Answer:
Explained below.
Step-by-step explanation:
Let X = systolic blood pressure measurements.
It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].
(a)
Compute the percentage of measurements that are between 71 and 89 as follows:
[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]
[tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of measurements that are between 71 and 89 is 99.73%.
(b)
Compute the probability that a person's blood systolic pressure measures more than 89 as follows:
[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.
(c)
Compute the probability that a person's blood systolic pressure being at most 75 as follows:
Apply continuity correction:
[tex]P(X\leq 75)=P(X<75-0.5)[/tex]
[tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]
Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.
(d)
Let x be the blood pressure required.
Then,
P (X < x) = 0.15
⇒ P (Z < z) = 0.15
⇒ z = -1.04
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]
Thus, the 15% of patients are expected to have a blood pressure below 76.9.
(e)
A z-score more than 2 or less than -2 are considered as unusual.
Compute the z score for [tex]\bar x[/tex] as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]
The z-score for the mean blood pressure measurement of 3 patients is more than 2.
Thus, it would be unusual.
Find the sum of 1 + 3/2 + 9/4 + …, if it exists. This is infinite series notation. The answer is NOT 4.75.
Answer:
D
Step-by-step explanation:
First, this looks like a geometric series. To determine whether or not it is, find the common ratio. To do this, we can divide the second term and the first term, and then divide the third term and the second term. If they equal to same, then this is indeed a geometric series.
[tex](3/2)/(1)=3/2\\(9/4)/(3/2)=(9/4)(2/3)=18/12=3/2[/tex]
Therefore, this is indeed a geometric series with a common ratio of 3/2.
With just this, we can stop. This is because since the common ratio is greater than one, each subsequent value is going to be bigger than the previous one. Because of this, the series will not converge. Therefore, the series has no sum.
To see this more clearly, imagine a few more terms:
1, 1.5, 2.25, 3.375, 5.0625...
Each subsequent term will just increase. The sum will not converge.
Answer:
No Sum --- it doesn't exist.
Step-by-step explanation:
The partial sums get arbitrarily large--the go to infinity.
The geometric series you are trying to sum has common ratio = 3/2.
The sum of the infinite series exists only when |common ratio| < 1.
The formula for the partial sum of n terms is (r^(n+1) - 1) / (r - 1) = (1.5^(n+1) - 1) / 0.5, or in decimals instead of fraction.. i.e. 1 + 1.5 + 2.25 + 5.0525 + 25.628 + 656.840..... therefore It would take a long time but you'd be adding up forever and goes to infinity.
The hypotenuse of a right triangle is 14 in. If the base
of the triangle is 2 inches determine the
length of the remaining side.
14 in
Х
2 in
O A &
B. 318
O c. 8v3
OD. 112
Answer:
13.85
Step-by-step explanation:
U use the pythagorean theorem
So 2^2 + x^2 = 14^2
Simplify the equation: 4+x^2=196
--> x^2=192
--> x=13.85
-Hope this helps :)
9514 1404 393
Answer:
c. 8√3
Step-by-step explanation:
The Pythagorean theorem applies.
14² = s² + 2²
s = √(14² -2²) = √192 = 8√3
The length of the remaining side is 8√3.
The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass? F = 16.1m F = F equals StartFraction 16.1 Over m squared EndFraction. F = 32.2m F = F equals StartFraction 32.2 Over m squared EndFraction.
Answer:
F = 32.2mStep-by-step explanation:
According to newton second law, the force of gravity on an object varies directly with its mass and it is expressed mathematically as Fαm i.e
F = mg where;
F is the force of gravity
m is the mass of the body
g is the proportionality constant known as the acceleration due to gravity.
If the constant of variation due to gravity is 32.2ft/s², the equation that represents F, the force on an object due to gravity according to m, the object’s mass can be gotten by substituting g = 32.2 into the formula above according to the law as shown;
F = m*32.2
F =32.2m
Hence the required equation is F = 32.2m
A package of 8-count AA batteries costs $6.40. A package of 20-count AA batteries costs $15.80. Which statement about the unit prices is true?
Answer:
The unit price of the 20 pack is $0.79 and the unit price for the 8 pack is $0.80.
Step-by-step explanation:
Simply Take the price of the pack of batteries divided by the number within the pack.
$6.40 / 8 == $0.80
$15.80 / 20 == $0.79
Cheers.
The question is incomplete. You can find the missing content below.
A package of 8-count AA batteries costs $6.40. A package of 20-count Of batteries costs $15.80. Which statement about the unit prices is true?
A) The 8-count pack of AA batteries has a lower unit price of $0.79 per battery.
B) The 20-count pack of AA batteries has a lower unit price of $0.80 per battery.
C) The 8-count pack of AA batteries has a lower unit prices of $0.80 per battery.
D) The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.
The correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.
What is inequality?Inequality is the relation between two numbers or variables or expressions showing relationships like greater than, greater than equals to, lesser than equals to, lesser than, etc.
For example 2<9
A package of 8-count AA batteries has cost = $6.40.
cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries
= $6.40/8= $0.8
A package of 20-count AA batteries has cost = $15.80.
cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries
= $15.80/20= $0.79
As 0.79<0.8
cost of 20-count AA batteries < cost of 8-count AA batteries
Therefore the correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.
Learn more about inequality
here: https://brainly.com/question/11613554
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Find the first term in the sequence when u(subscript)31=197 and d= 10.
Answer:
197 = 10(31-1) + a
197 = 300 + a
-103 = a
You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.
Answer:
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Solution Set : { x = 123, y = 246, z = 11 }
Step-by-step explanation:
Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,
x + y + z = 380,
And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.
5x + 3y + 10z = 1460
The silly string tickets were sold for twice as much as the car wash tickets.
y = 2x
Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.
System of Equations :
[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,
[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three
And we can continue, canceling the leading co - efficient in each row until this matrix remains,
[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]
x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold
In a survey of 200 publicly-traded companies, the average price-earnings ratio was 18.5 with a standard deviation of 8.2. When testing the hypothesis (at the 5% level of significance) that the average price-earnings ratio has increased from the past value of 16.8, the null and alternative hypotheses would be:________
Answer:
Null Hypothesis: H0:μ ≤ 16.8
Alternative Hypothesis: Ha: μ > 16.8
Step-by-step explanation:
We are told that affer testing the hypothesis (at the 5% level of significance), that the average price-earnings ratio increased from the past value of 16.8.
It means that the past value was not more than 16.8.
This follows that the null hypothesis is given as;
H0:μ ≤ 16.8
And since it has been discovered that the ratio increased from the past value of 16.8, the alternative hypothesis is;
Ha: μ > 16.8
What is the percentage of 204 over 1015, 1 over 8120, 1 over 5832, and 1 over 6?
Answer:
204/1015 (irreducible) = 20.1%
1/8120 (irreducible) = 0.01232%
1/5832 (irreducible) = 0.01715%
1/6 (irreducible) = 16.67%
Step-by-step explanation:
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers (k)left parenthesis, k, right parenthesis she can drive with 12 liters of fuel. She assumes the relationship between kilometers and fuel is proportional.
How many kilometers can Pamela drive with 12 liters of fuel?
Answer:
132 kilo meters
Step-by-step explanation:
Pro por tions:
9 lite rs ⇒ 99 km
12 lite rs ⇒ P km
P = 99*12/9
P = 132 km
Answer:
132
Step-by-step explanation:
give person above brainliest :))
Jayden, who burns 345 calories in 45 min
while hiking is preparing for a 6 hour hike.
He uses a special supplement beverage
pack that provides water, needed
electrolytes, and 310 calories. The goal is to
replace roughly 1/3 of the calories burned
while carrying as light a load as possible.
How many packs should he take?
This question is solved using proportions.
First, we find how many calories he will burn in the hike.Then, we find how many calories he will need to replace, and the number of packs needed.Doing this, we get that he should take 3 packs.
How many calories he burns in the hike?
In 45 minutes, he burns 345 calories. How many calories in 6*60 = 360 minutes?
45 minutes - 345 calories
360 minutes - x calories
Applying cross multiplication:
[tex]45x = 345*360[/tex]
[tex]x = \frac{345*360}{45}[/tex]
[tex]x = 2760[/tex]
He burns 2760 calories in the hike.
How many calories he wants to replace?
Roughly 1/3, so he have to find one third of 2760, that is:
[tex]\frac{2760}{3} = 920[/tex]
How many packs?
One pack recovers 310 calories, how many packs for 920 calories?
1 pack - 310 calories
x packs - 920 calories
Applying cross multiplication:
[tex]310x = 920[/tex]
[tex]x = \frac{920}{310}[/tex]
[tex]x = 2.97[/tex]
Rounding up, he should take 3 packs.
A similar question is found at https://brainly.com/question/14426926
A Ferris wheel has a diameter of 42 feet it rotates 3 times per minute approximately how far will a passenger travel during a 5 minute ride
Answer:
1978.2 or 630π feet
Step-by-step explanation:
The Ferris wheel will rotate 3 * 5 = 15 times during the 5 minute ride and the radius is 42 / 2 = 21 feet. Since C = 2πr, r = 21 and π ≈ 3.14, C = 2 * 3.14 * 21 = 131.88. However, this only accounts for one rotation so the answer is 131.88 * 15 = 1978.2 or 630π feet.
The numbers 1,2,3,4,5,6,7,8,9. How would you put them in each of a square block to create the sum on each line to make the number 15. The sum of each diagonals should also be 15.
Answer:
Here's one way:
4 9 2
3 5 7
8 1 6
Step-by-step explanation:
Can someone help??????????
Answer:
(C) 1 and 3
Step-by-step explanation:
Corresponding angles are angles that are at the same corner at the different intersections.
We can see that 1 is on the bottom right corner of the bottom line, now we need to see what angle is at the bottom right corner of the top line?
That's 3.
So 1 and 3 are congruent because they are corresponding.
Hope this helped!
The chief business officer of a construction equipment company arranges a loan of $9,300, at 12 1 /8 % interest for 37.5 months. Find the amount of interest. (Round to the nearest cent)
a. $2,761.21
b. $3,583.83
c. $3,523.83
d. $3,722.47
Answer:
C). $3523.83
Step-by-step explanation:
loan of principles p= $9,300,
at rate R= 12 1 /8 % interest
Rate R = 12.125%
for duration year T = 37.5 months
T= 37.5/12 = 3.125 years
Interest I=PRT/100
Interest I =( 9300*12.125*3.125)/100
Interest I = (352382.8125)/100
Interest I = 3523.83
Interest I= $3523.83
Fill in the blanks and explain the pattern.
XA, XB, XC, __,__,__
Answer:
XD,XE,XF
Step-by-step explanation:
XA,XB,XC,XD,XE,XF
IT IS BECAUSE OF THE ALPHABETICAL ORDER AFTER X
Which statements are true about triangle QRS?
Select
three options.
Answer:
The side opposite <Q is RS
The hypothenuse is QR
The side adjacent to <Q is QS
Step-by-step explanation:
Side RS is directly opposite <Q. The first statement provided in the options is correct.
The side that is opposite to <R is QS. The second statement in the options is not correct.
The longer leg of a right triangle is always the hypotenuse. Side QR in ∆QRS is the hypotenuse. The third statement given in the options is correct.
The side adjacent to <R is not SQ. RS is the side adjacent to <R. The fourth statement in the given options is not correct.
Side QS is adjacent to <Q. The fifth option is correct.
Answer:
A, C, E
Step-by-step explanation:
on edge! hope this helps!!~ （‐＾▽＾‐）
What is the slope of the line showed?
Answer:
2
Step-by-step explanation:
The formula for the slope of a line is rise over run. We know that the slope of the line will be positive because the line is going up from left to right.
Rise is the change on the y-axis, going up and down. Run is the change on the x-axis, going from left to right.
Let's start from the origin (0,0). To reach the next point on the line, we have to go up two points (rise) and over one point (run).
Slope = rise/run
Slope = 2/1
Slope = 2
Hope that helps.
Answer:
slope=2
Step-by-step explanation:
take two points from graph (0,0) and (1,2)
m=y2-y1/x2-x1
m=2-0/1-0
m=2
The volume of a cone varies jointly with the base (area) and the height. The volume is 12.5 ft3 when the base (area) is 15 ft2 and the height is 212 ft. Find the volume of the cone (after finding the variation constant) when the base (area) is 12 ft2 and the height is 6 ft
The volume of the cone, when the base area is 12 ft² and the height is 6 ft, is approximately 24 ft³.
To find the volume of the cone when the base area is 12 ft² and the height is 6 ft, we need to first determine the variation constant relating the volume, base area, and height.
Let's denote the volume of the cone as V, the base area as A, and the height as h. According to the problem, the volume varies jointly with the base area and the height.
Therefore, we can write the following equation:
V = k * A * h
Here k is the variation constant we want to find.
Given one set of values: when A = 15 ft² and h = 2 1/2 ft, V = 12.5 ft³.
Substitute these values into the equation and solve for k:
12.5 ft³ = k * 15 ft² * (2.5 ft)
Now, we can solve for k:
k = 12.5 ft³ / (15 ft² * 2.5 ft)
k = 0.3333 ft
Now that we have the value of the variation constant (k), we can find the volume when A = 12 ft² and h = 6 ft:
V = k * A * h
V = 0.3333 ft * 12 ft² * 6 ft
V = 23.9996 ft³
Therefore, the volume of the cone is 24 ft³.
Learn more about the volume of the cone here:
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The correct question is as follows:
The volume of a cone varies jointly with the base (area) and the height. The volume is 12.5 ft³ when the base (area) is 15 ft² and the height is 2 1/2 ft. Find the volume of the cone (after finding the variation constant) when the base (area) is 12 ft² and the height is 6 ft.
The graph shown below expresses a radical function that can be written in the form f(x)=a(x+k)^1/n + c. What does the graph tell you about the value of n in this function?
Answer: n is a positive odd number.
Step-by-step explanation:
Ok, we know that the function is something like:
f(x)=a(x+k)^1/n + c
In the graph we can see two thigns:
All the values of the graph are positive values (even for the negative values of x), but in the left side we can see that the function decreases and is different than the right side.
So this is not an even function, then n must be an odd number (n odd allows us to have negative values for y = f(x) that happen when x + k is negative).
Also, we can see that the function increases, if n was a negative number, like: n = -N
we would have:
[tex]f(x) = \frac{a}{(x+k)^{1/N}} + c[/tex]
So in this case x is in the denominator, so as x increases, we would see that the value of y decreases, but that does not happen, so we can conclude that the value of n must be positive.
Then n is a positive odd number.
Answer:
D) Positive Even Integer
Step-by-step explanation:
just did it
You catch an expected number of 1.51.5 fish per hour. You can catch a fish at any instant of time. Which distribution best characterizes the number of fish you catch in one hour of fishing
Answer:
The distribution is Poisson distribution
Step-by-step explanation:
From the question we are told that
An expected number of fish was caught per hour is 1.5
The distribution that best characterize the number of fish you catch in one hour of fishing is the Poisson distribution
This because generally the Poisson distribution is a distribution that shows the number of times a given event will occur within a defined period of time
The Tran family and the Green family each used their sprinklers last summer. The water output rate for the Tran family's sprinkler was 35L per hour. The water output rate for the Green family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1900L. How long was each sprinkler used?
Answer:
Tran family's sprinkler was used for 20 hours
Green's family's sprinkler was used for 30 hours
Step-by-step explanation:
Let the hours for which Tran family's sprinkler used is x hours
water output rate for the Tran family's sprinkler = 35L per hour
water output from Tran family's sprinkler in x hours = 35*x L = 35x
Let the hours for which Green family's sprinkler used is y hours
water output rate for the Green family's sprinkler = 40L per hour
water output from Green family's sprinkler in x hours = 40*y L = 40y
Given
The families used their sprinklers for a combined total of 50 hours
thus
x + y = 50 -------------------equation 1
y = 50-x
total water output of 1900L
35x+40y = 1900 -------------------equation 1
using y = 50-x in equation 2, we have
35x + 40(50-x) = 1900
35x + 2000 - 40x = 1900
=> -5x = 1900 - 2000 = -100
=> x = -100/-5 = 20
y = 50-20 = 30
Thus,
Tran family's sprinkler was used for 20 hours
Green's family's sprinkler was used for 30 hours
PLEASE HELPPPP
A standard I.Q. test produces normally distributed results with a mean of 100 and a standard deviation of 15 for the city of New York. Out of approximately 8,400,000 citizens, how many of these people would have I.Q.s below 67?
Answer:
approx 193200
Step-by-step explanation:
As known for normal distribution is correct the rule 95.4% of the results are situation within mean+-2*s ( where s is a standard deviation)
So the border is 100+-2*15=70 and that is approx=67.
95.4% of 84000000 citizens are= 8 400 000*0.954=8013600 persons
So the residual number of the citizens =8400000-8013600=386400 citizens
Because of the simmetry of normal distribution to find the number of the citizens that have IQ below 67 we have to divide 386400 by 2.
N=386000/2=193200
The double number lines show the ratio of cups to gallons. How many cups are in 333 gallons? _____ cups
Answer:
5328 cups.
Step-by-step explanation:
Given that 333 gallons
We know that
1 gallons = 16 cups
1 cups = 0.0625 gallons
Therefore,from the above conversion we can say that
Now by putting the values in the above conversion
333 gallons = 16 x 333 cups
333 gallons = 5328 cups
So , we can say that 333 gallons is equal to 5328 cups.
Thus the answer will be 5328 cups.
Answer:
48 cups(BTW he meant 33 galons, IVE had this before). lol you need to put the double number line image. first u have to divide 64/4 to get 16, Then it says "How many cups are in 3 gallons". There fore, U multiply 16 to 3 to get ur answer "48".
A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆ y = 3 − 5 x y^=3-5x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way:
1.) When amount of schooling increases by one year, the number of pregnancies decreases by 4.
2.) When amount of schooling increases by one year, the number of pregnancies increases by 4.
3.) When amount of schooling increases by one year, the number of pregnancies increases by 5.
4.) When amount of schooling increases by one year, the number of pregnancies decreases by 5.
Answer:
1. When amount of schooling increases by one year, the number of pregnancies will decrease by 4.
Step-by-step explanation:
Regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, there is regression equation given. X and Y are considered as dependent variables. When number of schooling increases by 1 year then number of pregnancies will decrease by 4
The Masim family’s monthly budget is shown in the circle graph provided in the image. The family has a current monthly income of $5,000. How much money do they spend on food each month? A. $250 B. $500 C. $750 D. 1,100 Please show ALL work! <3
Answer:
C. $750
Step-by-step explanation:
The amount of money to be spent monthly on food = percentage covered by food in the circle ÷ 100% × total monthly income
= [tex] \frac{15}{100}*5000 [/tex]
[tex] = \frac{15}{1}*50 [/tex]
[tex] 15*50 = 750 [/tex]
Amount of money spent each month by the Masims is $750.
Find the product of
the sum of
3/5 and 1%
and
Answer:
3/500
Step-by-step explanation:
3/5 x 1%
=> 3/5 x 1/100
=> 3/500
Hope it helps you
How would the margin of error change if the sample size increased from 200 to 400 students? Assume that the proportion of students who say yes does not change significantly.
Answer:
(MOE) the Margin of Error will decrease by the square root of 2
Step-by-step explanation:
The Margin of Error (MOE) is an inverse function of sample size n ( more precisely of the square root of sample size ). That relation means changes in sample size ( keeping constant other variables of the distribution) will imply opposite changes in the Margin of Error. If we double the sample size increasing it from 200 up to 400, the Margin of Error will decrease by the square root of 2
Simplify 3 x times the fraction 1 over x to the power of negative 4 times x to the power of negative 3.
Answer:
3x^2
Step-by-step explanation:
3 x times the fraction 1 over x to the power of negative 4 => 3x * 1/x^-4
= 3x *x^4 = 3x^5
times x to the power of negative 3 => x^-3
3x^5 * x^-3 = 3x^2
Answer:
3x^2
Step-by-step explanation:
i got it right on the test on god!
Please help me. What is the y intercept of the graph shown below?
Answer:
(0,2)
Step-by-step explanation:
the point where Oy intercepts the graph has x=0 and y= f(0)
so this is (0,2)
5) Suppose a slice of a 12-inch pizza has an area of 20 square inches. What is the angle of
this slice?
Answer:
The angle of the slice is 63.64 degrees
Step-by-step explanation:
Here in this question, we are concerned with calculating the angle of the slice.
What we should know are as follows;
1. A pizza is a perfect circular shape
2. A 12-inch pizza means the diameter of the pizza is 12 inches and consequently its radius will be 12/2 = 6 inches
3. A slice of a pizza represents a sector of the circle( a sector is part of a circle bounded by 2 radii and an arc)
Mathematically, to calculate the angle of the slice, we simply use the formula for the area of a sector.
Area of sector = theta/360 * pi * r^2
where Area of sector = 20 square inches
theta is the center angle we are looking for
r is the radius of the pizza which is 6 inches
Plugging these values into the area of sector equation, we have
20 = theta/360 * 22/7 * 6^2
20 = theta/10 * 22/7
22 theta = 10 * 20 * 7
theta = 1400/22
theta = 63.64 degrees which is approximately 64 degrees to the nearest degree
