Answer:
3 m
Step-by-step explanation:
[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} b h \quad\textsf{(where b is the area of the circular base and h is the height)}[/tex]
Given:
volume = 10 m³Area of base = 10 m²[tex]\implies \sf 10=\dfrac{1}{3} \cdot 10 \cdot h[/tex]
[tex]\implies \sf 10=\dfrac{10}{3}h[/tex]
[tex]\implies \sf 30=10h[/tex]
[tex]\implies \sf h=\dfrac{30}{10}=3[/tex]
Answer:
height: 3 meter
Explanation:
[tex]\sf volume : \frac{1}{3} \ x \ base \ area \ x \ height[/tex]
Here given:
base area: 10 m²height: hvolume: 10 m³Solve:
[tex]\longrightarrow \sf 10 = \frac{1}{3} \ x \ 10 \ x \ h[/tex]
[tex]\longrightarrow \sf 10 = \frac{10}{3} \ x \ h[/tex]
[tex]\longrightarrow \sf \frac{10 \ x \ 3}{10} = h[/tex]
[tex]\longrightarrow \sf 3 = h[/tex]
Find the surface area of the prism. A cube with side edges of 7 yards.
Answer:
294 yd²
Step-by-step explanation:
a cube has 6 congruent square faces.
the area of 1 face = 7 × 7 = 49 yd²
then surface area = 6 × 49 = 294 yd²
The sun came out and the temperature quickly rose 18 degrees. The a thunderstorm hits and the temperature drops 6 degrees. The sun comes back out the temperature raises 12 degrees. The temperature is now 94 degrees. What was the starting temperature?
Answer:
70
Step-by-step explanation:
Just do it backwards.
94 - 12 = 82.
82 + 6 = 88.
88 - 18 = 70.
Please help me do this question genius minds
[tex]\text{Given that,}\\\\\theta =\tan^{-1} \left(\dfrac y x \right)\\\\\\\dfrac{\partial \theta}{\partial x} = \dfrac{\partial }{\partial x} \tan^{-1} \left(\dfrac yx \right)\\ \\\\~~~~~~=\dfrac{1}{1 +\tfrac{y^2}{x^2}} \cdot y \dfrac{\partial }{\partial x} \left(\dfrac 1x \right)\\\\\\~~~~~~=\dfrac{yx^2}{x^2 +y^2} \cdot (-1)x^{-2}\\ \\\\~~~~~~=-\dfrac{yx^2}{x^2(x^2 +y^2)}\\\\\\~~~~~~=- \dfrac{y}{x^2 +y^2}\\\\\\[/tex]
[tex]\dfrac{\partial^2\theta}{ \partial x^2} = -\dfrac{\partial }{ \partial x} \left( \dfrac{y}{x^2+y^2} \right)\\\\\\~~~~~~=-y\dfrac{\partial}{\partial x} \left(\dfrac 1{x^2 +y^2} \right)\\\\\\~~~~~~=y (-1)(-1) (x^2 +y^2)^{-2} \dfrac{\partial }{\partial x}(x^2 +y^2)\\\\\\~~~~~~=\dfrac{y}{(x^2 +y^2)^2} \cdot (2x+0)\\\\\\~~~~~~=\dfrac{2xy}{(x^2 +y^2)^2}[/tex]
[tex]\text{Similarly,}~~\\ \\\dfrac{\partial \theta}{\partial y }= \dfrac{x}{x^2 +y^2}\\\\\\\dfrac{\partial^2 \theta}{\partial y^2 } = -\dfrac{2xy}{(x^2 +y^2)^2}\\\\\\\text{Now,}\\\\\dfrac{\partial^2 \theta}{\partial x^2 }+\dfrac{\partial^2 \theta}{\partial y^2 }\\\\\\=\dfrac{2xy}{(x^2 +y^2)^2} -\dfrac{2xy}{(x^2 +y^2)^2}\\\\\\=0[/tex]
one third of a number y is 2
Answer:
y = 6
1/3 indicates that we may have to multiply the number by 3 to get the whole number. Multiply 3 by the part given, 2.
3 × 2 = 6
a number 1-72 is chosen at random find each probability
P( multiple of 9)
The selection of a random number from 1 - 72 is an illustration of probability, and the probability of selecting a multiple of 9 is 1/8
How to determine the probability?The sample size is given as:
n = 72
There are 8 multiples of 9 from 1 to 72.
So, the probability that a multiple of 9 is selected is:
P(Multiple of 9) = 8/72
Simplify
P(Multiple of 9) = 1/9
Hence, the probability of selecting a multiple of 9 is 1/8
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. Carl bought one book for $3.95 and a second book for $4.95. What is his total cost? $9.90 $9.00 $8.90 $7.90
The Cost of Carl's first item is 3.95. The Cost of his second item is 4.95. To find the total amount we need to add these two numbers together.
3 plus 4 is 7
95 cents plus 95 cents is 1.90
7+1.90 is 8.90
The total cost is $8.90
Hope this helps!
help please What is the simplest form of the expression representing this product?
x+10/x2+7x-18 * 3x2-12x+12/3x+30
Answer:
x-2
x+9
Step-by-step explanation:
Answer:
[tex]\frac{x-2}{x+9}[/tex]
Step-by-step explanation:
Factorizing Fraction 1
[tex]\frac{x+10}{x^{2}+7x-18 }[/tex][tex]\frac{x+10}{(x+9)(x-2)}[/tex]Factorizing Fraction 2
[tex]\frac{3x^{2} -12x+12}{3x+30}[/tex][tex]\frac{x^{2} -4x+4}{x+10}[/tex][tex]\frac{(x-2)^{2} }{x+10}[/tex]Now, multiply the fractions :
[tex]\frac{x+10}{(x+9)(x-2)}[/tex] × [tex]\frac{(x-2)^{2} }{x+10}[/tex][tex]\frac{x-2}{x+9}[/tex]You start driving north for 6 miles, turn right, and drive east for another 19 miles. At
the end of driving, what is your straight line distance from your starting point?
Round to the nearest tenth of a mile.
Answer:
mi
Submit Answer
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4
G
Answer:
20 miles
Step-by-step explanation:
This is a Pythagorean Theorem Problem
1. We know that one side of the triangle is 6 miles. And we know that another side is 19 miles.
2. We use the pythagorean Theorem to solve. We get
[tex]19^2+6^2=C^2[/tex]
Where C is the distance.
Solving that we get that 20 miles is the answer.
What kind of reasoning is used here? If a = b and c = d, then a − c = b − d
The reasoning used here is coding and decoding.
What are coding and decoding?Coding is a portion of the logical reasoning element that is used to encrypt words, numbers, or codes utilizing specified rules and regulations. The process of decoding patterns into their original forms from supplied forms is known as decoding.
We have an expression:-
a = b and c = d, then a − c = b − d
Therefore the reasoning used here is coding and decoding.
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A survey of 100 students was taken. It was found that 60 students watched sports, and 34 of these
students did not like pop music. or the students who did not water sports, 70% liked pop music.
Complete the two-way frequency table.
Answer:
[tex]\left[\begin{array}{ccc}38&28&66\\22&12&34\\60&40&100\end{array}\right][/tex]
Step-by-step explanation:
70% of 40 is 28, with that number you can obtain the other data.
What I got is in the image below.
I got the rest of the numbers by subtracting and adding. I also managed to find the 70% by multiplying 40 (I subtracted 60 and 100 to get the total number of people who don't watch sports) by 0.7, getting that 28 of people who don't watch sports liked pop music. From there, getting the rest of the numbers is just a whole lot of adding and subtracting. I subtracted 60 and 34 to get the number of people who watch sports and like pop, which is 26. I also added 26 and 28 to get the total of people who like pop, which is 56. To get 46 for total number of people who don't like pop, I subtracted 40 and 28 which equals 12 (number of people who don't watch sports but don't like pop), then added 34 + 12 to get 46.
Need help on this one please
Answer: y = -2x - 4
Step-by-step explanation:
This question asks that you give your answer in slope-intercept form, which is written as y = mx + b, where m is the slope, and b is the y-intercept.
In order to write an equation for this line in slope-intercept form, you need to find the slope and the y-intercept. You can find the slope by selecting any two clear points on the graph and finding the [change in y] ÷ [change in x].
For example, I’ll use (-3, 2) and (-2, 0):
Change in y: 2 - 0 = 2
Change in x: -3 - (-2) = -1
Change in y ÷ Change in x = 2 ÷ (-1) = -2
So, the slope, m, is -2. Finding b, or the y-intercept is a lot more straightforward; you just find where the line intercepts the y-axis, or when x = 0. Looking at the graph, we can see that the y-intercept is -4, so b = -4.
Now, we can put these together in an equation.
y = mx + b, where m = -2 and b = -4
y = -2x -4
The local animal shelter had 12 dogs at the beginning of the month. Since then, the number of dogs at the shelter has decreased by 75%. How many dogs are at the animal shelter today?
Answer:
3
Step-by-step explanation:
75% is equal to 3/4
The easiest way to do this is to divide 12 by 4.
12/4 = 3
Now multiply this by three to get 3/4 of 12.
3 x 3 = 9
9 dogs left the shelter.
12 - 9 = 3
There are three dogs left.
How to multiply problem in photo?
_____
yStep-by-step explanation:
what is the volume of a cylinder, in cubic inches, with a height of 2 inches and a base diameter of 4 inches? Round to the neares tenths place
Answer:
V≈25.13in³
Step-by-step explanation:
Stephen has 42 coins that are all dimes and nickels. The value of the coins is $3.65. How many dimes and how many nickels does Stephen have
answer is 31 dimes, 11 nickels
see picture attachment for the math
equation is .05N + .10D = 3.65
value of nickels and dimes
using D + N = 42
change to find value of N = 42 - D
plug value of N into the equation and solve
Rewrite using the Distributive Property and GCF 13+36
Answer:
13(1+2)
Step-by-step explanation:
13(1)+13(2)=13+26
The GCF of 13, 26 is 13.
1/3x + 5 x= -6 need expression 1/3x = 5 is equal to __ when x = -6
Answer:
3
Step-by-step explanation:
To evaluate an expression with a particular value of the variable, put that value where the variable is and do the arithmetic.
__
1/3(-6) +5 = -2 +5 = 3
For x = -6, the value of the expression is 3.
Workers Inc. just bought 12 boxes of pens to put in their storage room for employees to use as needed. Each box contains 35
pens. If each of the 25 employees working for Workers Inc. takes 3 pens when they are first brought into the office, how many pens
will be left in the storage room?
A. 417
B. 395
C. 345
D.195
Answer:
C. 345Step-by-step explanation:
first you multiply 25 and 3. and get 75next multiply 12 and 35. and get 420
finally subtract the two and get 345
21 slices from 3 cakes = 84 slices from cakes equivalent rates
Answer:
12 cakes.
Step-by-step explanation:
There are 21/3 = 7 slices from each cake.
84 / 7 = 12.
Please help me with this really need the answer please
Angie read 2 books in 5 days, and each book contained 340 pages. If Angie read the same number of pages each day, how many
pages did she read per day?
A. 75
В.340
C.136
D. 680
The area of a triangle is 7.5 . The base of the triangle is 5 cm .what is the height of this triangle.
Area
1/2BH=7.51/2(5)H=7.52.5H=7.5H=7.5/2.5H=3cm= 3 cm
Step-by-step explanation:[tex] \frac{1}{2} BH = 7,5 \\ \\ (\frac{1}{2} \times5)H=7,5 \\ \\ 2,5H = 7,5 \\ \\ H=7,5 \div 2,5 \\ H=3 \: cm[/tex]
Answer by NinaDon't copy from anywhere ✅Don't Look at Rank ✅Could you help me with this question, please?
Answer:
B) 1/4 gallon
Step-by-step explanation:
There is 5/8 in a jug
[tex]\sf \dfrac{5}{8}=\dfrac{2}{8}+\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{8}[/tex]
There are 3 jugs containing (1/8). To these jugs 1/8 of the juice from (5/8) is poured.
So, now all the jugs will have (2/8) = 1/4
PLEASE HELP WILL MARK BRSINLIEST!!!!!
Answer:
a) Yes
b) Not a right triangle
Step-by-step explanation:
Part (a)The sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side.
7 + 8 = 15 > 9
7 + 9 = 16 > 8
8 + 9 = 17 > 7
Therefore, a triangle with side lengths 7, 8 and 9 can be made.
Part (b)To determine if the triangle is a right triangle, use Pythagoras' Theorem:
a² + b² = c² (where a and b are the legs, and c is the hypotenuse)
The hypotenuse is the longest side, therefore:
a = 7b = 8c = 9Substituting these values into the formula:
⇒ a² + b² = c²
⇒ 7² + 8² ≠ 9²
⇒ 113 ≠ 81
As 7² + 8² ≠ 9² then the triangle is not a right triangle.
Hannah purchased a box of greeting cards with assorted designs. The box contains four cards of each design: daisies, sunflowers, lilies, birds, puppies, butterflies, dolphins, and landscapes. She selects one card at random from the box.
Calculate the following probabilities.
selecting a card with a sunflower or butterfly design
selecting a card with a lily, daisy, puppy, or bird design
selecting a card with a landscape design
selecting a card with a dolphin, sunflower, or landscape design
selecting a card with a bird or puppy design
Now, determine the events that have the highest and lowest probabilities and graph the values on the number line
The probability of selecting a card with a sunflower or butterfly design is 1/4, and the probability of selecting a card with a lily, daisy, puppy, or bird design is 1/2.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total outcomes = 4×8 = 32 (because 4 cards of 8 design)
The probability of selecting a card with a sunflower or butterfly design:
= 4/32 + 4/32
= 8/32 = 1/4
The probability of selecting a card with a lily, daisy, puppy, or bird design:
= 4(4/32)
= 1/2
The probability of selecting a card with a landscape design:
= 4/32 = 1/8
The probability of selecting a card with a dolphin, sunflower, or landscape design:
= 3(4/32)
= 3/8
Similarly, we can calculate the rest of the probability.
Thus, the probability of selecting a card with a sunflower or butterfly design is 1/4, and the probability of selecting a card with a lily, daisy, puppy, or bird design is 1/2.
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Please help! 100points! A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.
an = 2(an − 1 + 4) and a1 = 5 (the n and n-1 is suppose to be a subscript, I just can't figure out how to make it like that)
Answer:
5, 18, 44, 96, 200
Step-by-step explanation:
Given
aₙ = 2(aₙ₋₁ + 4)a₁ = 5First term : 5
Second term : a₂ = 2(a₁ + 4)
a₂ = 2(5 + 4) = 2(9) = 18Third term : a₃ = 2(a₂ + 4) = 2(18 + 4) = 2(22) = 44
Fourth term : a₄ = 2(a₃ + 4) = 2(44 + 4) = 2(48) = 96
Fifth term : a₅ = 2(a₄ + 4) = 2(96 + 4) = 2(100) = 200
Hence, the first 5 terms of the sequence are :
5, 18, 44, 96, 200Answer:
5, 18, 44, 96, 200
Step-by-step explanation:
[tex]\textsf{Given sequence}: \quad a_n=2(a_{n-1}+4)[/tex]
[tex]\textsf{Given first term}: \quad a_1=5[/tex]
[tex]\implies a_1=5[/tex]
[tex]\implies a_2=2(a_{1}+4)=2(5+4)=2(9)=18[/tex]
[tex]\implies a_3=2(a_{2}+4)=2(18+4)=2(22)=44[/tex]
[tex]\implies a_4=2(a_{3}+4)=2(44+4)=2(48)=96[/tex]
[tex]\implies a_5=2(a_{4}+4)=2(96+4)=2(100)=200[/tex]
Hello everyone!!
This is easy;
[tex] \frac{5x}{2} + \frac{9}{5} = 25[/tex]
[tex] \frac{5x}{2} + \frac{9}{5} = 25 \\ \frac{25x + 18}{10} = 25 \\ 25x + 18 = 250 \\ \frac{250 - 18}{25} = x \\ x = \frac{232}{25} [/tex]
hope it helps
Please refer to the attachment
Determine which of the following statements is true concerning the values described in column #1 and column #2.
Column #1
The x-coordinate of the vertex of the graph of y = −2x2 − 4x + 12
Column #2
The x-coordinate of the vertex of the graph of y = x2 − 4x + 3
A. The value found in column #1 is greater than the value found in column #2.
B. The value found in column #1 is less than the value found in column #2.
C. The value found in column #1 is equivalent to the value found in column #2.
D. The relationship between column #1 and column #2 cannot be determined by the information given.
The following statements are true concerning the values described in columns #1 and column #2. B. The value found in column #1 is less than the value found in column #2.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree
The equation of curve 1, which is in the shape of a parabola is, when represented in general form
[tex]y = -2x^2 - 4x + 12\\\\y = -2(x^2 - 2x + 6)\\\\\dfrac{y}{-2} = (x^2 - 2x + 6)\\\\\dfrac{y}{-2} +7=(x+1)^2[/tex]
So,
x+1=0
x= -1
and,
y = 14
Therefore, the Coordinate of a vertex is (-1,14).
The x-coordinate of the vertex of the function [tex]y = -2x^2 - 4x + 12[/tex] is equal to -1.
The equation of curve 2 , which is in the shape of a parabola is , when represented in general form
[tex]y = x^2 - 4x + 3\\\\y =( x-2)^2-1\\\\y+1 =( x-2)^2[/tex]
So,
x-2=0
x= 2
and, y+1=0
y= -1
Therefore, the Coordinate of a vertex is (2,-1).
The x-coordinate of the vertex of the function [tex]y = x^2 - 4x + 3[/tex] is equal to 2.
The following statements are true concerning the values described in columns #1 and column #2. B. The value found in column #1 is less than the value found in column #2.
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Analyze the diagram below and answer the question that follows how much larger is the value for d X then the value of y
[tex]\sf \large \boxed{110 ^\circ}[/tex]
The Image given shows (vertically opposite angles) :1st equation: x + 2y = 502nd equation: x - 2y = 130Make x the subject in first equation:x + 2y = 50x = 50 - 2yInsert this in second equation:(50 - 2y) - 2y = 13050 - 2y - 2y = 130-4y = 130 - 50-4y = 80y = -20Find the value of x:x = 50 - 2yx = 50 - 2(-20)x = 90Difference between them:x - (y)90 - (-20)110Element X is a radioactive isotope such that its mass decreases by 62% every year. If an experiment starts out with 650 grams of Element X, write a function to represent the mass of the sample after
t
t years, where the daily rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per day, to the nearest hundredth of a percent.
Use the general formula for decay substance
[tex]\\ \rm\Rrightarrow N=N_o(1-r)^t[/tex]
r is rate of decay. t is timeFor our equation r=62%=0.62
So
function becomes
[tex]\\ \rm\Rrightarrow N=650(1-0.62)^t[/tex]
[tex]\\ \rm\Rrightarrow N=650(0.38)^t[/tex]
Change for a year
[tex]\\ \rm\Rrightarrow N=650(0.38)[/tex]
[tex]\\ \rm\Rrightarrow N=247g[/tex]
Amount decayed=650-247=403g
Daily decay
403/3651.1gPercentage decay
[tex]\\ \rm\Rrightarrow \dfrac{1.1}{650}\times 100[/tex]
[tex]\\ \rm\Rrightarrow 0.169[/tex]
[tex]\\ \rm\Rrightarrow 16.9\%[/tex]
