Answer:
72 cm³
Step-by-step explanation:
Volume of a triangular pyramid = a*(h/3), where a is the area of the base triangle and h is the height from the base to the highest point.
We need to first find a, the area of the bas triangle:
Area of triangle = (1/2)bh, where b is the length of the base and h is the perpendicular height.
a = (1/2)12*4
a = 6*4
a = 24 cm²
Knowing a, we can know find the volume:
Volume = a*(h/3)
= 24*(9/3)
= 24*3
= 72 cm³
Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below/attached
What are solutions to the equations
Answer:
A
Step-by-step explanation:
Answer:
x= -6 ,1
Step-by-step explanation:
B is the answer
x= -6 ,1
PA = 0.5 PB = 0.3 and p A and b equals 0.15 what is p A or b
Answer:
P(A) = 0.2, P(B) = 0.5, P(A\B) = 0.3:
P(A\B) = P(A and B) P(B)
0.3 = P(A and B) 0.5
0.15 P(A and B)
P(A and B) = 0.15
B. P(A or B) = P(A) + P(B) - P(A and B)
0.2 + 0.5 - 0.15
0.70 - 0.15 = 0.55
The area of a circle is 4 square centimeters. What is the circumference?
3. The third side of a triangle measures (3x-5) cm. If the length of the midline is 14 m,
what is x?
A 8
C. 10
B. 9
D. 11
Answer:
D. 11
Step-by-step explanation:
Midsegment theorem:
The length of the midsegment of a triangle is half the length of it's third side.
In this question:
Third side: 3x - 5
Midsegment: 14m
So
[tex]\frac{3x - 5}{2} = 14[/tex]
[tex]3x - 5 = 28[/tex]
[tex]3x = 33[/tex]
[tex]x = \frac{33}{3}[/tex]
[tex]x = 11[/tex]
The correct answer is given by option D.
1. A company has a cash portfolio measured in millions. The drift is 0.1 per month, variance is 0.16per month. The initial cash is 2.0. a) Find the probability distribution after 6 months and after 1 year. b) Find the probability of a negative cash position at the end of 6 months and the end of 1 year. c) At what time in the future is the probability of a negative distribution greatest.
Answer:
Step-by-step explanation:
From the information given:
The probability distribution at the end of 6 months is determined as follows:
After 6 months;
Mean of probability distribution = value of Initial cash + [tex]\alpha[/tex]T
=2.0 +(0.1 × 6)
=2.6
After 6 months;
The probability distribution's standard deviation is estimated by using the following formula:
Standard deviation:
[tex]= b\sqrt{T}[/tex]
[tex]= 0.4 \times \sqrt{6}[/tex]
= 0.9798
Hence, after 6 months;
The company's cash position is supposed to be allocated monthly, with the following expenses.
Mean 2.6
Standard deviation 0.9798
Variance 0.96
After 12 months, the probability distribution is as follows:
Mean = value of Initial cash + [tex]\alpha[/tex]T
= 2.0 +(0.1 × 12)
= 3.2
The standard deviation is:
The standard deviation of probability distribution = [tex]b \sqrt{T}[/tex]
[tex]= 0.4 \times \sqrt{12}[/tex]
= 1.3856
Hence, after 6 months;
The company's cash position is supposed to be allocated monthly, with the following expenses.
Mean 3.2
Sandard deviation 1.3856
Variance 1.92
b)
in 6-month distribution, the probability of the negative value of the cash position is as follows.
Now, for us to find the negative cash distribution;
We need to estimate the z -scores value.
The z-score inform us greatly on the concept of how far a particular data point is from the mean.
For a normal distribution;
[tex]z = \dfrac{x-\mu}{\sigma}[/tex]
Here;
the value of x = zero as a result that if it exceeds zero. the cash position will be negative.
∴
[tex]z = \dfrac{x-\mu}{\sigma}[/tex]
[tex]z = \dfrac{0 - 2.6}{0.9798}[/tex]
[tex]z = -2.6536[/tex]
Using the standard distribution tables, it is now possible to calculate that the likelihood N(-2.65) equals 0.004 or 0.4 percent.
As a result, there's a 0.4 percent chance of getting a negative cash balance after six months.
For 12 months distribution:
The Probability of negative cash position is calculated as follows:
[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-3.2}{1.3856} \\ \\ z = -2.3094[/tex]
Using the standard distribution tables,
N(-2.31) equals 0.0104 or 1.04 percent.
As a result, there's a 1.04 percent chance of getting a negative cash balance after 1 year
c) To determine the time period over which the likelihood of achieving a negative cash condition is highest, it's necessary to examine the z-score more closely. Essentially, the z-score measures the difference between a given value(x) and the mean of all potential values [tex](\mu)[/tex], expressed in terms of the total set's standard deviation [tex](\sigma)[/tex]
This suggests that the higher the z-score, the greater the difference occurring between x and [tex]\mu[/tex], and thus the likelihood of receiving x is minimal. As a result, the best chance of finding a certain value is when the z-score is the lowest.
To do so, calculate the derivative of the z-score in relation to the time interval. The point where the derivative is equivalent to zero is where the z-scores are at their lowest.
The first step is to go over the z-score formula in more detail, as seen below.;
[tex]z = \dfrac{x-\mu}{\sigma} \\ \\ z = \dfrac{0-(initial \ value + \alpha T)}{b \sqrt{T}} \\ \\ z = \dfrac{-initial \ value }{b\sqrt{T}}-\dfrac{a \sqrt{T}}{b} \\ \\[/tex]
Now, compute the derivative of this equation with respect to T as follows:
[tex]\dfrac{dz}{dT}= \dfrac{initial \ value \times T^{-\dfrac{3}{2}}}{2b} - \dfrac{aT^{-\dfrac{1}{2}}}{2b}[/tex]
Now, figure out the value of T at which this derivative is equal to zero by substituting all values as follows:
[tex]0 = \dfrac{2.0 \times T^{-\dfrac{3}{2}}}{2\times 0.4}- \dfrac{0.1 \times T^{-\dfrac{1}{2}}}{2 \times 0.4} \\ \\ \\ 0.1 \times T^{-\dfrac{1}{2}}= 2.0 \times T^{-\dfrac{3}{2}} \\ \\ \\T = \dfrac{2}{0.1} \\ \\ \\ T = 20[/tex]
As a result, the time period in which achieving a negative cash condition is = 20 months.
Gina needs to buy a bathroom mirror that is 3 feet wide and 6 feet long. If the mirror sells for $3.00 per square foot, what will the total cost of the mirror be?
Answer:
$54
Step-by-step explanation:
beacuse 6x3=18 and 18x3=54 so your answer will be $54
sorry if im wrong mark me brainliest if im right
PLEASE HELP ME!!!! PLEASE HELP QUICK ILL GIVE U 73 POINTS PLS HELP
Answer:
3
Step-by-step explanation:
In this problem we need to kind of write the picture into an equation so the first thing we see are 4 xs on the far left-hand side this is representing "4x" then we see 5 - blocks on the right which represents "-5" because we have 5 minuses then on the other side we see 7 + blocks which represent just "7". After we identify everything in the picture we can write an equation so 4x -5 = 7. Then we solve so we need to separate x on one side and all the other numbers to the other to do that we can move the -5 to the side the 7 is on and because of math when we move a number to another side of the equation we have to switch the sign it has so if it was -5 then on the other side it would be 5 then we add 7 to 5 which would equal 12. Then we are left with 4x = 12 and to keep x on its own side we need to divide 4 from the other side because it is multiplying on the x side and again we need to switch the sign. then we are left with x=3. Hope this helps!
What is the value of the missing angle?
Answer:
65°
Step-by-step explanation:
All angles in a triangle added up make 180° so you have to add 68° and 47° whih equals 115° and then simply subtract it from 180° so 180°-115°=65°
The line passes through the points (3, 7) and (4, 9)
Answer:
I'm confused as to what your asking?
Answer:
y= 2x +1
Step-by-step explanation:
slope 9-7/4-3 = 2/1= 2
y-7 = 2(x -3)
y-7 = 2x -6
y = 2x +1
Factor out the greatest common monomial factor from polynomial. Show your work or explain your reasoning
Answer:
7(1 +3x)
Step-by-step explanation:
The simplest monomial is a constant that is a prime number. That constant is a factor of the coefficient of the only other monomial in the expression, so it can factored from both terms.
= 7 + 7·3x
= 7(1 +3x)
i'll give brainliest
reflect (-4,4) in the x-axis
Answer:
(-4,-4)
Step-by-step explanation:
Anytime you reflect a coordinate point across the x-axis, the y-coordinate becomes its opposite and the x-coordinate stays the same.
In this coordinate: (-4,4)
Reflecting (-4,4) across the x-axis means the x-coordinate (-4) would stay the same and the y-coordinate (4) would become its opposite (-4).
The new coordinates after being reflected across the x-axis are (-4,-4).
Find the measure of 44.
s
24
158°
ts
64 = [?]
Answer:
∠4 = 22
Step-by-step explanation:
Hello There!
The angles shown are consecutive interior angles
If you didn't know consecutive interior angles are supplementary angles meaning that the sum of the two angles is 180
So we can find the missing angle by subtracting the given angle (158 in this case) from 180
180 - 158 = 22
so we can conclude that ∠4 = 22
180.timr3fzgncvdfccfxdfdxxfhk
180-158=22
the measure is 44
In a certain clothing store 6 shirts and 3 ties cost $79.50 and 3 shirts and 2 ties cost $41 determine the cost of each shirt
9514 1404 393
Answer:
$12 for each shirt
Step-by-step explanation:
If we let 's' and 't' represent the costs of a shirt and tie, respectively, then we can write the general form equations ...
6s +3t -79.50 = 0
3s +2t -41.00 = 0
The solution for s can be found using the "cross multiplication" technique.
Differences of products can be formed:
d1 = (6)(2) -(3)(3) = 3
d2 = (3)(-41) -(2)(-79.50) = 36
Then we have ...
1/d1 = s/d2 ⇒ s = d2/d1 = 36/3 = 12
The cost of each shirt is $12.00.
___
2 ties cost 41-36 = 5, so each one is $2.50.
_____
Additional comment
The use of simple elimination on this set of equations would eliminate the s-variable, so would mean additional work to find s after finding t. The t-variable could be eliminated by multiplying one equation by one coefficient, and the other by a different coefficient. As long as we're doing that amount of work, we may as well do just enough cross-multiplication to get the one answer we need. This is where the "cross-multiplication" method of solution comes in handy.
This method solves the general-form equations ...
ax +by +c = 0dx +ey +g = 0by considering the two rows of coefficients:
a, b, c, ad, e, g, dThen differences of cross-products are formed in adjacent columns:
d1 = ae -db
d2 = bg -ec
d3 = cd -ga
The solutions are ...
1/d1 = x/d2 = y/d3 ⇒ x = d2/d1, y = d3/d1
A CD has a diamter of 4.75 inches, Find the circumference, Use calculator pi or 3.14. Round to the nearest hundredth, if necessary.
WILL GIVE BRAINLIEST!!!
Answer:
15 in.
Step-by-step explanation:
c. Translate the follom
4.) 51 - (x+5)
5.) 3(7-8)
Step-by-step explanation:
1. 51-x-5
= 46-x Answer
2. 21-24
= -3 Answer
Find the area of the polygon.
The length of segment GI is 8. True or false?
Answer: false
Step-by-step explanation: that’s what my teacher told me sorry if it’s wrong
Answer:
It is false
Definetely false
2. If GFE~GJH, find the value of FG.
Answer:
77 unitsStep-by-step explanation:
Given two similar triangles.
Corresponding parts of similar figures have same ratio.
Use ratios to find the value of x:
(4x - 5)/(x + 7) = 35/12.5(4x - 5)/(x + 7) = 14/55(4x - 5) = 14(x + 7)20x - 25 = 14x + 9820x - 14x = 98 + 256x = 123x = 123/6x = 20.5Find the value of FG:
FG = 4*20.5 - 5 = 77a hardware factory produces 3.6 •10^5 bolts in 2400 minutes. what is the factory rate of production in bolts per minute
HELP. NO links. Please help I've been on this for a while
Answer:61
Step-by-step explanation:
Answer:
[tex]\Huge\boxed{C.61}[/tex]
Step-by-step explanation:
Hello There!
Remember this is the triangle angle rule:
The angles of a triangle MUST have a sum of 180
That being said we can find the missing angle by subtracting the given angles ( 87 and 32 in this case) from 180
so missing angle = 180 - 87 - 32
180 - 87 = 93
93 - 32 = 61
so we can conclude that the answer is c
The manager of a restaurant recorded how many people are in different groups of customers and how much does group spent on food and beverages. The scatterplot below shows the date if she recorded. Based on this scatterplot, about how much money would a group of 10 people be expected to spend on food and beverages at this restaurant?
Answer:
$135
Step-by-step explanation:
During the month of April, Samantha Kept
track of the number of days she saw a
hummingbird in her garden. She saw a
hummingbird 18 days during that 30 day
month. Based on this information, how
many days will she see a hummingbird
during the 180 day summer?
Answer:
she will see 108 humming birds
Step-by-step explanation:
30x6= 180
so mutiply how many times she sees one in a month by 6
Answer:
3240
Step-by-step explanation:
Find the value of x in the diagram
Answer:
x = 21
Step-by-step explanation:
Based on the inscribed angle theorem, we would have:
120° = 2(3x - 3)°
Solve for x
120 = 2*3x - 2*3
120 = 6x - 6
Add 6 to both sides
120 + 6 = 6x
126 = 6x
Divide both sides by 6
126/6 = x
21 = x
x = 21
Local versus absolute extrema. If you recall from single-variable calculus (calculus I), if a function has only one critical point, and that critical point is a local maximum (or say local minimum), then that critical point is the global/absolute maximum (or say global/absolute minnimum). This fails spectacularly in higher dimensions (and thereís a famous example of a mistake in a mathematical physics paper because this fact was not properly appreciated.) You will compute a simple example in this problem. Let f(x; y) = e 3x + y 3 3yex . (a) Find all critical points for this function; in so doing you will see there is only one. (b) Verify this critical point is a local minimum. (c) Show this is not the absolute minimum by Önding values of f(x; y) that are lower than the value at this critical point. We suggest looking at values f(0; y) for suitably chosen y
Answer:
Step-by-step explanation:
Given that:
a)
[tex]f(x,y) = e^{3x} + y^3 - 3ye^x \\ \\ \implies \dfrac{\partial f}{\partial x} = 0 = 3e^{3x} -3y e^x = 0 \\ \\ e^{2x}= y \\ \\ \\ \implies \dfrac{\partial f}{\partial y } = 0 = 3y^2 -3e^x = 0 \\ \\ y^2 = e^x[/tex]
[tex]\text{Now; to determine the critical point:}[/tex]- [tex]f_x = 0 ; \ \ \ \ \ f_y =0[/tex]
[tex]\implies e^{2x} = y^4 = y \\ \\ \implies y = 0 \& y =1 \\ \\ since y \ne 0 , \ \ y = 1, \ \ x= 0\\\text{Hence, the only possible critical point= }(0,1)[/tex]
b)
[tex]\delta = f_xx, s = f_{xy}, t = f_{yy} \\ \\ . \ \ \ \ \ \ \ \ D = rt-s^2 \\ \\ i) Suppose D >0 ,\ \ \ r> 0 \ \text{then f is minima} \\ \\ ii) Suppose \ D >0 ,\ \ \ r< 0 \ \text{then f is mixima} \\ \\ iii) \text{Suppose D} < 0 \text{, then f is a saddle point} \\ \\ iv) Suppose \ D = 0 \ \ No \ conclusion[/tex]
[tex]Thus \ at (0,1) \\ \\ \delta = f_{xx} = ge^{3x}\implies \delta (0,1) = 6 \\ \\ S = f_{xy} = -3e^x \\ \\ \implies S_{(0,1)} = -3 \\ \\ t = f_{yy} = 6y \\ \\[/tex]
[tex]\implies t_{0,1} = 6[/tex]
[tex]Now; D = rt - s^2 \\ \\ = (6)(6) -(-3)^2[/tex]
[tex]= 36 - 9 \\ \\ = 27 > 0 \\ \\ r>0[/tex]
[tex]\text{Hence, the critical point} \ (0,1) \ \text{appears to be the local minima}[/tex]
c)
[tex]\text{Suppose we chose x = 0 and y = -3.4} \\ \\ \text{Then, we have:} \\ \\ f(0,-3.4) = 1+ (-3.4)^3 + 3(3.4) \\ \\ = -28.104 < -1[/tex]
[tex]\text{However, if f (0,1) = 1 +1 -3 = -1 \\ \\ f(0,-3.4) = -28.104} < -1} \\ \\ \text{This explains that} -1 \text{is not an absolute minimum value of f(x,y)}[/tex]
Please answer thank u ASAP.
Answer:
a?
Step-by-step explanation:
Verify the Identity.
tan²xsin²x = tan²x-sin²x
tan²(x) - sin²(x) = sin²(x)/cos²(x) - sin²(x)
… = sin²(x) (1/cos²(x) - 1)
… = sin²(x) (sec²(x) - 1)
… = sin²(x) tan²(x)
Suppose that the height (in centimeters) of a candle is a linear function and the amount of time (in hours) it has been burning. After 9 hours of buring, a candle has a hight of 22.2 centimeters. After 23 hours of burning, it's heigh is 16.8 centimeters. What is the height of candle after 19 hour
Answer: cockme
Step-by-step explanation:
cockme
(3f–3)^2 pls help
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PLS HELPPPPPPP MEEEEE
Answer:
4.7 · 10^7
Step-by-step explanation:
What is the intercept of the equation
Answer:
-2
Step-by-step explanation:
Plug y=0 into the equation and solve the resulting equation 0=3x+6 for x