Answer:
V = 5747.02 ft^3
Step-by-step explanation:
We're given the general formula for volume (V) and we must use this general formula and the information we're given to find the volume of the hemisphere.r stands for radius, which is 1/2 the distance between the center of a circle and the edge. The 14 in the diagram represents the radiusIn the formula r^3 means that the radius is cubed and thus 14 must be multiplied by itself three times (14 * 14 * 14)
Therefore, to solve for volume, we plug in 14 for r in the general formula:
[tex]V=2/3\pi (14)^3\\V=2/3\pi (14)(14)(14)\\V=2/3\pi *2744\\V=5747.020161\\V=5747.02[/tex]
Lastly, volume is always in units cubed (e.g., ft^3 or mi^3 since volume deals with the three-dimensional space of an object
sasha buys 5 boxes crackers for 12.25 if each box cost the same amount how much does 1 box cost
Sasha buys 5 boxes crackers for 12.25 if each box cost the same amount one box of crackers costs $2.45.
To find the cost of one box of crackers, we can use the concept of unit rate, which is the cost per one unit. In this case, we want to find the cost per one box of crackers.
If Sasha bought 5 boxes of crackers for a total of $12.25, we can set up a proportion to find the cost of one box of crackers:
5 boxes / $12.25 = 1 box / x
Here, "x" represents the cost of one box of crackers. We can solve for "x" by cross-multiplying the proportion:
5 boxes * x = $12.25 * 1 box
5x = $12.25
x = $12.25 / 5
x = $2.45
To check our answer, we can multiply the cost of one box by the number of boxes Sasha bought:
$2.45 * 5 boxes = $12.25
This confirms that our answer is correct.
To learn more about cost click on,
https://brainly.com/question/13067937
#SPJ1
Complete question is:
Sasha buys 5 boxes crackers for 12.25, if each box cost the same amount, then how much does 1 box of the crackers cost?
Find the lateral area of the right prism with height 0.3 dm if the base of the prism is a parallelogram with sides of 6 cm and 20 mm.
Note that the lateral area of the right prism is 16cm²
How did we arrive at this?The first step is to convert the sides of the paralllogram to the same unit
6cm = 60mm
so
Perimeter of base = 2( 60 + 20) = 160 mm
Thus, the lateral area of the prism is
A = p x h = 160 x 0.3dm
But we cant have different units, so we say:
160 mm x 30mm
= 4,800mm
Converting this to centimeters, we have
480cm²
hence, the lateral area of the right prism 480cm²
Learn more about right prism:
https://brainly.com/question/20837986
#SPJ1
Answer: The lateral area of the prism is 48 cm²
Work:
We have,
Lateral area is the surface area of the sides or lateral faces of a three-dimensional object, excluding the surface area of the bases.
Now,
From the figure,
There are 4 rectangular-shaped sides.
And,
1 dm = 10 cm
0.3 dm = 3 cm
Now,
Lateral area of the prism.
= 4 x 3 + 3 x 3 + 4 x 3 + 5 x 3
= 12 + 9 + 12 + 15
= 48 cm²
Thus,
The lateral area of the prism is 48 cm²
Which piecewise function is shown on the graph?
When be graph the functions given, we find that option A is correct.
What is meant by to graph a function?
To graph a function, you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point. Keep plugging in x-values to get coordinates to plot more points on the graph, and then you will see your graphed function once the dots are connected.
Using the graph,
For x < = -2, y = 5.
For -2 < x < 1, the function is a polynomial.
We have two options, either y = x² - 5 or y = x² + 5
The polynomial must have the point (0,-5) on it.
For y = x² - 5 , when x = 0, y = -5.
Hence, it is the correct option.
For x >= 1,
Using graph, we see that when y = 0, x lies between 3 and 4.
For equation, y = 2⁽ˣ⁻²) - 2 , when y = 0, x = 3, so it is not correct.
For equation, y = 2⁽ˣ⁻²) - 3 , when y = 0, x = 3.584, hence it is correct.
To know more about functions check the below link:
https://brainly.com/question/11624077
#SPJ9
What is the answer for -1h ≤ 14
Answer:
h ≥ -14
Step-by-step explanation:
-1h ≤ 14
h ≥ -14
So, the answer is h ≥ -14
100 points!!!
Angel uses this method to work out some harder divisions. Use Angel's method to work these out.
a. 225 ÷ 5 b. 363 ÷ 5 c. 373 ÷ 3
d. 447 ÷ 6 e. 758 ÷ 8 f. 920 ÷ 12
This is kinda easy but I just can't figure out What's the method. Please solve at least 3 questions if you can So I have a better understanding of what's happening.
Angel's Method:
for the first one 225÷5=45. For the second one to do 363÷5 you have to decrease 363 to the closest number divisible by 5 and that number is 360 so 360÷5=72 then for the remaining 3 instead of doing 3÷5 you can do 30÷5 then bring the decimal point 1 digit forward so 30÷5=6 then when you bring the decimal point forward its 0.6 then add both and its 72.6. for the third one its the same thing so 372÷3=124 but since you cant do 10÷3 you have to use fractions so 1÷3 means 1/3 then add both of them together and its 124 1/3
AWARDING 50 POINTS !!! This circle graph shows the plant categories in a botanical garden. There are 190 trees in the garden.
What is the total number of trees, shrubs, and cacti in the garden?
Enter your answer in the box.
Answer:
500
Step-by-step explanation:
You want to know the total number of plantings if 190 trees comprise 38% of them.
EquationThe given relationship can be written as the equation ...
190 = 0.38 × total
Solutiontotal = 190/0.38 = 500 . . . . . . . divide by the coefficient of 'total'
There are 500 plantings in the garden.
Cruz has 64 stamps, of which 1/8 of the stamps have bees on them, and 3/16 of the stamps have flowers. The rest of the stamps have butterflies. How many stamps have butterflies on them? Explain.
Answer:
44 butterfly stamps
Step-by-step explanation:
1/8=2/16
2/16+3/16=5/16
16/16-5/16=11/16
64÷16=4
4×11=44
44/64
You invest $1800 in an account paying 6.3% interest compounded daily. What is the account's effective annual yield?
According to the concept of compound interest, the effective annual yield on your investment of $1800 at a 6.3% interest rate compounded daily is 6.49%.
To find the effective annual yield, we need to use the formula for compound interest:
A = P(1 + r/n)ⁿˣ
Where A is the amount of money at the end of the investment period, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.
In this case, we know that the principal amount P is $1800, the annual interest rate r is 6.3%, and the interest is compounded daily, which means that n is 365 (the number of days in a year). We need to find the effective annual yield, which is the total amount of interest earned in one year.
To calculate the effective annual yield, we can use the following formula:
Effective Annual Yield = (1 + r/n)ⁿ - 1
Plugging in the values, we get:
Effective Annual Yield = (1 + 0.063/365)³⁶⁵ - 1
Effective Annual Yield = 0.0649 or 6.49%
To know more about compound interest here
https://brainly.com/question/29335425
#SPJ1
A continuous random variable has a rectangular distribution f(x)={█(1/(b-a):a
The rectangular distribution f(x) = 1/(b-a) for a ≤ x ≤ b is a valid probability density function.
What is distribution?In mathematics and statistics, a distribution refers to the pattern of values or frequencies of a variable within a set of data. It describes the spread and behavior of data and can be represented by graphs, tables, or mathematical functions.
According to given information:The rectangular distribution is a continuous probability distribution where the probability density function (PDF) is constant over a certain interval and zero elsewhere. In this case, we have a rectangular distribution with parameters a and b, where a is the lower bound of the interval and b is the upper bound of the interval.
The probability density function (PDF) of this rectangular distribution is given by:
f(x) = 1/(b-a) for a ≤ x ≤ b
and f(x) = 0 elsewhere.
To verify that this function is a valid probability density function, we need to check two conditions:
Non-negativity: f(x) is non-negative for all xTotal probability: The area under the curve of f(x) is equal to 1The first condition is satisfied because f(x) is always positive on the interval [a, b]. The second condition is satisfied because the area under the curve of f(x) from a to b is equal to:
[tex]\int\limits^a_b f(x) dx = \int\limits^a_b (1/(b-a)) dx = [x/(b-a)]_b^a= (b-a)/(b-a) = 1[/tex]
Therefore, the rectangular distribution f(x) = 1/(b-a) for a ≤ x ≤ b is a valid probability density function.
To know more about distribution visit:
https://brainly.com/question/23286309
#SPJ1
The Federal Bureau of Investigation reported the statistics in the following table for
homicides in 2019. Use the data to answer
Weapon: Handgun : 6368 Rifle : 364 Shotgun : 200 Unknown firearm: 3326
Weapon: Cutting instrument: 1476 Other weapons: 1593 Hands, feet, etc: 600 Total: 13927
(i)If there were three unrelated murders in Detroit in June 2019, find the probability that all three were committed with a gun.
(ii)Find the probability that a murder was committed with a handgun given that a gun was used.
(iii) Find the probability that if four unrelated murders are studied, two involved a gun
and two involved a cutting instrument.
The probability that all three murders were committed with a gun is: 0.252.
The probability that one murder was committed with a gun is:
P(Gun) = (6368 + 364 + 200 + 3326)/13927 = 0.632
Therefore, the probability that all three murders were committed with a gun is:
P(3 Guns) = P(Gun) * P(Gun) * P(Gun) = [tex]0.632^3[/tex] = 0.252
The probability that a murder was committed with a handgun given that a gun was used is:
P(Handgun | Gun) = P(Handgun and Gun) / P(Gun)
We need to find P(Handgun and Gun). From the table, we see that 6368 murders were committed with a handgun and 6368 + 364 + 200 = 6932 murders were committed with a gun. Therefore:
P(Handgun and Gun) = 6368/13927
And:
P(Handgun | Gun) = (6368/13927) / (6368 + 364 + 200 + 3326)/13927 = 0.542
The probability that two murders involved a gun and two involved a cutting instrument is:
P(2 Guns and 2 Cutting instruments) = (C(4,2) * C(6932,2) * C(1476,2)) / C(13927,4)
Where C(n,r) is the number of combinations of n things taken r at a time.
Thus, calculating this gives: P(2 Guns and 2 Cutting instruments) = 0.150
For more details regarding probability, visit:
https://brainly.com/question/30034780
#SPJ1
Jane is buying a new sports car for $68,000. The dealer is providing financing at an annual rate of 15% using the add-on method. If Jane wants to pay off the car in 3 years, what will
her monthly payment be?
(Round to the nearest cent
Answer:
$2,738.89/per month
Step-by-step explanation:
this is a loan shark. 15% is robbery.
The Add on Method is an alternative method of paying interest after it is added onto the principal at maturity. In this method, the interest on the loan is calculated annually and multiplied by the number of years left for repayment.
Calculate the annual interest: Multiply the interest rate by the amount you originally borrowed: 15% x $68,000 = $10,200.
Calculate the add-on interest amount: Multiply the annual interest amount by the number of years in the loan: $10,200 x 3 years = $30,600.
so total she'll have to pay over 3 years = 98600
98600/36 months = 2738.89/per month
Please help me! 20 points!!!
A rocket can travel at 8,000 meters per second. If d is the distance in meters and t is the time in seconds, what is the formula for how far the rocket travels in t seconds?
Enter your answer as a formula including "d(t)=".
The formula for how far the rocket travels in t seconds is d(t) = 8,000t.
What is speed?In Mathematics and Science, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;
Miles per hour (mph).Kilometers per hour (kph).Meter per seconds (m/s).How to calculate the speed?In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
Making distance the subject of formula, we have:
Distance, d(t) = speed × time
Distance, d(t) = 8,000 × t
Distance, d(t) = 8,000t
Read more on speed here: brainly.com/question/8163450
#SPJ1
The lengths of a particular animal's pregnancies are approximately normally distributed, with mean μ=257 days and standard deviation a = 8 days.
(a) What proportion of pregnancies lasts more than 267 days?
(b) What proportion of pregnancies lasts between 255 and 261 days?
(c) What is the probability that a randomly selected pregnancy lasts no more than 245 days?
(d) A "very preterm baby is one whose gestation period is less than 239 days. Are very preterm babies unusual?
a. It should be noted that about 10.56% of pregnancies last more than 267 days.
b. It should be noted that about 26.76% of pregnancies last between 255 and 261 days.
c. The probability that a randomly selected pregnancy lasts no more than 245 days is about 6.68%.
d. Only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event.
How to explain the probabilityIn this case, to see, to see if very preterm babies are uncommon, we must compare the likelihood of a pregnancy lasting less than 239 days to some criterion. We can employ the z-score:
z = (239 - 257) / 8 = -2.25
To the left of 239, there is:
P(X < 239) = P(Z < -2.25) = 0.0122
This suggests that only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event. As a result, very premature newborns are considered rare.
Learn more about probability on
https://brainly.com/question/24756209
#SPJ1
a. It should be noted that about 10.56% of pregnancies last more than 267 days.
b. It should be noted that about 26.76% of pregnancies last between 255 and 261 days.
c. The probability that a randomly selected pregnancy lasts no more than 245 days is about 6.68%.
d. Only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event.
How to explain the probabilityIn this case, to see, to see if very preterm babies are uncommon, we must compare the likelihood of a pregnancy lasting less than 239 days to some criterion. We can employ the z-score:
z = (239 - 257) / 8 = -2.25
To the left of 239, there is:
P(X < 239) = P(Z < -2.25) = 0.0122
This suggests that only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event. As a result, very premature newborns are considered rare.
Learn more about probability on
https://brainly.com/question/24756209
#SPJ1
Cut this figure into 3 congruent parts along the sides of the cells. Can you cut it into 4 congruent parts?
its a 4 by 4, minus one square
Yes, the shape can be cut into 3 congruent parts but not 4. This is a whole number division problem. See the attached shape for how to divide the figure into 3 congruent parts.
What is Whole number division?In mathematics, when two numbers are divided without remainders, it is known as integer division or whole number division.
This specific kind of calculation comes in handy when you desire to find out just the quotient or how many times one number divides into another, disregarding any leftover fraction.
For instance, if we utilize integer division to calculate what happens when ten is divided by two; we're left with five as our answer since two divides equally into ten precisely five times without remaining any leftovers.
Conversely speaking though and in regards to regular arithmetic calculations; dividing ten by three amounts up to three with a remainder value attached since three cannot do so equally.
Learn whole number division at;
https://brainly.com/question/28452301
#SPJ1
A recent survey reported that 87% of Americans approve of human embryonic stem cell research. If an American is selected at random, find the probability that he or she will disapprove or have no opinion on the issue. The probability that he or she will disapprove or have no opinion on the issue is %?
The probability that an American will disapprove or have no opinion on the issue is 13%.
What is Probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Probability is used to describe random phenomena, such as the roll of a dice, the flip of a coin, the occurrence of an earthquake, or the outcome of a hand of poker. It is also used to describe the likelihood of certain events happening based on past data or current conditions.
This can be calculated by subtracting the reported approval rate of 87% from 100%. This means that 13% of Americans disapprove or have no opinion on the issue of human embryonic stem cell research.
It is important to note that this survey's data only pertains to the opinions of Americans and not to any other group of people. Therefore, the probability that any individual randomly selected from the global population will disapprove or have no opinion on the issue may be different.
To know more about probability click-
http://brainly.com/question/24756209
#SPJ1
Help asap quickly math homework
Since line segment SP is a diameter, the measure of arc PTS is 180 degrees. 180 - 42 = 138 degrees, which is the measure of arc PT. 97 + 42 + 138 = 277 degrees for the measure of arc PTR
The ratio of lime to sand in mortar is 3:7. How much lime must be mixed with 56 bags of sand to make mortar?
The ratio of the sand is 3:7 and it can be write as 6:14 or 7:21 ... They means the same thing.
Now we know that we have 56 bags of sand, the left side of the number should be 56. Like this:
? : 56
Since we know that 3:7 can be write as 6:14 or 7:21 ... we can even write it as 24:56, it's still 3:7.
Ruby is visiting San francisco. From her hotel she walks 4 block east and 3 blocks north to a coffee shop. Then she walks 7 blocks west and 1 blocks north to a museum. Where is the museum in relation to her hotel?
The museum in relation to her hotel is at distance and direction as 3 blocks to the west and 4 blocks to the north.
Given that,
Ruby is visiting San francisco.
The figure representing the situation is given below.
Here it is easier to find the relation of the museum with the hotel.
When Ruby walk a certain distance to the west, she will reach straightly north to the museum.
Distance to the west = 7 - 4 = 3 blocks
Then she can walk 3 + 1 = 4 blocks to reach the museum.
Hence the museum is at a distance of 3 blocks to the west and 4 blocks to the north.
Learn more about Directions here :
https://brainly.com/question/28836995
#SPJ1
a city has a population of 280,000 people. Suppose that each year the population grows by 7.25%. What will the population be after 12 years?
Step-by-step explanation:
Use a compounding formula like this:
P (t) = 280 000 (1 + .0725) ^t
t is years .0725 is 7.25% in decimal form
P (12) = 280 000 ( 1.0725)^12 = 648,523 population
factor each completely
6r2 + 31r + 18
Therefore, the expression 6r² + 31r + 18 factors completely into (3r + 2)(2r + 9).
What is factor?In mathematics, factoring is the process of finding the factors or divisors of a given number or algebraic expression. When we factor a number or expression, we find the numbers or expressions that can be multiplied together to obtain the original number or expression. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, since these numbers can be multiplied together in different combinations to obtain 12. Factoring is an important skill in algebra, as it helps us to simplify algebraic expressions and solve equations.
Here,
To factor the quadratic expression completely, we need to find two binomials whose product is equal to the given expression. We can start by looking for two numbers whose product is 6 x 18 = 108 and whose sum is 31. After some trial and error, we find that the numbers are 6 and 18.
We can now write the expression as:
=6r² + 31r + 18
18*6=108
27*4=108
27+4=31
= 6r² + 27r + 4r + 18
= 3r(2r + 9) + 2(2r + 9)
= (3r + 2)(2r + 9)
To know more about factor,
https://brainly.com/question/29128446
#SPJ1
Need help with his page 50 points
Answer: B, C, B
Step-by-step explanation:
see images for explanation
Answer:
[tex]\textsf{11)} \quad \text{b.}\;\;2\frac{3}{4}[/tex]
[tex]\textsf{12)} \quad \text{c.}\;\;7\frac{1}{2}[/tex]
[tex]\textsf{13)} \quad \text{b.}\;\;\dfrac{2}{3}x+4=10[/tex]
Step-by-step explanation:
Question 11To find the answer to the given equation when y = 4, substitute y = 4 into the equation:
[tex]\begin{aligned} y=4 \implies \dfrac{3}{4}+\dfrac{2(4)}{4}&= \dfrac{3}{4}+\dfrac{8}{4}\\\\&= \dfrac{3}{4}+2\\\\&= 2\frac{3}{4}\end{aligned}[/tex]
Therefore, the answer is 2³/₄.
[tex]\hrulefill[/tex]
Question 12To find the answer to the given equation when y = 8, substitute y = 8 into the equation:
[tex]\begin{aligned}y=8 \implies \dfrac{12}{8}+\dfrac{3(8)}{4}&= \dfrac{12}{8}+\dfrac{24}{4}\\\\&= \dfrac{12}{8}+6\\\\&= \dfrac{8+4}{8}+6\\\\&= \dfrac{8}{8}+\dfrac{4}{8}+6\\\\&= 1+\dfrac{1}{2}+6\\\\&=7\frac{1}{2}\end{aligned}[/tex]
Therefore, the answer is 7¹/₂.
[tex]\hrulefill[/tex]
Question 13To determine which equation is true if x = 9, substitute x = 9 into each equation.
[tex]\begin{aligned} \text{a)} \quad \dfrac{2}{3}(9)-6&=12\\\\\dfrac{18}{3}-6&=12\\\\6-6&=12\\\\0&=12\end{aligned}[/tex]
[tex]\begin{aligned} \text{b)} \quad \dfrac{2}{3}(9)+4&=10\\\\\dfrac{18}{3}+4&=10\\\\6+4&=10\\\\10&=10\end{aligned}[/tex]
[tex]\begin{aligned} \text{c)} \quad 3(9)-12&=21\\27-12&=21\\15&=21\end{aligned}[/tex]
[tex]\begin{aligned} \text{d)} \quad 3(9)+12&=19\\27+12&=19\\39&=19\end{aligned}[/tex]
Therefore, the only equation that holds true is option b.
Kleen Company acquired patent rights on January 10 of Year 1 for $881,100. The patent has a useful life equal to its legal life of eight years. On January 7 of Year 4, Kleen successfully defended the patent in a lawsuit at a cost of $49,200.
Required:
a. Determine the patent amortization expense for Year 4 ended December 31.
b. Journalize the adjusting entry on December 31 of Year 4 to recognize the amortization. Refer to the Chart of Accounts for exact wording of account titles.
From the set {1, 12, 17}, use substitution to determine which value of x makes the equation true. 36x + 31 = 535 A. 12 B. none of these C. 1 D. 17
ANWSER FAST!!!
The value of x in the equation is B) None of these.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is 36x+31=535
Now substitute x=1 then,
=> 36(1)+31=535
=> 36+31=535
=> 67 ≠ 535
Now substitute x = 12 then
=> 36(12)+31=535
=> 432+31 = 535
=> 463 ≠ 535
Now substitute x= 17 then
=> 36(17)+31=535
=> 612+31 = 535
=> 643 ≠ 535.
Hence the correct option is B) None of these.
To learn more about equation refer the below link
https://brainly.com/question/29336774
#SPJ1
Consider the equation (y - 4) = 3(x - 5). Convert the equation from point-slope form to slope-intercept form.
The slope-intercept form of (y - 4) = 3(x - 5) is expressed as:
y = 3x - 11
How to Convert an Equation From Point-slope Form to Slope-intercept Form?The slope-intercept form is expressed as y = mx + b, where we have the variables:
m as the slope
b as the y-intercept.
Given the equation in point-slope form as (y - 4) = 3(x - 5), we can convert as follows:
(y - 4) = 3(x - 5)
y - 4 = 3x - 15
y - 4 + 4 = 3x - 15 + 4
y = 3x - 11
Learn more about the slope-intercept form on:
https://brainly.com/question/30104695
#SPJ1
Nico, Aditi, Erick, Raj, and Sandra are solving the equation. Two-fifths (5 + x) = 8 Each student begins to solve the problem as shown. Nico Aditi Erick Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves) Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8 Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5 Raj Sandra Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half) Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8 Which students are correct in their approach to solving the problem? Select three options. Nico Aditi Erick Raj Sandra
The students that are correct in their approach to solving the problem are Nico, Raj and Sandra.
How to explain the informationIt should be noted that we can start by simplifying the left side of the equation by distributing the two-fifths:
(2/5)(5) + (2/5)x = 8
2 + (2/5)x = 8
Next, the next thing is that we can isolate the variable term on one side of the equation by subtracting 2 from both sides:
(2/5)x = 6
x = 6 / (2/5)
x = 6 * (5/2)
x = 15
Therefore, the solution to the equation is x = 15.
Learn more about word problem on
https://brainly.com/question/21405634
#SPJ1
I need help with this question. I cannot seem to get past it. Please help me
Answer:
dont know either
Step-by-step explanation:
dont know either
Mathematics
Calculate the percentage, show your solution.
90% of 60
help, thanks!
Answer:
Your answer is 90% of 60 = 54.
how do i solve this equation using factoring method?
x² - 14x + 9 = 0
Certainly!
The text is asking how to solve the equation x² - 14x + 9 = 0 using the factoring method. Factoring is a method of finding the roots of a quadratic equation by expressing it as a product of two linear factors. The roots of a quadratic equation are the values of x that make the equation equal to zero. In this case, we are trying to find the values of x that satisfy the equation x² - 14x + 9 = 0.
According to a survey, 65% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly selected, and the number cleared by arrest or exceptional means is recorded.
(a) Find the probability that exactly 40 of the murders were cleared.
(b) Find the probability that between 35 and 37 of the murders, inclusive, were cleared.
(c) Would it be unusual if fewer than 20 of the murders were cleared? Why or why not?
The probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.
(a) The probability that exactly 40 of the murders were cleared can be found using the binomial probability formula.
In this case, n = 50, k = 40, and p = 0.65. Thus, the probability that exactly 40 of the 50 murders were cleared is P(40 successes) = (50C40)(0.65)⁴⁰(0.35)¹⁰ = 0.064.
(b) The probability that between 35 and 37 of the murders, inclusive, were cleared can be found by adding the probabilities of each individual outcome.
For example, the probability of exactly 35 successes is (50C35)(0.65)³⁵(0.35)¹⁵ = 0.069.
Similarly, the probability of exactly 36 successes is (50C36)(0.65)³⁶(0.35)¹⁴ = 0.051.
Adding these two probabilities together gives the probability of between 35 and 37 successes, inclusive, as 0.069 + 0.051 = 0.120.
(c) It would not be unusual if fewer than 20 of the murders were cleared. This is because the probability of this outcome can be calculated using the same formula as before. In this case, if k = 19, then P(19 successes) = (50C19)(0.65)¹⁹(0.35)³¹ = 0.057, which is a relatively high probability.
Therefore, the probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ1
ASAPP Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d = 163t
D. d = 81.50t
Answer:
C. d = 163t
Step-by-step explanation:
This equation represents a direct proportionality between the number of dollars earned (d) and the amount of time worked (t), with a constant of proportionality of 163 dollars per hour.
Hope this helps!