the central one. Hope this helps!
The calculated product of the numbers is 1000
The graph with a negative rate to be (c)
How to calculate the product of the numbersFrom the question, we have the following parameters that can be used in our computation:
100 times 10
When represented as an equation, we have
100 times 10 = 100 * 10
Evaluate the products
So, we have the following result
100 times 10 = 1000
Next, we interpret the graph
From the graphs, we have the graph with a negative rate to be (c)
Using the above as a guide, we have the following:
the result is 19/125
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Jessica has to make a trip of 8925 MI. if she travels 425 miles a day how long will the trip take?
Answer:
21 days.
Step-by-step explanation:
You just divide the total number of miles by miles traveled a day.
8925÷425=21
It will takes 21 days.
Answer:21 days
Step-by-step explanation:
If you spin the spinner 90 times,
how many times should the
number 3 be selected?
Answer:
15
Step-by-step explanation:
1/6 of 90 is 15
The number of times 3 should be selected is 45/2.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We know that;
Number of spins= 90
Number of selected= 3
Now,
If the spinner has 4 equal sections and one of them has a 3, then the probability of landing on 3 is 1/4.
To find the expected number of times that the spinner lands on 3 in 90 spins, we need to multiply 1/4 by 90.
=1/4 * 90
=45/2
Therefore, by algebra the answer will be 45/2.
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11(11d+3z+8)for d = 10 and z = 12
Answer: 1,694
Step-by-step explanation: 11(11d + 3z + 8) d = 10 and z = 12
121d + 33z + 88
121(10) + 33(12) + 88
1210 + 396 + 88
1,694
the ratio of savings to expenditure is 2:8 find the savings if the expenditure is 24,000
Answer:
the savings is 6000
Step-by-step explanation:
We are told that the ratio of savings to expenditure is 2: 8, that is, that person saves 2 when he spends 8.
They tell us to find the savings when the cost is 24,000, so we are left with:
24000 * 2/8 = 6000
which means that when 24000 are spent the savings is 6000
BASE
Which angle has a positive measure?
Answer:
An angle with a positive measure will have rotated counterclockwise, or doesn't cross over itself at the start of the rotation. As you can see, the only graph that initially turns counterclockwise is the first graph.
Step-by-step explanation:
Solve xy^m=yx^3 for m
Answer:
m = 1 + 2log(x)/log(y)
Step-by-step explanation:
Taking logarithms, you have ...
log(x) +m·log(y) = log(y) +3log(x)
m·log(y) = log(y) +2·log(x) . . . . subtract log(x)
m = (log(y) +2·log(x))/log(y) . . . divide by the coefficient of m
m = 1 +2·log(x)/log(y) . . . . . . . simplify a bit*
_____
* The "simplified" form will depend on your preference. Here, I like the integer 1 brought out because most logs are irrational. The result may be very slightly more accurate if we add 1, rather than log(y)/log(y)--depending on your calculator.
n Hamilton County, Ohio the mean number of days needed to sell a home is days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of homes in a nearby country showed a sample mean of days with a sample standard deviation of days. Conduct a hypothesis test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of days in the nearby county. Round your answer to four decimal places.
Answer:
There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.
Test statistic t=-1.8974
P-value = 0.0326
Step-by-step explanation:
The question is incomplete:
"In Hamilton County, Ohio the mean number of days needed to sell a home is 86 days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of 40 homes in a nearby county showed a sample mean of 80 days with a sample standard deviation of 20 days. Conduct a hypothesis test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county. Round your answer to four decimal places."
This is a hypothesis test for the population mean.
The claim is that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=86\\\\H_a:\mu< 86[/tex]
The significance level is 0.05.
The sample has a size n=40.
The sample mean is M=80.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=20.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{20}{\sqrt{40}}=3.1623[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{80-86}{3.1623}=\dfrac{-6}{3.1623}=-1.8974[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=40-1=39[/tex]
This test is a left-tailed test, with 39 degrees of freedom and t=-1.8974, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.8974)=0.0326[/tex]
As the P-value (0.0326) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.
You purchased a rare painting for $150 that is increasing in value by 3% annually. How many years will it take until it is doubled in value? Round to the nearest whole year
Answer:
23 years.
Step-by-step explanation:
It is given that the initial price of painting is $150 and its values increasing by 3% annually.
We need to find how many years will it take until it is doubled in value.
The value of painting after t years is given by
[tex]y=150(1+0.03)^t[/tex]
[tex]y=150(1.03)^t[/tex]
The value of painting after double is 300. Substitute y=300.
[tex]300=150(1.03)^t[/tex]
Divide both sides by 150.
[tex]2=(1.03)^t[/tex]
Taking log both sides.
[tex]\log 2=\log (1.03)^t[/tex]
[tex]\log 2=t\log (1.03)[/tex]
[tex]t=\dfrac{\log 2}{\log (1.03)}[/tex]
[tex]t=23.44977[/tex]
[tex]t\approx 23[/tex]
Therefore, the required number of years is 23.
Select all of the following that are quadratic equations. 5 x - 1 = 3 x + 8 5 x - 3 = 0 x2 - 2 x = 4 x + 1 2 x2+ 12 x = 0 x3 - 6 x2 + 8 = 0 9 x2 + 6 x - 3 = 0
Answer:
Answers are below.
Step-by-step explanation:
x2 - 2 x = 4 x + 12
x2+ 12 x = 0
x2 + 8 = 0
9x2 + 6 x - 3 = 0
These are all quadratic equations because they have x2 in all of them.
If this answer is correct, please make me Brainliest!
Answer:
x^2 - 2x = 4x + 1
2x^2 + 12x = 0
9x^2 + 6x - 3 = 0.
Step-by-step explanation:
A quadratic equation will contain a term with an exponent of 2 as the highest exponent.
In scheduling your time, which of the following will help you reach your goals?
a) Limiting the time you spend on any one task
b) Finding ways to multitask
c) Sticking to a daily routine
d) All of the above
in triangle ABC, what is the measurement of angle c? A=2x B=6x C=2x
Answer:
36 degrees
Step-by-step explanation:
This problem can be solved with the help concept of sum of angles of any triangle.
sum of angles of any triangle is 180.
Given angular value of triangle ABC is A=2x B=6x C=2x
Thus sum of A, B , C is 180
A+B+C = 180 plug in th evalue of angle A, B and C
=>2x+6x+2x = 180
=> 10x=180
=> x = 180/10 = 18
Value of angle C in terms of x is 2x
Thus angular value of angle c = 2*18 = 36 degrees.
The amount of time people spend exercising in a given week follows a normal distribution with a mean of 3.8 hours per week and a standard deviation of 0.8 hours per week.
i) Which of the following shows the shaded probability that a person picked at random exercises less than 2 hours per week?
ii) What is the probability that a person picked at random exercises less than 2 hours per week? (round to 4 decimal places)
iii) Which of the following shows the shaded probability that a person picked at random exercises between 2 and 4 hours per week?
iv) What is the probability that a person picked at random exercises between 2 and 4 hours per week? (round to 4 decimal places)
Answer:
i and iii) In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4
ii) [tex]P(X<2)=P(\frac{X-\mu}{\sigma}<\frac{2-\mu}{\sigma})=P(Z<\frac{2-3.8}{0.8})=P(z<-2.25)[/tex]
And using the normal standard table or excel we got:
[tex]P(z<-2.25)=0.0122[/tex]
iv) [tex]P(2<X<4)=P(\frac{2-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{4-\mu}{\sigma})=P(\frac{2-3.8}{0.8}<Z<\frac{4-3.8}{0.8})=P(-2.25<z<0.25)[/tex]
And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:
[tex]P(-2.25<z<0.25)=P(z<0.25)-P(z<-2.25)= 0.5987-0.0122= 0.5865[/tex]
Step-by-step explanation:
Let X the random variable that represent amount of time people spend exercising in a given week, and for this case we know the distribution for X is given by:
[tex]X \sim N(3.8,0.8)[/tex]
Where [tex]\mu=3.8[/tex] and [tex]\sigma=0.8[/tex]
Part i and iii
In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4
Part ii
We are interested on this probability:
[tex]P(X<2)[/tex]
We can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we have:
[tex]P(X<2)=P(\frac{X-\mu}{\sigma}<\frac{2-\mu}{\sigma})=P(Z<\frac{2-3.8}{0.8})=P(z<-2.25)[/tex]
And using the normal standard table or excel we got:
[tex]P(z<-2.25)=0.0122[/tex]
Part iv
We want this probability:
[tex]P(2<X<4)[/tex]
Using the z score formula we got:
[tex]P(2<X<4)=P(\frac{2-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{4-\mu}{\sigma})=P(\frac{2-3.8}{0.8}<Z<\frac{4-3.8}{0.8})=P(-2.25<z<0.25)[/tex]
And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:
[tex]P(-2.25<z<0.25)=P(z<0.25)-P(z<-2.25)= 0.5987-0.0122= 0.5865[/tex]
Estimate the range of 1,294 × 48 use a hyphen (-) to separate the two numbers
Answer:
54000-65000
Step-by-step explanation:
round the numbers first down to 1200 and 45, and multiply, then round up for the larger, like 1300 and 50 to get your answer.
All equations are identies, but not all identies are equations
True or False
ANSWER: It is false that All equations are identities, but not all identities are equations, as all identities are equations, but only some equations are identities.
HOPE THIS HELP
Which represents 236 as the sum of a whole number and a fraction? CLEAR CHECK 2+36 3+36 3+56 4+16
Question:
Which represents [tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction?
[tex]2+ \frac{3}{6}[/tex]
[tex]3 + \frac{3}{6}[/tex]
[tex]3+ \frac{5}{6}[/tex]
[tex]4+ \frac{1}{6}[/tex]
Answer:
[tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction is equivalent to [tex]2+ \frac{3}{6}[/tex]
Step-by-step explanation:
Given
Mixed Fraction: [tex]2 \frac{3}{6}[/tex]
Required
Express as the sum of a whole number and fraction.
Given that [tex]2 \frac{3}{6}[/tex] is a mixed fraction; it can be converted to the sum of a whole number and a fraction by following the steps below.
1. Convert the mixed fraction to improper fraction
[tex]2 \frac{3}{6} = \frac{(6 * 2 + 3)}{6}[/tex]
2. Split the numerator
[tex]2 \frac{3}{6} = \frac{((6 * 2) + (3))}{6}[/tex]
3. Split fraction to 2
[tex]2 \frac{3}{6} = \frac{(6 * 2)}{6} +\frac{(3)}{6}[/tex]
Simplify
[tex]2 \frac{3}{6} = \frac{(12)}{6} +\frac{(3)}{6}[/tex]
[tex]2 \frac{3}{6} = 2 + \frac{3}{6}[/tex]
Hence, [tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction is equivalent to [tex]2+ \frac{3}{6}[/tex]
Simplify the expression by combining like terms.
Write the terms in alphabetical order of the
variables.
6x - 6y + 6z + 18x - 11y + 2z
Answer:
24x - 17y + 8z
Step-by-step explanation:
How much do you need to subtract from 47/6 to make 7
Answer:
5
Step-by-step explanation:
47-5=42
42/6=7
5/6 is the number we have to subtract from 47/6 to make 7
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We have to find the number when we need to subtract from 47/6 to make 7.
Let the unknown number be x
47/6-x=7
Add x-7 on both the sides
47/6-7=x
Take LCM as 6
(47-42)/6=x
When 42 is subtracted from 47 we get 5.
5/6=x
Hence, 5/6 we have to subtract from 47/6 to make 7
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Glaucoma is a disease of the eye that is manifested by high intraocular pressure. The distribution of intraocular pressure in the general population is approximately normal with mean 16 mm Hg and standard deviation 3 mm Hg.
(a) What percentage of people have an intraocular pressure lower than 12 mm Hg?
(b) Fill in the blank. Approximately 80% of adults in the general population have an intraocular pressure that is greater than ________ (how many?) mm Hg.
Answer:
(a) 9.18% of people have an intraocular pressure lower than 12 mm Hg.
(b) 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.
Step-by-step explanation:
We are given that the distribution of intraocular pressure in the general population is approximately normal with mean 16 mm Hg and standard deviation 3 mm Hg.
Let X = intraocular pressure in the general population
So, X ~ Normal([tex]\mu=16,\sigma^{2} = 3^{2}[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X-\mu}{\sigma } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 16 mm Hg
[tex]\sigma[/tex] = standard deviation = 3 mm Hg
(a) Percentage of people have an intraocular pressure lower than 12 mm Hg is given by = P(X < 12 mm Hg)
P(X < 12) = P( [tex]\frac{ X-\mu}{\sigma } }[/tex] < [tex]\frac{ 12-16}{3 } }[/tex] ) = P(Z < -1.33) = 1 - P(Z [tex]\leq[/tex] 1.33)
= 1 - 0.9082 = 0.0918 or 9.18%
The above probability is calculated by looking at the value of x = 1.33 in the z table which has an area of 0.9082.
(b) We have to find that 80% of adults in the general population have an intraocular pressure that is greater than how many mm Hg, that means;
P(X > x) = 0.80 {where x is the required intraocular pressure}
P( [tex]\frac{ X-\mu}{\sigma } }[/tex] > [tex]\frac{ x-16}{3 } }[/tex] ) = 0.80
P(Z > [tex]\frac{ x-16}{3 } }[/tex] ) = 0.80
Now, in the z table the critical value of z which represents the top 80% of the area is given as -0.842, that is;
[tex]\frac{ x-16}{3 } } = -0.842[/tex]
[tex]x -16 = -0.842 \times 3[/tex]
x = 16 - 2.53 = 13.47 mm Hg
Therefore, 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.
Solving for Unknown Values
Use parallelogram ABCD. What are the values of x and
y?
FERTE
A
4y-3
B
x =
y =
3x-9
42
D
37
C
Answer:x=17 y=10
Step-by-step explanation:
133+103=420-___ need help
Which values are solutions to the inequality below. Check all that apply
x^2 >64
A.6
B. 8
C.11
D.-6
E.-8
F.-11
Answer:
x=8
Step-by-step explanation:
[tex]square \: both \: side \\ \sqrt{ {x}^{2} } = \sqrt{64 } \: \: \: \\ \\x = 8[/tex]
The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measured 120ft by 80ft, and the expansion will increase its area by 4,400ft^2. By how many feet should the parking lot be increased?
Answer:
20
Step-by-step explanation:
The current area is 120(80)=9600 and he want to expand it by 4400 so that the new area will be 9600+4400=14000
14000=(120+x)(80+x)
14000=9600+200x+x^2
x^2+200x-4400=0
x^2-20x+220x-4400=0
x(x-20)+220(x-20)=0
(x+220)(x-20)=0, since x is an increase it must be greater than zero so
x=20ft
(120+20)(80+20)=14000ft^2
A copy machine makes 24 copies per minute. How many copies does it make in 3 minutes and 45 seconds?
copies
Х
?
Answer:
90 copies
Step-by-step explanation:
24*3= 72
1/2*24= 12 for 30 seconds
1/2*6= 6 for 15 seconds
45/15=3
72+18= 90
What is the solution to this equation?
5x - x + 12 + 2x - 7 = 10
A. X=
15
6
B. X=
15
7
C.
X =
V01
D. x=
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x=5 (over)/6
Decimal Form:
x=0.8¯3
(Hopefully this helped you solve the problem.)
Use matrix algebra to show that if A is invertible and D satisfies ADequalsI, then Upper D equals Upper A Superscript negative 1. Choose the correct answer below. A. Left-multiply each side of the equation ADequalsI by Upper A Superscript negative 1 to obtain Upper A Superscript negative 1ADequalsUpper A Superscript negative 1I, IDequalsUpper A Superscript negative 1, and DequalsUpper A Superscript negative 1. B. Add Upper A Superscript negative 1 to both sides of the equation ADequalsI to obtain Upper A Superscript negative 1plusADequalsUpper A Superscript negative 1plusI, IDequalsUpper A Superscript negative 1, and DequalsUpper A Superscript negative 1.
Answer:
D=A^-1
Step-by-step explanation:
Given that A is invertible and matrix D satisfies AD=I
Where I is an identity matrix
D is the inverse of A
Multiply both sides of AD=I by A^-1
A^-1(.AD) =A^-1 I
A^-1 .A=I
Therefore D=A^-1
Which is the graph of r = 4 sine?
Answer:
you need to include a picture of all the graphs