We must evaluate the following:
[tex]\sqrt[]{-108}[/tex]We can write the argument of the square root in the following way:
[tex]undefined[/tex]
Find the volume of a cone with a base radius of 5 ft and a height of 10 ft.
Write the exact volume in terms of it, and be sure to include the correct unit in your answer.
The volume of cone is 261.79 ft³
Solution:
To solve Volume of cone we need radius and height of cone,
Base Radius of cone = 5 ft
Height of cone = 10 ft
Formula for Volume of cone V = π r² h/3
So,
The radius of cone is 5ft and
height of cone is 10ft ,
Volume V= π × 5ft² × 10ft/3
= 261.79939 ft³
Equation :
V = π r² h/3V= volume , π= 3.14 , r= radius , h= heightTo learn more about Volume of cone refer:
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playing blackjack. blackjack, or twenty-one as it is frequently called, is a popular gambling game played in casinos. a player is dealt two cards. face cards (jacks, queens, and kings) and tens have a point value of 10. aces have a point value of 1 or 11. a 52-card deck contains 16 cards with a point value of 10 (jacks, queens, kings, and tens) and four aces. a. what is the probability that both cards dealt are aces or 10-point cards? b. what is the probability that both of the cards are aces? c. what is the probability that both of the cards have a point value of 10? d. a blackjack is a 10-point card and an ace for a value of 21. use your answers to parts (a), (b), and (c) to determine the probability that a player is dealt blackjack. (hint: part (d) is not a hypergeometric problem. develop your own logical relationship as to how the hypergeometric probabilities from parts (a), (b), and (c) can be combined to answer this question.)
The probabilities for the ace cards are 0.1433, 0.0045, 0.0905, 0.0482.
what is a blackjack card game?
It derives from the Twenty-One line of gambling banking games and utilises 52-card decks.
Face cards and number 10: 16 cards have point value 10 Ace cards:
4 cards have point value 1 or 11 total number of cards =
Part a)
P(Ace or 10 point card has following cases)
case l: both are Ace cards = (4/52)*3/51 =
0.0045
Case II: both are 10 point cards = (16/52)*(15/51) =
0.0905
Case III: first card Ace, second card 10 point = (4/52)*(16/51 0.0241 Case IV: first card 10 pt, second card Ace: = (16/52)"(4/51) = 0.0241
Total = 0.1433
Part b) P(both cards are Ace) = (4/52)*(3/51) = 0.0045
Partc) P(both cards have point value 10) = (16/52) * (15/51) = 0.0905
Part d) P(Ace and 10 point) = 0.0241+0.0241 = 0.0482
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given f(x) = -x -4 find f (-2)
Answer:
-2
Step-by-step explanation:
f(-2) = -(-2) - 4
= 2-4
= -2
georgie works 15 hours each week
she earns 5 pound per hour
georgie saves 1/3 of hr earnings each week
how many weeks does it take georgie to save 200 pound
(4, -3); 2x - 7y = 12
what the perpendicular given line?
The slope that is perpendicular to the line (2x - 7y = 12) is -7/2.
What is the slope?The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points lying on a straight line, a slope can be calculated using a variety of methods.So, let's represents the given equation (2x - 7y = 12) in the slope-intercept form y = mx + b:
Add -2x on both sides as follows:
-7y = -2x - 12Divide everything by -7 as shown:
y = 2/7x + 12/7The slope of the line is 2/7.The perpendicular line's slope is equal to the given line's negative reciprocal: -7/2
Therefore, the slope that is perpendicular to the line (2x - 7y = 12) is -7/2.
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The correct question is given below:
How do you find the slope that is perpendicular to the line 2x - 7y = 12?
What is the LCD of 11/7 and 3/8?
Using the LCD of 2 fractions formula, it was determined that the LCD of 11/7 and 3/8 is 33.
What does LCD mean in mathematics?When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.
LCD of 11/7 and 3/8 is given as follows:
We know that,
LCD of 2 fractions = (LCD of a,b)/(HCF of a,b) where a and b are two fractions.
LCD = (LCD of 11/7 and 3/8)/(HCF of 11/7 and 3/8)
= 33/1
Therefore, the LCD of 11/7 and 3/8 is found to be 33 which was calculated using the formula of LCD of 2 fractions.
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8% turned into a fraction
Answer: 0.8
Step-by-step explanation: 0.8 as a fraction is expressed as 4/5
hope this helps
Answer: 2/25 or 8/100.
Step-by-step explanation:
Determine the slope of a line passing through the given points. If the slope is undefined, write undefined. Enter your answer as a decimal if necessary. a. ( 5 , − 4 ) and ( 0 , 1 ) b. ( − 1 , 8 ) and ( 7 , 10 ) c. ( − 4 , 12 ) and ( − 4 , 5 ) Tools are not currently accessible
The slope of the given line that runs through the points are:
1. Defined
2. Defined
3. undefined.
What is an Undefined Slope of a Line?An undefined slope of a line can be described as the slope of a vertical line that has no run but only rise. That is, the x-coordinates do not change even though the y-coordinates of the line are changing.
Thus, the change in x-coordinates is always 0.
Slope = change in y / change in x.
a. (5 , − 4) and (0 , 1):
Slope = (-4 - 1)/(5 - 0)
Slope = -5/5 = -1 [the slope is defined]
b. (−1 , 8) and (7 , 10):
Slope = (10 - 8)/(7 -(-1))
Slope = 2/8
Slope = 1/4
c. (-4, 12) and (-4, 5)
Slope = (12 - 5)/(-4 -(-4))
Slope = 7/0 [cannot divide, therefore, the slope is undefined]
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What is AC?
A √162 = 12.7
B√98 = 9.9
C√117 ≈ 10.8
D√72 = 8.5
The most appropriate choice for distance formula will be given by Length of AC = [tex]\sqrt{72} = 8.5 units[/tex]
What is distance?
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over").
What is distance formula?
Distance formula is used to find the distance between two points.
Let A and B be two points with coordinate [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively
Distance between A and B = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
Here,
Coordinate of A = (1, 1)
Coordinate of E = (4, 4)
Coordinate of C = (7, 7)
Length of AE =
[tex]\sqrt{(4-1)^2 + (4-1)^2}\\\sqrt{9 + 9}\\\sqrt{18}\\3\sqrt{2} units[/tex]
Length of EC =
[tex]\sqrt{(7-4)^2 + (7-4)^2}\\\sqrt{9 + 9}\\\sqrt{18}\\3\sqrt{2} units[/tex]
Length of AC = Length of AE + Length of EC
= [tex]3\sqrt{2} + 3\sqrt{2} = 6\sqrt{2} units[/tex] =[tex]\sqrt{72} units = 8.5 units[/tex]
Fourth option is correct
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211, 207, 203, ...
Find the 38th term.
The 38th term of the sequence is 63
How to calculate the 38th term ?The first step is to write out the parameters
The first term (a) = 211
The common difference (d) = 207 - 211
= -4
The 38th term of the sequence can be calculated as follows
a₃₈ = a + (n-1)d
a₃₈ = 211 + (38-1)(-4)
a₃₈ = 211 + 37(-4)
a₃₈ = 211 - 148
a₃₈ = 63
Hence the 38th term is 63
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HELP PLS ASAP,,ITS DUE REALLY SOON
.........THX
Altitudes and depths are measured with respect to sea level. Sea level corresponds to an altitude of 0. Determine the distance which separates a plane flying at an altitude of 3 250m and a submarine travelling at a depth of 326m below sea level.
Answer:3576m
Step-by-step explanation:
3250+326=3576
In triangle XYZ, angle Y is right and sin X =5/13. Which of the following trig. Ratios are correct?
In triangle XYZ, angle Y is right and sin X =5/13 the correct trigonometry ratios are
tan Z = 12/5cos Z = 5 / 13How to determine the correct trigonometry ratioInformation given in the question include
In triangle XYZ
angle Y
sin X = 5 / 13
A right angle triangle has three sides namely Adjacent, Opposite and Hypotenuse
from Sin X = opposite = Hypotenuse = 5 / 13
we have that
opposite = 5
Hypotenuse = 13
Using Pythagoras theorem
Hypotenuse^2 = opposite^2 + Adjacent^2
13^2 = 5^2 + Adjacent62
Adjacent = √(169 - 25)
Adjacent = 12
The correct options are tan Z = 12/5 and cos Z = 5 / 13
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what is 3 (6+99) - 45
Given:
[tex]3(6+99)-45[/tex]Rewrite as a simplified fraction.3.16
The decimal number 3.16 in the form of the simplest fraction is 79/25.
The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.
Consider the decimal number,
Let x = 3.16
Then,
x = 3.16 = 316/100
The fraction then can be simplified as,
x = ( 158 × 2)/ (50 × 2)
x = 158/50
x = ( 79 × 2)/ ( 25 × 2 )
x = 79/25
Hence, the number 3.16 in the simplest fraction is 79/25.
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Each baby dinosaur made 151515 paintings and each adult dinosaur made 777 paintings. The entire herd made 208208208 paintings in total, and there were 333 times as many baby dinosaurs as adult dinosaurs.
How many baby dinosaurs and adult dinosaurs were there?
Using the expression, 15x + 7y = 208 there were x = 12 baby dinosaurs and y = 4 adult dinosaurs.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Each baby dinosaur made 15 paintings and every adult dinosaur made 7 paintings.
The total number of paintings the entire herd made is 208.
There were 3 times as many baby dinosaurs as adult dinosaurs.
Now, let x be the number of baby dinosaurs and y be the number of adult dinosaurs.
Then,
x = 3y
So,
The expression for the total number of paintings will be:
208 = 15x + 7y
208 = 15(3y) + 7y
208 = 45y + 7y
208 = 52y
y = 4
So,
x = 3y = 3(4) = 12
There were 12 baby dinosaurs and 4 adult dinosaurs.
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Tell whether x and y show direct variation. Explain your reasoning if so, find k
y+3=x+6
yes; The equation can be written as y=kx, k = 1
yes; The equation can be written as y = kx, k = 3
No The equation can be written as y
kx, k = 9
no; The equation cannot be written as y = kx.
Answer:
A
Step-by-step explanation:
I just need points bro, Bob bob bob bob bob bob bob bob bob
Find the values of the variables and the measure of the angles.
Since ∠GFE is a right triangle, we can conclude:
[tex]\begin{gathered} b+32=90 \\ b=90-32 \\ b=58 \end{gathered}[/tex]the sum of the internal angles of a triangle is 180, therefore, for the triangle GHF:
[tex]\begin{gathered} 55+a+b=180 \\ \text{ Since b=58} \\ 55+a+58=180 \\ a+113=180 \\ a=67 \end{gathered}[/tex]Finally, for the triangle GEF:
[tex]\begin{gathered} a+90+d=180 \\ 67+90+d=180 \\ 157+d=180 \\ d=180-157 \\ d=23 \end{gathered}[/tex]The cost of 5 kg of oranges is sane as the cost of 3 kg of apples. How many kilograms of oranges are required to exchange 9 kg of apples ?
Answer:
7kg
Step-by-step explanation:
A mountain climbing team meets at a basecamp and drives up to a trailhead to start their climb. The trailhead is at 0 feet above sea level. For each of the first three
days, they climb 250 feet vertically. The fourth day, they climb another 150 feet vertically to the summit of the mountain. Over the final three days, the climbers
descend the mountain, decreasing their altitude by 325 feet each day until they get back to the basecamp where they first met.
Select options below
1. During their climb, the climbers increase their altitude by Select Option
vertical feet.
2. After they summit the mountain, they decrease their altitude by Select Option vertical feet.
3. This means the basecamp where they first met is Select Option
Answer:
1. 900
2. 975
3. 75 feet below sea level? which makes no sense but that's what the math says.
unit rate for 3ounces cost $2.73
The unit rate for 3 ounces cost $2.73 is 0.91 dollars per ounces.
How to find unit rate?Unit rate is the ratio of two different units, with denominator as 1.
In other words, a unit rate is a rate where the second quantity is one unit , such as $28 per pound, 30 metres per hour, 15 Nigerian naira per Brazilian Real, etc.
Therefore, let's find the unit rate for 3 ounces cost $2.73.
Hence,
unit rate = cost / amount in weight
cost = $2.73
amount in weight = 3 ounces
Therefore,
unit rate = 2.73 / 3
unit rate = 0.91 dollars per ounces
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I need help please this is going in my grade book:((
Josie has more race to complete.
Define fraction.The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is [tex]\frac{1}{2}[/tex].
Given Data
Josie has completed [tex]\frac{8}{25}[/tex]
Caroline has completed 40%
Converting percentage into fraction,
[tex]\frac{34}{100}[/tex]
Simplifying,
[tex]\frac{17}{50}[/tex]
For comparing, we need to have same denominators.
So,
[tex]\frac{8}{25}[/tex] ×[tex]\frac{2}{2}[/tex]
[tex]\frac{16}{50}[/tex]
[tex]\frac{17}{50}[/tex] > [tex]\frac{16}{50}[/tex]
Josie has more race to complete.
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Use the remainder theorem to find the remainder when 3x^4 - 5x^2 - 20x + 8 is divided by x - 1.-414-140
SOLUTION
The given equatiion is:
[tex]3x^4-5x^2-20x+8[/tex]To be divided by x-1
set the expression to zero:
[tex]\begin{gathered} x-1=0 \\ x=1 \end{gathered}[/tex]Substitute x=1 into the polynomial:
[tex]3(1)^4-5(1)^2-20(1)+8[/tex]This gives:
[tex]3-5-20+8=-14[/tex]Therefore the remainder is -14.
At their going out business sale, Bill’s Bikes sold 36 bikes and had 58 left. Which equation could be used to find x, the number of bikes the store had originally.
The equation that could be used to find x, the number of bikes the store had originally, is (x-94) = 0.
According to the question,
We have the following details:
Bill has sold 36 bikes and is left with 58 bikes more.
Now, the number of bikes the store had originally is given to be x.
So, we have:
x = Number of bikes sold + Number of bikes left
x = 36+58
x = 94
x-94 = 0 (94 was positive on the right hand side. So, it is negative on the left hand side.)
Hence, the equation that could be used to find number of original bikes in Bill's store is x-94 = 0.
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Line s has a slope of 1/3 Line t is perpendicular to line s. What is the slope of line t?
The line t has a slope of the value of -3
How to determine the slope of line t?The lines are given as
Line s and line t
The slope of line s is given as
Slope of line s = 1/3
Also, from the question;
We understand that line s and line t are perpendicular lines
The condition for perpendicular lines is represented as
The product of the slopes of the lines = -1
This means that
Slope of line s * Slope of line t = -1
This gives
1/3 * Slope of line t = -1
Divide both sides by 1/4
Slope of line t = -3
Hence, the slope is -3
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Find the length of side BC.
Give your answer to 3 significant figures.
C
A
71°
6.3 cm
B
From the given diagram, the size of side BC is 19.4 rounded to 3 significant figures
What is trigonometric function?The trigonometric functions are real functions that relate the angle of a right-angled triangle to side length ratios. They are widely used in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many others.The values of all trigonometric functions based on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.From the given diagram, the size of side BC is 19.4 rounded to 3 significant figures
Given
The right angle triangle with a side and an angle
We must find out the hypotenuse BC
We are given with adjacent side AB
Let's use trigonometric ratio
[tex]$&\cos (B)=\frac{\text { adjacent }}{\text { hypotenuse }} \\[/tex]
[tex]$&\cos (71)=\frac{A B}{B C} \\[/tex]
[tex]$&\cos (71)=\frac{6.3}{B C} \\[/tex]
[tex]$&B C \cos (71)=6.3 \\[/tex]
[tex]$&B C=\frac{6.3}{\cos (71)}[/tex]
Use the calculator to find out BC
BC=19.3508
Round the answer to 3 significant figures
So BC= 19.4
Length of side BC = 19.4
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what is -15 divided (-3) ?
Answer:
its positive 5 a negative divided by a negative is a positive
Step-by-step explanation:
Answer:
Positive 5
Step-by-step explanation:
a negative divided by a negative or a negative multiplied by a negative will always equal a positive. This equation is equal to 15 divided by 3 which is equal to 5.
the lenght of a flower is 529 cm covet it to m
Find the value of x, y, and z. (see picture)
z=72°+57°(EXTERIOR ANGLES OF A TRIANGLE)
z=129°
x+57°=180°(ANGLES ON A STRAIGHT LINE)
x=180°-57°
x=123°
y+72°=180°(ANGLES ON A STRAIGHT LINE)
y=180°-72°
y=108°
HOPE THIS HELPS.
The information is in the photo. Please help. Goodnight .
The ratio of hexagons to triangles is 2/1.
What are Ratios?The ratio is the relationship or comparison between two amounts of the same unit to determine how much larger one number is than the other. A ratio is a mathematical term that compares two comparable or dissimilar numbers by division. If you want to compare one data point (A) to another data point (B), your formula would be A/B.Given:
In the figure,
Number of hexagons = 4
Number of triangles = 2
We have to determine the ratio of hexagons to triangles.
Ratio = Number of hexagons/Number of triangles
Ratio = 4/2
Reducing it we get,
Ratio = 2/1
Therefore, the required ratio is 2/1.
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The profit for a certain commodity, n, where n is in units, is given by the functionP(n) =25n^2 + 300n + 1125At the break-even point, the profit is zero, i.e., P(n) = 0. Find the number of units where the break-even point is located, i.e., find n when P(n) = 0.The number of units, n, where the break-even point is located, isHint: Did you factor the GCF? Then reduce your equation to smaller coefficients?
Given the function:
[tex]P\mleft(n\mright)=-25n^2+300n+1125[/tex]You know that "P" is the profit for a certain "n" commodity (in units).
You need to find the value of "n" when:
[tex]P(n)=0[/tex]In order to find it, you can follow these steps:
1. Substitute this value into the function:
[tex]P(n)=0[/tex]Then:
[tex]\begin{gathered} 0=-25n^2+300n+1125 \\ \\ -25n^2+300n+1125=0 \end{gathered}[/tex]2. Divide both sides of the equation by -25:
[tex]\begin{gathered} \frac{-25n^2}{(-25)}+\frac{300n}{(-25)}+\frac{1125}{(-25)}=\frac{0}{(-25)} \\ \\ n^2-12n-45=0 \end{gathered}[/tex]3. Factor the equation by finding two numbers whose Sum is -12 and whose Product is -45. These are 3 and -15, because:
[tex]\begin{gathered} 3-15=-12 \\ \\ (3)(-15)=-45 \end{gathered}[/tex]Then:
[tex](n+3)(n-15)=0[/tex]4. Set up these two equations:
[tex]\begin{gathered} n+3=0\text{ (Equation 1)} \\ \\ n-15=0\text{ (Equation 2)} \end{gathered}[/tex]5. Solving form "n" from each equation, you get:
[tex]\begin{gathered} n+3=0\text{ }\Rightarrow n_1=-3 \\ \\ n-15=0\Rightarrow n_2=15 \end{gathered}[/tex]Since the number of units cannot be negative, the answer is:
[tex]n=15[/tex]