Based on the rate that Leon's car uses gas, the time that Leon will stop to get gas is 3:36 pm.
When will Leon stop to get gas?Leon will stop to get gas when the tank is 1/4 full which is:
= 1/4 x 12
= 3 gallons
The rate at which the car uses gas is:
= Gallons used / Time traveled
= 5 / 2
= 2.5 gallons per hour
The number of hours till he has to stop is:
= (12 gallons - 3 gallons) / 2.5
= 3.6 hours
The time that Leon will stop is:
= 12pm + 3.6 hours
= 12 pm + 3 hours 36 minutes
= 1536 hours
= 3:36 pm
Find out more on calculations involving consumption per hour at https://brainly.com/question/25049845.
#SPJ1
Can you help me please!!!!
Answer:
Irrational
Step-by-step explanation:
[tex]\sqrt{9}= 3[/tex]
3 × √3 = 3√3 which is irrational
Hope this helped and brainliest please
Product is multiplication:
√3 x √9 = 3√3 = 5.19615....
Because the fraction does not end, it is not rational.
Answer: Irrational
At 13:00, a water tank contained 180 litres of water. Water flowed from the tank at a constant rate until, at 17:30, the tank was completely empty. Calculate the rate of flow of water from the tank in litres per hour. If your answer is a decimal, give it to 1 d.p.
The drain rate is constant and thus equal to the average drain rate over the entire 4.5 hour period. This rate is
[tex]\dfrac{0 \,\mathrm L - 180 \,\mathrm L}{4.5 \,\rm h} = -40 \dfrac{\rm L}{\rm h}[/tex]
which is to say, water flows from the tank at a rate of 40 L/h.
What type of function is f(x) = 2x³ - 4x² + 5? O Exponential O Logarithmic O Polynomial O Radical
Answer:
Polynomial
Step-by-step explanation:
⇒ It cannot be option 1 as y does not vary with an exponent
⇒ It cannot be option 2 as y does not relate to any logarithmic values of x
⇒ It cannot be a option 4 as there no irrational numbers under a root
⇒ Therefore it is a polynomial, as it is written in the form : y = ax³ + bx² + cx + d (cubic polynomial)
Suppose the average age of family members is 34 with a standard deviation of 4. if 100 members of the community decided to have a summer outing bonding and relaxation, find the probability that the average of these members is less than 35?
Using the normal distribution, it is found that there is a 0.9938 = 99.38% probability that the average of these members is less than 35.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, we have that the parameters are given as follows:
[tex]\mu = 34, \sigma = 4, n = 100, s = \frac{4}{\sqrt{100}} = 0.4[/tex].
The probability that the average of these members is less than 35 is the p-value of Z when X = 35, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35 - 34}{0.4}[/tex]
Z = 2.5
Z = 2.5 has a p-value of 0.9938.
0.9938 = 99.38% probability that the average of these members is less than 35.
More can be learned about the normal distribution at https://brainly.com/question/24663213
#SPJ1
X is a normally distributed random variable with mean 46 and standard deviation 22.
What is the probability that X is between 2 and 90?
A. .99
B. .95
C. .85
D. .65
Answer:
B. 0.95
Step-by-step explanation:
The probability that the value of the random variable is in the given range is the area under the normal probability distribution curve over that range. The value of this area is conveniently provided by any number of calculators, apps, or spreadsheets. It can also be determined using the "empirical rule" that tells you the probability over certain normalized ranges.
__
normalized rangeA standard normal probability density function (PDF) has a mean of 0 and a standard deviation of 1. The range in this problem can be normalized to some number of standard deviations above or below the mean. The mean is given as 46, and the standard deviation is given as 22.
In this problem, the lower limit of the range is ...
z = (2 -46)/22 = -2
standard deviations from the mean.
Similarly, the upper limit is ...
z = (90 -46)/22 = +2
standard deviations from the mean.
empirical ruleThe empirical rule tells us that 95% of the area of the PDF lies between -2 and +2 standard deviations from the mean.
P(2 < X < 90) ≈ 0.95
_____
Additional comment
The empirical rule for other ranges is ...
± 1 standard deviation: 68%
±2 standard deviations: 95%
±3 standard deviations: 99.7%
Consider the graph of the linear function h(x) = -x + 5. Which could you change to move the graph down 3 units?
O the value of b to -3
the value of m to -3
the value of b to 2
O the value of m to 2
Intro
Done
Answer:
the value of b to 2
The value of b changes to 2.
The correct option is C.
What is Linear Equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
We have,
Equation: h(x) = -x + 5
Now, using the slope intercept form
y = mx + b
From which we get
m = -1 and b=5
Now, we need to move the graph 3 units down then we need to subtract given function by 3, we get
y = -x+5 -3
y = -x +2.
Here y-intercept is 2.
Learn more about Linear Equation here:
https://brainly.com/question/4025726
#SPJ7
How many rational numbers lie between any two fractions?
Answer:
Infinite number of rational numbers exist between any two distinct rational numbers. We know that a rational number is a number which can be written in the form of qp where p and q are integers and q =0.
How would I solve this?
Answer:
(-2, -2)
Step-by-step explanation:
the solution of the system of equation put simply is the point of intersection between the 2 lines
hence, the answer is (-2,-2)
A right circular cone is intersected by a plane that passes through the cone's
vertex and is perpendicular to its base, as in the picture below. What is
produced from this intersection?
A. A single line
B. A pair of intersecting lines
C. A point
D. A pair of parallel lines
Answer:
B. A pair of intersecting lines
Step-by-step explanation:
The attached image can give you an idea of what you get when a plane perpendicular to the base of a cone intersects the vertex of the cone.
__
In the problem statement here, we assume a double-napped cone with no defined base. That means the lines of intersection with the sides of the cone will meet at the vertex point and extend indefinitely in either direction.
The intersection is a pair of intersecting lines.
Needing help with these 2 problems
Answer:
15) 3.2
17) 13.4
Step-by-step explanation:
To find the missing lengths, you need to use the Pythagorean theorem:
a² + b² = c²
In this form, "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides.
You are trying to find one of the side lengths (not the hypotenuse) in 15). To find the other length, you can plug the other values into the equation and simplify to find "b".
15) a = 4.1 c = 5.2
a² + b² = c² <----- Pythagreom Theorem
(4.1)² + b² = (5.2)² <----- Plug values in for "a" and "c"
16.81 + b² = 27.04 <----- Raise numbers to the power of 2
b² = 10.23 <----- Subtract 16.81 from both sides
b = 3.2 <----- Take the square root of both sides
You are trying to find the hypotenuse in 17). Since you have been given the lengths of the other sides, you can plug them into the equations and simplify to find "c".
17) a = 4.4 b = 12.7
a² + b² = c² <----- Pythagreom Theorem
(4.4)² + (12.7)² = c² <----- Plug values in for "a" and "b"
19.36 + 161.29 = c² <----- Raise numbers to the power of 2
180.65 = c² <----- Add
13.4 = c <----- Take the square root of both sides
In any triangle ABC, if c=30°,b= 4, a=2 find A and B.
Using the Law of Cosines,
[tex]c^{2}=2^{2}+4^{2}-2(2)(4)(\sin 30^{\circ})\\\\c^{2}=12\\\\c=2\sqrt{3}[/tex]
Using the Law of Sines,
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}\\\\\frac{\sin A}{2}=\frac{\sin 30^{\circ}}{2\sqrt{3}}\\\\\frac{\sin A}{2}=\frac{1}{4\sqrt{3}}\\\\\sin A=\frac{1}{2\sqrt{3}}\\\\A=\boxed{\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]
So, as angles in a triangle add to 180 degrees,
[tex]B=180^{\circ}-30^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)\\\\B=\boxed{150^{\circ}-\sin^{-1} \left(\frac{1}{2\sqrt{3}} \right)}[/tex]
NEED ANSWER ASAP HELP
Given ABC with altitude h
Prove: sin(B)/b=sin(C)/c
Using the given information in the diagram, we have proven that sin(B)/b = sin(C)/c
Proving the Sine ruleFrom the question, we are to prove that sin(B)/b=sin(C)/c
Consider the right triangle with sides a, c, and h
Using SOH CAH TOA, we can write that
sin(B) = h/c
∴ h = c × sin(B) --------- (1)
Also,
Consider the other right triangle
Using SOH CAH TOA, we can write that
sin(C) = h/b
∴ h = b × sin(C) ---------- (2)
Equate equations (1) and (2)
That is,
c × sin(B) = b × sin(C)
This can then be expressed as
sin(B)/b = sin(C)/c
Hence, the given expression is proven as shown above
Learn more on Proving the Sine rule here: https://brainly.com/question/12271113
#SPJ1
Simplify the expression 5^3 x 5^-5
A. 5^2
B. 1/5
C. 1/5^2
D. -52
[tex] {5}^{3} \: \times \: {5}^{ - 5} [/tex]
We first compute the product.[tex] {5}^{ - 2} [/tex]
We can transform the product into positive if we use this formula:[tex] \boxed{ {a}^{ - n} \: = \: \frac{1}{ {a}^{n} } }[/tex]
We apply it:[tex] {5}^{ - 2} \: = \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]
Answer:[tex]\text{Option C.} \: \boxed{ \bold{\frac{1}{ {5}^{2} } }}[/tex]
MissSpanish4 5/6 - 2 1/2
please help!
Answer:
2.33
Step-by-step explanation:
What conclusions can you draw from the first battles in the civil war?
At the stadium, there are eight lines for arriving customers, each staffed by a single worker. The arrival rate for customers is 190 per minute and each customer takes (on average) 2 seconds for a worker to process. The coefficient of variation for arrival time is 1.2 and the coefficient of variation for service time is 1.5. (1) How much time (in seconds) will an average customer spend in queue
Answer:
3.287 Customers
Step-by-step explanation:
Interarrival time (a) = 60 seconds per minute / 190 customers per minute = 0.316 seconds.
Utilization = p / (a × m) = 2 / (0.316 × 8) = 0.792.
Number in queue = Tq / a = 1.038 / 0.316 = 3.287 customers.
Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.
What is the measure of angle L in parallelogram LMNO?
can someone help me to number 2,4&5.
just 2,4&5 that's all thank you.
Answer:
See below ~
Step-by-step explanation:
What is the equivalent to 8 ounces?
Answer:
16 Tablespoons
Step-by-step explanation:
According to a survey, 48% of adults in the united states believe that unidentified flying objects (ufos) are observing our planet. you ask 8 randomly chosen adults whether they believe ufos are watching earth.
The expected number of adults that believe ufos are watching earth is 4
How to determine the number of adults?The given parameters are:
p = 48%
Sample size, n = 8
The expected number of adults that believe ufos are watching earth is calculated as:
E(x) = np
This gives
E(x) = 8 * 48%
Evaluate
E(x) = 3.84
Approximate
E(x) = 4
Hence, the expected number of adults that believe ufos are watching earth is 4
Read more about expected values at:
https://brainly.com/question/15858152
#SPJ4
Complete the equations below. 15.3 ÷ 3 = tenths + 3 15.3÷ 3 = tenths 15.3 ÷ 3 =
The value of the complete equation is 5.1.
We have given the equation,
15.3 ÷ 3 = tenths + 3 15.3÷ 3 = tenths 15.3 ÷ 3
What is the equation?
An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Therefore we have,
[tex]15.3/3=15+0.3 \ tenths/3\\=5+0.1 \ tenths\\=5.1[/tex]
Therefore the value of the complete equation is 5.1.
To learn more about the complete solution of the equation visit:
https://brainly.com/question/2226590
#SPJ1
The number of swimsuits purchased at a department store is positively correlated with each of these variables. a change in which variable most likely caused a change in the number of swimsuits purchased?
The variable that is most likely to have a positive correlation with the number of swimsuits purchased is the temperature changing outside.
What is positive correlation?Correlation measures the relationship between two variables. When there is a positive correlation, it means that the two variables move in the same direction. If one of the variables increases, the other variable increases. If one of the variables decreases, the other variable decreases.
When it is summer, it is expected that the number of swimsuits bought would increase. When it is winter, it is expected that the number of swimsuits bought would decrease.
Here are the options:
A. The number of swimsuit cover-ups the store has in stock
B. The number of sand castles built by store customers
C. The temperature outside changing
D. The number of minutes it takes the store's employees to get to work
To learn more about correlation, please check: https://brainly.com/question/27246345
#SPJ1
calculate 20% of R400
Answer:
80Step-by-step explanation:
400: 100 you find 1% you multiply it by 20 and you have 20%
400 : 100 * 20 =
4 * 20 =
80
A square purple rug has a green square in the center. The side length of the green square is x inches. The width of the purple band that surrounds the green square is 3 in. What is the area of the purple band?
3n + 19 = 28
How do I solve this
Answer:
to solve this you need to find out what number n is to make it equal 28.
Step-by-step explanation:
19+3 =22 so 3 is not it
19+9=28
answer is 9
hopefully this is right and this gets to you on time
Answer:
err Im not sure if this is a multiple-choice but n=3
Step-by-step explanation:
3(n) + 19 is 28 meaning you have to find what multiplies with 3 to get 9 because 19+9 is 28
Hope this helps
How many solutions exist for the system of equations graphed below?
a.) none
b.) one
c.) two
d.) infinitely many
Answer:
one
Step-by-step explanation:
When a system of equations is graphed, the solution is the coordinate that is plotted at the intersection of the two lines.
If the two lines cross once, there is only one solution.
If the two lines are on top of each other then there are infinitely many solutions.
If the two lines are parallel ( and never touch ) then there are no solutions
By looking at the graph we notice the two lines intersect once. So we can conclude that there is only one solution.
I NEED HELP ASAP
A box has 1 red marble, 3 blue marbles, and 4 green marbles. Maya draws a blue marble randomly from the box, replaces it, and then draws another marble randomly. What is the probability of drawing 2 blue marbles in a row? Explain your answer.
Answer:
8
Step-by-step explanation:
each times she draws there is 3 blue marbles that she can pick so her chance of picking one blue marble out of the box is 3/8 hope i helped!
Answer: 3/8
Step-by-step explanation:
Explore
create a dot plot of a sample of the population whose
mean is the same as the population mean.
your sample should have more than six, but fewer than
20 data points.
count
number
2
10
12
8
hean
10
12
8
mean
934
The 2nd dot plot in the attachment represents the dot plot that has the same sample mean as the population mean
How to create the dot plot?The dot plot that completes the question is added as an attachment.
Start by calculating the mean of the data plot using:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
Substitute the values on the dot plot
[tex]\bar x = \frac{2*1+3*3+4*2+5+6*3+7*5+8*2+9*4+11*2+12*2}{25}[/tex]
[tex]\bar x = 7[/tex]
This means that the population mean of the dot plot is 7
Next, we create another dot plot that has the same mean as 7.
There are no direct rules to this, so we make use of the trial by error method.
After several attempts, we have the following frequency table:
Data point Frequency
2 1
3 2
4 0
5 4
6 5
7 2
8 5
9 0
10 2
12 3
The mean of the frequency table is:
[tex]\bar x = \frac{2 * 1 + 3 * 2 + 4 * 0 + 5 * 4 + 6 * 5 + 7 * 2 + 8 * 5 + 9 * 0 + 10 * 2 + 12 * 3}{1+2+0+4+5+2+5+0+2+3}[/tex]
Evaluate
[tex]\bar x = \frac{168}{24}[/tex]
Evaluate the quotient
[tex]\bar x = 7[/tex]
This means that the sample mean is 7 (same as the population mean)
Lastly, we represent the frequency table using a dot plot (the 2nd dot plot in the attachment)
Read more about dot plot at:
https://brainly.com/question/21862696
#SPJ1
Which equation is represented by the graph below?
←+
+
1 2 3 4 5 x
5
54
3.
2-
1
--5-4-3-2-11
-2
-3
The function of the curve is an exponential function. So, the function would be y = e^x.
What are exponential functions?When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.
Their usual form is specified below. They are written in several such equivalent forms.
For example, [tex]y^x[/tex]
where a is a constant is an exponential function.
We can see that the curve of the function is decreasing constantly.
Thus, the function of the curve is an exponential function. So, the function would be y = e^x.
Learn more about exponential growth and decay here:
https://brainly.com/question/2193820
#SPJ1
Mickey drew a scale drawing of the room in his junior high building using the scale 1 centimeter (cm) - 1.5 meters (m). the office in his scale drawing measured 2.6 cm * 3.2 cm. what
are the actual dimensions of the office?
2.6 m x 3.2 m
1.7 m x 2.1 m
3.9 m x 4.8 m
4.1 m x 47 m
Answer:
3.9m x 4.8m
Step-by-step explanation:
1 cm = 1.5m
→ Multiply both sides by 2.6
2.6 cm = 3.9m
→ Multiply from the original statement, both sides by 3.2
3.2 cm = 4.8 m
→ Combine them
3.9m x 4.8m