You want to buy an ice cream cone but you want to make sure it’s worth your money, the cone has a radius of 1.4 inches and a height of 4.5 inches. How much ice cream will fit inside?
30 points please show work thanks so much :)
The amount of ice cream that can fit into the cone is about 9.24 in³.
What is volume?
Volume is the amount of space occupied by a three dimensional shape and object. The volume of a cone is given by:
Volume (V) = (1/3) * π * radius² * height
From the dimensions of radius = 1.4 in and height = 4.5 in, hence:
V = (1/3) * π * 1.4² * 4.5 = 9.24 in³
The amount of ice cream that can fit into the cone is about 9.24 in³.
Find out more on volume at: https://brainly.com/question/12410983
Using the volume of the cone, it is found that 9.24 cubic inches of ice cream will fit inside.
What is the volume of a cone?The volume of a cone of radius r and height h is given by:
[tex]V = \frac{\pi r^2h}{3}[/tex]
In this problem, the cone has a radius of 1.4 inches and a height of 4.5 inches, hence r = 1.4, h = 4.5, then:
[tex]V = \frac{\pi 1.4^2(4.5)}{3} = 9.24[/tex]
9.24 cubic inches of ice cream will fit inside.
More can be learned about the volume of a cone at https://brainly.com/question/14281550
factorise [8x^{2}-30x-27=0
Answer:
Step-by-step explanation:
8x² - 30x - 27 = 0
8 = 4 * 2
-27 = -9 * 3
-30 = 4*(-9) + 2*3
so (4x + 3)(2x - 9) = 0
Please help me with this I need it now :)
Answer:
reverse it x-15=4 do 15+4=x
Step-by-step explanation:
help please!
I need to prove this using identities
show all steps
cos(pi/2+x)/cos(pi+x)=tanx
Answer: see proof below
Step-by-step explanation:
Use the Sum & Difference Identity: cos (A + B) = cos A · cos B - sin A · sin B
Recall the following from Unit Circle: cos (π/2) = 0, sin (π/2) = 1
cos (π) = -1, sin (π) = 0
Use the Quotient Identity: [tex]\tan A=\dfrac{\sin A}{\cos A}[/tex]
Proof LHS → RHS:
[tex]\text{LHS:}\qquad \qquad \dfrac{\cos \bigg(\dfrac{\pi}{2}+x\bigg)}{\cos \bigg(\pi +x\bigg)}[/tex]
[tex]\text{Sum Difference:}\qquad \dfrac{\cos \dfrac{\pi}{2}\cdot \cos x-\sin \dfrac{\pi}{2}\cdot \sin x}{\cos \pi \cdot \cos x-\sin \pi \cdot \sin x}[/tex]
[tex]\text{Unit Circle:}\qquad \qquad \dfrac{0\cdot \cos x-1\cdot \sin x}{-1\cdot \cos x-0\cdot \sin x}[/tex]
[tex]=\dfrac{-\sin x}{-\cos x}[/tex]
Quotient: tan x
LHS = RHS [tex]\checkmark[/tex]
find the slope and the y-intercept for the graph of y = -4.
a -4;none
b 1;-4
c 0; -4
d -4;0
thank you for the help
Answer:
C, 0;-4
Step-by-step explanation:
y=-4 means that no matter what the x value is, the y value will ALWAYS be -4. It does not change based on what x is, and we can tell that just by looking at it because x isn't even in the equation. I've attached an image of that the graph would look like.
The slope of the graph references how many units the y value increases for each increase in the x value. For example, a slope of 1/2 means that each time the x value increases by 2, the y value would increase by 1. But because y's value never changes, the slope is 0. No matter how much the x value changes, the increase in y values will be 0.
Since the y-axis is at where x=0, the y-intercept basically asks, "What is y's value when x is 0?" But like I mentioned before y's value never changes. It's always -4, no matter what the x value is. Therefore, the y-intercept is at -4.
Rewrite the following quadratic function in vertex form.
f(x)=6x^2−6x+1
Answer:
f(x)=6(x-0.5)²-0.5.
Step-by-step explanation:
1) the rule is:
f (x) = a(x - h)² + k, where (h, k) is the vertex of the parabola;
2) according to the rule above:
f(x)=6(x²-x+0.25)-0.5; ⇔
f(x)=6(x-0.5)²-0.5.
Help!
What is the answer to this question?
Answer:
b = 73°
Step-by-step explanation:
They are vertical angles to each other.
A machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%). Prior to shipment produced parts are passed through an automatic inspection machine, which is supposed to be able to detect any part that is obviously defective and discard it. However, the inspection machine is not perfect. A part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input. Slightly defective parts are marked as defective and discarded 40% of the time, and obviously defective parts are correctly identified and discarded 98% of the time.
Required:
a. What is the total probability that a part is marked as defective and discarded by the automatic inspection machine?
b. What is the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped?
c. What is the probability that a part is 'bad' (obviously defective) given that it makes it through the inspection machine and gets shipped?
Answer:
(a) 0.0686
(b) 0.9984
(c) 0.0016
Step-by-step explanation:
Given that a machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%).
Let A, B, and C be the events of defect-free, slightly defective, and the defective parts produced by the machine.
So, from the given data:
P(A)=0.90, P(B)=0.03, and P(C)=0.07.
Let E be the event that the part is disregarded by the inspection machine.
As a part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input.
So, [tex]P\left(\frac{E}{A}\right)=0.02[/tex]
Now, from the conditional probability,
[tex]P\left(\frac{E}{A}\right)=\frac{P(E\cap A)}{P(A)}[/tex]
[tex]\Rightarrow P(E\cap A)=P\left(\frac{E}{A}\right)\times P(A)[/tex]
[tex]\Rightarrow P(E\cap A)=0.02\times 0.90=0.018\cdots(i)[/tex]
This is the probability of disregarding the defect-free parts by inspection machine.
Similarly,
[tex]P\left(\frac{E}{A}\right)=0.40[/tex]
and [tex]\Rightarrow P(E\cap B)=0.40\times 0.03=0.012\cdots(ii)[/tex]
This is the probability of disregarding the partially defective parts by inspection machine.
[tex]P\left(\frac{E}{A}\right)=0.98[/tex]
and [tex]\Rightarrow P(E\cap C)=0.98\times 0.07=0.0686\cdots(iii)[/tex]
This is the probability of disregarding the defective parts by inspection machine.
(a) The total probability that a part is marked as defective and discarded by the automatic inspection machine
[tex]=P(E\cap C)[/tex]
[tex]= 0.0686[/tex] [from equation (iii)]
(b) The total probability that the parts produced get disregarded by the inspection machine,
[tex]P(E)=P(E\cap A)+P(E\cap B)+P(E\cap C)[/tex]
[tex]\Rightarrow P(E)=0.018+0.012+0.0686[/tex]
[tex]\Rightarrow P(E)=0.0986[/tex]
So, the total probability that the part produced get shipped
[tex]=1-P(E)=1-0.0986=0.9014[/tex]
The probability that the part is good (either defect free or slightly defective)
[tex]=\left(P(A)-P(E\cap A)\right)+\left(P(B)-P(E\cap B)\right)[/tex]
[tex]=(0.9-0.018)+(0.03-0.012)[/tex]
[tex]=0.9[/tex]
So, the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped
[tex]=\frac{\text{Probabilily that shipped part is 'good'}}{\text{Probability of total shipped parts}}[/tex]
[tex]=\frac{0.9}{0.9014}[/tex]
[tex]=0.9984[/tex]
(c) The probability that the 'bad' (defective} parts get shipped
=1- the probability that the 'good' parts get shipped
=1-0.9984
=0.0016
9,874.35 - 6490.02
step by step
Answer:
[tex]9874.35 \\ 6490.02 \\ 3384.33[/tex]
which algebraic expression is correct on this mathematical phrases?the qoutient of a and b multiplied by the difference of t and s
A.(axb)-(s-t) B. (axb)+(t-s) C.(a÷b)-(sxt) D.6a+2
please answer this fast i need it right now i'll give you brainleist
Answer:
D
Step-by-step explanation:
quotient of a and b: a ÷ b
multiplied: ×
difference of t and s: t - s
Therefore: (a ÷ b) × (t - s)
Answer:
D. (a/b) x (t-s)
Step-by-step explanation:
Given :-
The quotient of a and b multiplied by the difference of t and s.
Solving :-
Quotient of a and b = a/b
Difference of t and s = t - s
Multiplied together :-
(a/b) x (t-s)
Solution :-
D. (a/b) x (t-s)
What's a non-included angle?
Answer:
It is the side where the rays of the angles overlap. The "non-included" side in AAS can be either of the two sides that are not directly between the two angles being used.
“Firms will loss _?_ if the firm shuts down in the short run”
Answer:
The correct answer was C!
Step-by-step explanation:
On a map, Peach Street is modeled by the equation 4x - y = 7. Apple Street is perpendicular to Peach Street and passes through the point
(12, 2). Find the equation that models Apple Street (1 point)
A. Y=1/4x+5
B. Y=-1/4x-1
C. Y=1/4x-1
D. Y=-1/4x+5
Did you ever get the answer
Angle T and angle V are complementary angles. If cos T = 0.75, which statment is always true?
Complementary angles T and V would add up to 90 degrees
The true statement is sin V = 0.75
How to determine the correct statement?The given parameters are:
cos T = 0.75
Angles T and V are complementary angles
The second highlight above means that:
T + V = 90cos T = sin Vsin T = cos VSubstitute 0.75 for cos T in cos T = sin V
0.75 = sin V
Rewrite as:
sin V = 0.75
Hence, the true statement is sin V = 0.75
Read more about complementary angles at:
https://brainly.com/question/16281260
In Ben's apartment complex, residents are fined $9 per day each day the rent is late. Last month, Ben wrote the apartment complex a check for $702 when his monthly rent is only $585. How many days late was Ben's rent?
Answer:
13 days late-poor guy
Step-by-step explanation:
(702-585)/9
117/9
13
Griffin bought 1.2 pounds of almonds for $6.60. His friend, Sam, bought almonds for $0.70 per pound cheaper. Which equation represents the cost, c, Sam paid for x pounds of almonds?
A.c = 4.80x
B. c = 5.50x
C. c = 5.90x
D. c = 7.30x
Answer:
Step-by-step explanation:
A
Answer: C
Step-by-step explanation:
0.70 divided by 1.2=0.59
0.59*1.2= 0.70
c=5.90x
A parabola has an axis of symmetry at x = 0.5 and one of the x-intercepts is at x=-3. Where is
the other x-intercept?
Answer:
4
Step-by-step explanation:
distance from .5 to -3 is 3.5
now add the same distance to the other side
.5 plus 3.5 is 4
In Table 2, at this rate, how much would it cost to buy 9 books?
Answer:
There is no table attached, if you attach is I will gladly help :)
Step-by-step explanation:
write each equation in slope-intercept form (3,4); and (-6,-2)
Answer:
y = 2/3x + 2
Step-by-step explanation:
Slope intercept form is y=mx+b where m is the slope and b is the y intercept.
Given 2 points you can find the slope using (y-y1)/(x-x1)
m = (-2-4)/(-6-3) = -6/-9 = 2/3
To find b use one of the points and m and plug into the slope intercept form and then solve for b.
y=mx+b
4=2/3(3) + b
4=2 + b
b=2
Now we can write the final equation as : (plug m and b back in)
y = 2/3x + 2
To write in slope-intercept form, we must first find the slope.
[tex]Slope = \frac{y2-y1}{x2-x1} =\frac{4-(-2)}{3-(-6)} =\frac{6}{9}=\frac{2}{3}[/tex]
Now lets put into the point-slope form which requires the use of any one of the two points given which in this case can be (3,4) and the slope 2/3
[tex]y - y_{0} =m(x-x_{0} )\\y-4=\frac{2}{3} (x-3)\\[/tex]
Now to put into the slope-intercept form, we must solve for y:
[tex]y - 4 = \frac{2}{3} x -2\\y = \frac{2}{3} x +2[/tex]
Hope that helps!
A food safety guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 99% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi?
0.57 0.68 0.10 0.93 1.29 0.55 0.86
What is the confidence interval estimate of the population mean mu?
_ppm < mu < _ ppm
Answer:
hi there friend
Step-by-step explanation:
CI=(0.431,1.0376)CI=(0.431,1.0376)
Explanation:
Given that:
The sample size , n = 7
The mean of the observation:
Mean = Sum of observation / Total number of observation
= (0.56+ 0.72+ 0.10 + 0.99 + 1.32 + 0.52 + 0.93) / 7 = 0.7343
The standard deviation:
S.D. = \sqrt {\frac {\sum_{i=1}^{i=7}(x_i-\bar{x})^2}{n-1}}S.D.=
n−1
∑
i=1
i=7
(x
i
−
x
ˉ
)
2
Calculating SD as:
S.D. = \sqrt {\frac {(0.56-0.7343)^2+(0.72-0.7343)^2+.....+(0.52-0.7343)^2+(0.93-0.7343)^2}{7-1}}S.D.=
7−1
(0.56−0.7343)
2
+(0.72−0.7343)
2
+.....+(0.52−0.7343)
2
+(0.93−0.7343)
2
SD = 0.3928
Degree of freedom = n-1 = 6
The critical value for t at 2% level of significance and 6 degree of freedom is 2.043.
So,
90 \% \ confidence\ interval=Mean\pm Z\times \frac {SD}{\sqrt {n}}90% confidence interval=Mean±Z×
n
SD
So, applying values , we get:
CI=0.7343\pm 2.043\times \frac {0.3928}{\sqrt {7}}CI=0.7343±2.043×
7
0.3928
CI=(0.431,1.0376)CI=(0.431,1.0376)
if you doubled a recipe that makes 2 doz. cookies how many cookies would you expect to make
Answer:
48
Step-by-step explanation:
remember 1 dozen of something is 12 of that object
so 1 dozen cookies is 12 cookies
two dozen means two times one dozen
or 2-times twelve (because there are twelve of an object in a dozen)
2 times 12 is 24
now you double the recipe that makes 2 dozen cookies
so you have 24 cookies and you multiply that by 2 to double it and you get 48
A campsite provides a locking, rectangular box with the dimensions shown to secure
food from bears. What is the volume?
(PUT NUMBER ONLY)
3 feet
2 feet
5 feet
Answer:
30 feet^3
Step-by-step explanation:
2*5*3=30
V= bhw
what is the elapse time between 10:35am and 1:10pm
2 hours, 35 minutes, and 0 second
Step-by-step explanation:
10 am to 1 pm is 2 hours
and you have the 35 in which you add there for giving you the answer 2 hours, 35 minutes, and 0 second
Answer:
2 hours 35 minutes
Step-by-step explanation:
Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 9 ounces. The process standard deviation is 0.15, and the process control is set at plus or minus 1 standard deviation. Units with weights less than 8.85 or greater than 9.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)
Answer:
[tex]1-P(8.85 < X < 9.15)=0.3173[/tex]
Step-by-step explanation:
We need to first calculate the probability that a unit between the weight of 8.85 and 9.15 ounces is NOT a defect, then subtract it from 1.
It just so happens that 8.85 and 9.15 are both 1 standard deviation from the mean of 9, so by the Empirical Rule, [tex]P(8.85 < X < 9.15)=0.6827[/tex].
Thus, the probability of a unit being a defect is [tex]1-P(8.85 < X < 9.15)=1-0.6827=0.3173[/tex]
In January, the depth of a lake was 1,178 feet. In August, the depth of the lake was 1,001.3 feet. What is the percentage decrease of the depth of the lake from January to August?
Answer:
15%
Step-by-step explanation:
decrease in depth = 1,178 - 1,001.3 = 176.7
percentage decrease = 176.7/1,178 = 0.15 = 15%
All the prime numbers
Answer:
13 23 43
Step-by-step explanation:
Prime numbers are numbers that are divisible by 1 and itself or numbers that have only 2 factors which is 1 and itself.
Prove the following
please help
Step-by-step explanation:
3. (1 + cos x) (1 − cos x)
Distribute using FOIL.
1 − cos²x
Use Pythagorean identity.
sin²x
4. sin x / (1 − cos x)
Multiply by the conjugate.
sin x (1 + cos x) / ((1 − cos x) (1 + cos x))
Distribute using FOIL.
sin x (1 + cos x) / (1 − cos²x)
Use Pythagorean identity.
sin x (1 + cos x) / sin²x
Divide.
(1 + cos x) / sin x.
Split the fraction.
(1 / sin x) + (cos x / sin x)
csc x + cot x
A small can contain 2 cups of soup. do 3 small cans have a greater amount than a 1 - quart container of soup.
Answer:
quarts. 11. fluid ounces = —. 1. 4. — quart. 12. quarts = 6 gallons. 13. 16 pints = gallons. 14. ... How many times must a 1-cup measuring cup be filled to equal 4 pints? 2. Leroy has 2 containers. ... can hold. Write cup, pint, quart, or gallon. 15. a bathtub. 16. a container of orange juice. 17. a juice box. 18. a small milk carton. 1
Step-by-step explanation:
What is the slope of a line perpendicular to the line in the graph?
Answer:
-[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Please i need your help
Answer:
it okay I can help you with that