Step-by-step explanation:
1/3 πr²h
Given
diameter (d) = 8ft
radius (r) = d/2 = 8/2 = 4 ft
height (h) = 3 ft
Volume of cone
[tex] \frac{1}{3} \times \pi {r}^{2} h[/tex]
[tex] \frac{1}{3} \times 3.14 \times {4}^{2} \times 3[/tex]
[tex] \frac{150.72}{3} [/tex]
=50.24 ft³
The cone formula is V=1/3(pi*r^2)h, plug in what you know 150pi=1/3(pi*r^2)8.
Multiply both sides by 3: 450pi=(pi*r^2)8
Divide by 8: 56.25pi=pi*r^2
Divide by pi: 56.25=r^2
Square root both sides: 7.5=r
Multiply by 2 to find diameter: d=15
Angles PTQ and STR are vertical angles and congruent.
Which chords are congruent?
O QP and SR
O QR and PO
PR and RS
PR and PS
Answer: QP and SR on ed
Step-by-step explanation:
The chords in the circle that are congruent are PQ and SR.
CircleCircle is the locus of a point such that its distance from a fixed point known as the center is constant.
Given from the diagram that:
∠PTQ = ∠STR (Vertical opposite angles are congruent)
Hence:
PQ = SR
The chords in the circle that are congruent are PQ and SR.
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The length of a rectangle is nine inches more than its width. Its area is 850 square inches. Find the width and length of the rectangle.
Answer:
width= 25 inches
length= 34 inches
Step-by-step explanation:
width x length = 850 in²
w x (9+ w ) = 850 in²
9w+ w²=850 in²
9w + w²-850 =0
solve for w using quadratic formula
w= {-9 ±√(9)²-4(1)(-850)} ÷2(1)
w= 25; -34
The width is 25 because measurements can't be negative.
width= 25
length= 25+9=34
Evaluate 6c + e2 when c = 6 and e = 2
[tex]c=6, e=2; so\\6\times6+2\times2=40[/tex]
What is the value of z in 1/4 raised to the 3z-1 = 16 raised to the z+2 times 64 raised to the z-2
Answer:
3/8
Step-by-step explanation:
In terms of powers of 4, we have ...
(4^-1)^(3z -1) = (4^2)^(z+2)×(4^3)^(z-2)
Taking logarithms base 4*, we have ...
-(3z -1) = 2(z +2) +3(z -2)
-3z +1 = 5z -2 . . . . simplify
3 = 8z . . . . . . . . . . add 3z+2
z = 3/8 . . . . . . . . . .divide by 8
_____
* This is equivalent to equating exponents of the same base. You're making use of the rules of exponents ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
1/a = a^-1
and the logarithm relations ...
logb(b^x) = x
log(xy) = log(x) +log(y)
Two number cubes each have sides that are labeled 1 to 6. Isis rolls the 2 number cubes. What is the probability that the sum of the numbers rolled will equal 4?
Answer:
The probability that the sum of the numbers rolled will equal 4 is [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Total possible outcome is 36
The sample space for the dice is shown below
[tex]\left[\begin{array}{cccccc}1,1&1,2&1,3&1,4&1, 5&1,6\\2,1&2,2&2,3&2,4&2, 5&2,6\\3,1&3,2&3,3&3,4&3, 5&3,6\\4,1&4,2&4,3&4,4&4, 5&4,6\\5,1&5,2&5,3&5,4&5, 5&5,6\\6,1&6,2&6,3&6,4&6, 5&6,6\end{array}\right][/tex]
From the above sample, the event of sum equals 4 is:
(1, 3)
(2, 2)
(3, 1)
Number of outcome with sum equals 4 is 3
[tex]Probability = \frac{number of possible outcome}{number of total outcome} \\Probability = \frac{3}{36} = \frac{1}{12}[/tex]
The probability that the sum of the numbers rolled will equal 4 is [tex]\frac{1}{12}[/tex]
Answer:
0.3333
Step-by-step explanation:
Out of 6x6 = 36 different scenarios that could happen when rolling the 2 cubes, there are 3 cases where the sum of the numbers rolled will equal 4:
(1,3) (3,1) and (2,2)
So the probability for these 3 cases to happen out of 36 is
[tex]\frac{3}{36} = \frac{1}{3}[/tex] or 0.3333
Please help me with these square root problems, Part 1. Please show and check the work.
[tex]1. \sqrt{2x-5} - \sqrt{x+6} =0\\\\2. \sqrt{2x-5} + \sqrt{x+6}=0\\ \\3. \sqrt{x-5} - \sqrt{x+6}= 2\\ \\4. \sqrt{2x-5} -\sqrt{x+6}=2[/tex]
Answer:
x = 11
Step-by-step explanation:
sqrt (2x - 5) = sqrt (x + 6)
Square both sides
2x - 5 = x + 6
x = 11
Verify:
sqrt[2(11) - 5] = sqrt(11 + 6)
sqrt(17) = sqrt(17)
Answer:
x = 11
Step-by-step explanation:
√2x-5 - √x+6 = 0
√2x-5 = √x+6
(√2x-5)² = (√x+6)²
2x - 5 = x + 6
2x - x = 6 + 5
x = 11
A 3 cm * 3 cm rectangle sits inside a circle with radius of 4 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
44.24
Step-by-step explanation:
Khan academy
Answer:
Step-by-step explanation:
determine which of the following are functions. select all that apply
Relation (A) and polynomial (D) y = -4x² + 45x + 9 are functions rest are not function.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
In option (A) ;
For every single unique input, there is single unique output so it will function.
In option (B) ;
Here for x = 0,2 and y = 5 so it means for two inputs one output so it will not be a function.
In option (C) ;
For x = 0 , y = 2 , 4 so two output for one input it means it is also not a function.
In option (D) ;
y = -4x² + 45x 9 it gives one input for one output.
Hence "Relation (A) and polynomial (D) y = -4x² + 45x + 9 are functions rest are not function".
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Given question is incomplete so image has been attached
John determined that the unit rate for his trip to Orlando was 70 miles every 2 hours. Why is John's determination incorrect? Calculate the actual unit rate for his trip.
Answer:
John's determination incorrect because he didn't give a unit rate which is miles per hour (mph).
The actual unit rate for his trip is v;
v = 70 miles ÷ 2 hours
v = 35 miles per hour
v = 35mph
Step-by-step explanation:
Given;
John travels 70 miles in 2 hours
John's determination incorrect because he didn't give a unit rate which is miles per hour (mph).
The actual unit rate for his trip is;
v = 70 miles ÷ 2 hours
v = 35 miles per hour
v = 35mph
15 POINTS PLZ HELP
It’s all in pic
Answer:
D
Step-by-step explanation:
it's In the picture
please like and Mark as brainliest
Answer:
Volume of the cylinder = D) 113.04 cubic cm
Step-by-step explanation:
[tex] \boxed{ \bold{formula = \pi \: {r}^{2} \: h }}[/tex]
= 3.14 × 2 × 2 × 9
= 3.14 × 36
= 113.04 cm³
Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds. This function is shown in the graph below.
What do the x-intercepts represent in this real life situation in regards to the height of the soccer ball at that time?
# 15. Tycho wants to prepare a schedule for his exercise over the next few months. Every
week, he wants to exercise on the same days of the week. He does not want to exercise on
two consecutive days. He wants to exercise three days per week. How many schedules can he
choose from?
(A) 6
(B) 7
(C) 9
(D) 10
(E) 35
There are a total of 9 possible schedules that Tycho can choose from.
Thus, option (C) is correct.
Let consider the days of the week as Monday (M), Tuesday (T), Wednesday (W), Thursday (Th), Friday (F), Saturday (Sa), and Sunday (Su).
To create a schedule for exercise, Tycho needs to choose three days of the week to exercise such that no two exercise days are consecutive.
So, the possibilities are:
1. Tycho chooses Monday, Wednesday, and Friday.
The schedule is MW FSu.
2. Tycho chooses Monday, Wednesday, and Saturday.
The schedule is MW SaSu.
3. Tycho chooses Monday, Thursday, and Saturday.
The schedule is MT F SaSu.
4. Tycho chooses Monday, Thursday, and Sunday.
The schedule is MT SaSu.
5. Tycho chooses Tuesday, Thursday, and Saturday.
The schedule is TThSaSu.
6. Tycho chooses Tuesday, Thursday, and Sunday.
The schedule is TTSaSu.
7. Tycho chooses Tuesday, Friday, and Sunday.
The schedule is TFSaSu.
8. Tycho chooses Wednesday, Friday, and Sunday.
The schedule is W F SaSu.
9. Tycho chooses Wednesday, Thursday, and Saturday.
The schedule is W T FSaSu.
Thus, total of 9 possible schedules that Tycho can choose from.
Thus, option (C) is correct.
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Lucy invested $30,000 in an account paying an interest rate of 6.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 9 years?
Answer:
A≈54300
Step-by-step explanation:
To calculate the final amount in the bank account, we can use the formula A = P(e(rt)), where A is the final amount, P is the principal amount, e is the base of natural logarithms, r is the interest rate, and t is the time in years. In this case, Lucy invested $30,000 at an interest rate of 6.6% compounded continuously for 9 years. By substituting these values into the formula and evaluating the expression, the final amount in the account after 9 years is approximately $53,509.79.
Explanation:To calculate the final amount in the bank account, we can use the formula: A = P(e(rt)), where A is the final amount, P is the principal amount, e is the base of natural logarithms, r is the interest rate, and t is the time in years. In this case, Lucy invested $30,000 at an interest rate of 6.6% compounded continuously for 9 years.
First, we need to convert the interest rate to a decimal by dividing it by 100: 6.6% = 0.066. Then, we can substitute the values into the formula: A = 30000(e0.066*9)). Using a calculator, we can evaluate this expression to get the final amount, which is approximately $53,509.79.
Please. Help me answer this question.
The sum of the measures of a regular 25 sided polygon is 4140 degrees. What is the measure of each interior angle?
Answer: 165.6
Step-by-step explanation:
The formula for finding the interior angle of a polygon is
= (2n - 4) x right angle
= (2n - 4)90 ,or
(n - 2)180
Now since the sum total of the interior angle of the 25 sided regular polygon = 4140 using the formula above,
Therefore, the value of each of the interior angle will be
= 4140/25
= 165.6
Final answer:
Each interior angle of a regular 25-sided polygon, with sum of the interior angles at 4140 degrees, measures 165.6 degrees.
Explanation:
The sum of the measures of a regular 25-sided polygon is 4140 degrees. To find the measure of each interior angle of a regular polygon, we use the formula:
(n - 2) × 180° = Sum of interior angles,
where n is the number of sides in the polygon. Since we are given that the sum of the interior angles is 4140 degrees for a 25-sided polygon, we can plug in the values into our formula:
(25 - 2) × 180° = 4140 degrees,
which simplifies to:
23 × 180° = 4140 degrees.
This confirms the given sum of the interior angles. To find the measure of one interior angle, we divide the sum by the number of angles:
4140 degrees ÷ 25 = 165.6 degrees.
So the measure of each interior angle in a regular 25-sided polygon is 165.6 degrees.
Alexa is pushing a construction barrel up a ramp 4 feet long into the back of a truck. She is using a force of 120 pounds in a horizontal direction and the ramp is 45 degrees from the horizontal. How much work is Alexa doing?
Answer:
Alexa did about 339.41 foot-pound of work in moving the barrel up the ramp.
Step-by-step explanation:
Work done is defined as the dot product of Force and displacement i.e.
W = F.d
Expanding the dot product, we get:
W = Fd cos(Ф)
Here,
W is the amount of work done, F is the Force applied, d is the displacement and Ф is the angle made by Force F with the horizontal. If we observe the given statement we can clearly see that:
Force applied = F = 120 pounds
Displacement = d = 4 feet
Angle of F with horizontal = Ф = 45 degrees
Substituting the values in the formula we get:
W = 120 x 4 x cos(45)
W = 339.41 foot-pound
This means, Alexa did about 339.41 foot-pound of work in moving the barrel up the ramp.
Final answer:
Alexa is doing approximately 339.33 pounds-feet of work to push the construction barrel up a 4-foot ramp at a 45-degree angle, calculated using the cosine of the angle to find the component of the force parallel to the direction of motion.
Explanation:
To calculate the work done by Alexa, we need to consider the component of the force she exerts that is parallel to the direction of motion up the ramp. Since the force exerted is in the horizontal direction and the ramp is at a 45-degree angle to the horizontal, we use the cosine of the angle to find this component. The formula for work is:
Work = Force × Distance × cos(θ)
Where the force is 120 pounds, the distance is 4 feet, and θ (theta) is the angle of the ramp, which is 45 degrees.
The component of the force parallel to the ramp is 120 pounds × cos(45°) = 120 pounds × 0.7071 (since the cosine of 45 degrees is √2/2, which approximately equals 0.7071).
The work performed by Alexa is:
Work = 120 pounds × 0.7071 × 4 feet × = 339.325 pounds-feet
Alexa is doing approximately 339.33 pounds-feet of work to push the construction barrel up the ramp.
k + 22 = 29
Solve the equation.
Look at the attached picture⤴
Hope it will help u...
Answer:
k=7
Step-by-step explanation:
To solve, we need to isolate the variable: k
k +22 =29
Subtract 22 from both sides to "reverse" the addition
k+22=29
-22 -22
k=7
If a stone is thrown up at 10 m per second from a height of 100 meters above the surface of the moon, its height in meters after t seconds is given by s = 100+10t-0.8t^2 . What is its acceleration?
Answer:
-1.6 m/s
Step-by-step explanation:
According to the equations of motion, the height in meters (s) after t seconds is:
[tex]s(t) = s_0+v_0t+a\frac{t^2}{2}[/tex]
If the initial position is 10 m and the initial velocity is 10 m/s:
[tex]s(t) = 100+10+a\frac{t^2}{2}[/tex]
When comparing it with the given height equation, it is possible to obtain the acceleration as follows:
[tex]100+10+a\frac{t^2}{2} =100+10t-0.8t^2\\\frac{a}{2}=-0.8\\ a=-1.6\ m/s[/tex]
Acceleration is -1.6 m/s.
The label on Adriana's carton of juice has this information listed. One serving size equals 12 cup. Each serving has 30% of the recommended daily amount of vitamin C. Yesterday, Adriana drank 214cups of juice. What percent of the recommended daily amount of vitamin C was in the juice Adriana drank yesterday? 33.75% 67.5% 120% 135%
Answer:
135%
Step-by-step explanation:
we know that
One serving size equals 1/2 cup. Each serving has 30% of the recommended daily amount of vitamin C.
step 1
Using proportion
Find out the number of servings if Adriana drank 2 1/4 cups of juice
so
[tex]\frac{1}{\frac{1}{2}}=\frac{x}{2\frac{1}{4}}[/tex]
Convert mixed number to an improper fraction
[tex]2\frac{1}{4}=2+\frac{1}{4}=\frac{9}{4}[/tex]
substitute in the proportion
[tex]\frac{1}{\frac{1}{2}}=\frac{x}{\frac{9}{4}}\\\\x=\frac{(9/4)}{(1/2)}\\\\x=4.5\ servings[/tex]
step 2
we know that
Each serving has 30% of the recommended daily amount of vitamin C.
so
Multiply the number of servings by 30%
[tex]4.5(30\%)=135\%[/tex]
The diagram shows a square with a perimeter of 40 cm
Answer:
10cm
Step-by-step explanation:
If you are asking what is the length of each side?
The answer is simple first divide the total perimeter by the number of sides.(ONLY FOR A SQUARE) then you get your length.
\text{Min}Minstart text, M, i, n, end text Q_1Q 1 Q, start subscript, 1, end subscript \text{Median}Medianstart text, M, e, d, i, a, n, end text Q_3Q 3 Q, start subscript, 3, end subscript \text{Max}Maxstart text, M, a, x, end text 121212 181818 232323 262626 292929 The five-number summary suggests that about 75\%75%75, percent of lakes in Minnesota have more than what number of house boats? Choose 1 answer:
Answer:
18 Houseboats
Step-by-step explanation:
Given the set of numbers
12 18 23 26 29
Minimum = 12
First Quartile, Q₁ = 18
Median, Q₂ = 23
Third Quartile, Q₃ = 26
Maximum = 29
The first 25% of lakes have less than or equal to 18 houseboats.
Therefore, the 5-Number Summary suggests that about 75% of lakes in Minessotta have more than 18 Houseboats.
Answer:
18
YEET
Step-by-step explanation:
On a coordinate plane, 2 lines are shown. The first solid straight line has an equation of y greater-than-or-equal-to negative one-fifth x + 1, has a negative slope, and goes through (negative 5, 2) and (0, 1). Everything above the line is shaded. The second dashed solid line has equation y less-than 2 x + 1, has a positive slope, and goes through (negative 2, negative 3) and (0, 1). Everything to the right of the line is shaded. Which ordered pairs make both inequalities true? Check all that apply. (–2, 2) (0, 0) (1,1) (1, 3) (2, 2)
Answer:
The answers are (1,1) and (2,2) or C and E
Step-by-step explanation:
Just did it on edge 2021
The ordered pairs are (1,1) and (2, 2).
What are ordered pairs?In arithmetic, an ordered pair is a pair of gadgets. The order in which the items appear in the pair is good-sized: the ordered pair is different from the ordered pair except for a = b. Ordered pairs also are known as 2-tuples, or sequences of period 2.
What are ordered pairs examples?An ordered pair is a pair of numbers in a specific order. for instance, (1, 2) and (- 4, 12) are ordered pairs. The order of the two numbers is crucial: (1, 2) isn't equal to (2, 1) -- (1, 2)≠(2, 1)
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What is the length of PR?
Answer:
[tex]8\sqrt{3}[/tex]
Step-by-step explanation:
2/3 pi radians = 2/3 * 180 = 2 * 60 = 120 degrees
split triangle in half:
30, 60, 90 triangle
1/2 PR= 4 root 3
Please help me with the Square Root problems, Part 4. Please Show and Check the work.
[tex]13. x + 2 = 4\sqrt{x-2} \\\\14. \sqrt{2x-1} +\sqrt{3x-12} = 0\\\\15. x = 2\sqrt{x-4} + 4\\\\16. x-2= \sqrt{9x-36}[/tex]
Answers and Step-by-step explanations
13. Square both sides: x^2 + 4x + 4 = 16(x - 2) = 16x - 32
Move all the terms to one side: x^2 - 12x + 36 = 0
Factorize: (x - 6)^2 = 0 ⇒ x = 6
14. Move one of the roots to one side: [tex]-\sqrt{2x-1} =\sqrt{3x-12}[/tex]
Square both sides: 2x - 1 = 3x - 12
Solve for x: x = 11
15. Subtract 4 from both sides: x - 4 = [tex]2\sqrt{x-4}[/tex]
Square both sides: x^2 - 8x + 16 = 4(x - 4) = 4x - 16
Move all the terms to one side: x^2 - 12x + 32 = 0
Factorize: (x - 4)(x - 8) = 0 ⇒ x = 4 or x = 8
16. Square both sides: x^2 - 4x + 4 = 9x - 36
Move all the terms to one side: x^2 - 13x + 40 = 0
Factorize: (x - 5)(x - 8) = 0 ⇒ x = 5 or x = 8
Hope this helps!
Answer:
13. x = 6
14. No real solutions
15. x = 4, 8
16. x = 5, 8
Step-by-step explanation:
13. Square both sides
(x + 2)² = 4²(x - 2)
x² + 4x + 4 = 16x - 32
x² - 12x + 36 = 0
x² - 6x - 6x + 36 = 0
x(x - 6) - 6(x - 6) = 0
(x - 6)(x - 6) = 0
x = 6
14. sqrt(2x - 1) = -sqrt(3x - 12)
No real solutions because a positive square root can not be equal to a negative square root
15. x - 4 = 2sqrt(x - 4)
(x - 4)² = 4(x - 4)
(x - 4)² - 4(x - 4) = 0
(x - 4)(x - 4 - 4) = 0
(x - 4)(x - 8) = 0
x = 4, 8
16. x - 2 = sqrt(9x - 36)
(x - 2)² = (9x - 36)
x² - 4x + 4 - 9x + 36 = 0
x² - 13x + 40 = 0
x² - 5x - 8x + 40 = 0
x(x - 5) - 8(x - 5) = 0
(x - 8)(x - 5) = 0
x = 5, 8
In ΔDEF, the measure of ∠F=90°, the measure of ∠E=79°, and EF = 23 feet. Find the length of DE to the nearest tenth of a foot.
Answer:
120.4ft
Step-by-step explanation:
Find the diagram in the attachment.
The triangle shown is a right angled triangle with the side DE as the hypotenuse, EF is adjacent side while DF is the opposite side.
To get DE, we will use the SOH CAH TOA trigonometry identity
Using CAH which is defined as:
Cos(theta) = Adjacent/Hypotenuse
Cos 79°= 23/Hypotenuse
Hypotenuse = 23/cos79°
Hypotenuse = 23/0.191
Hypotenuse = 120.4feet
DE = 120.4feet (to nearest tenth)
Answer:
Step-by-step explanation:
The triangle DEF is right angle triangle
The missing F
F=90 E=79 = 11
E=79 EF= 23
Find the Length of DE to the nearest tenth of a foot
what is the answer to the equation |n-6|+8=22
Answer:
n=20,−8
Step-by-step explanation:
An object is thrown off a 256-foot-tall building, and the distance of the object from the ground is measured every second. The function that models the height, h, of the object after t seconds is h(t) = –16t2 + 96t + 256. Determine the time when the object hits the ground.
After how many seconds does the object hit the ground?
2
4
8
16
Answer:
C. 8
At 8 seconds the object will hit the ground.
Answer: C. 8
Step-by-step explanation:
just did this
the diameter of a clock’s face is 6 inches. find the length of the minor arc formed my the hands of the clock at 4:00.
please help!
Answer:
4:30
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Solve the equation.
- 2c + 6 = -8
Answer:
7
Step-by-step explanation:
We need to isolate the variable:
-2c + 6 = -8
-2c + 6 - 6 = -8 - 6
-2c = -14
-2c/-2 = -14/-2
c = 7
Thus, c = 7.
Hope this helps!
Method:
-2c+6=-8
-6 -6
-2c=-14
/-2 /-2
Answer:c=7
Amanda can word process 7 words in 6 seconds. At this rate, how many words can she word process in 3 minutes?
210
350
35
3.5
Answer:
He can process 210 words in 3 minutes