Answer:
363.741 feet
Step-by-step explanation:
Let the height of the cliff be represented by x. Applying the appropriate trigonometric function, we have;
Tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]
Tan [tex]60^{0}[/tex] = [tex]\frac{x}{210}[/tex]
cross multiply to have;
x = 210 × Tan [tex]60^{0}[/tex]
= 210 × 1.7321
= 363.741
The cliff is 363.741 feet high.
The triangles are similar. Solve for the missing segment.
Answer:
56
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{35+20}{20}[/tex] = [tex]\frac{32+?}{32}[/tex] ( cross- multiply )
20(32 + ?) = 1760 ( divide both sides by 20 )
32 + ? = 88 ( subtract 32 from both sides )
? = 56
Answer:
[tex]\boxed{56}[/tex]
Step-by-step explanation:
We can use ratios to solve since the triangles are similar.
[tex]\frac{20}{32} =\frac{35}{x}[/tex]
Cross multiplication.
[tex]20x=35 \times 32[/tex]
Divide both sides by 20.
[tex]\frac{20x}{20} = \frac{35 \times 32}{20}[/tex]
[tex]x=56[/tex]
On a separate piece of graph paper, graph y = |x - 3|; then click on the graph until the correct one appears.
ps : there's another picture it just didn't let me edit it its the opposite side of the shape facing up the graph.
Answer: Graph is shown in the attached image below
This is a V shaped graph with the vertex at (3,0). The V opens upward
Explanation:
The equation y = |x-3| is the result of shifting the parent function y = |x| three units to the right. The vertex moves from (0,0) to (3,0). The "x-3" portion moves the xy axis three units to the left. If we held the V shape in place while the xy axis moved like this, then it gives the illusion the V shape moved 3 spots to the right.
Side note: the equation y = |x-3| is composed of two linear functions y = x-3 and y = -x+3. The value of x will determine which gets graphed. When x < 3, then we'll graph y = -x+3; otherwise we graph y = x-3. This is known as a piecewise function.
Michael is 5 years old than rui feng and. Vishal is thrice as old as micheal if rui feng is 3 years old find Michael present age and sum of their ages in 6 years time
Answer:
a) Micheal's present age = 8 years old
b) The sum of their ages in 6 years time = 63 years.
Step-by-step explanation:
From the above question, we know that
Rui feng is 3 years old
We are told that
• Michael is 5 years old than Rui feng
Micheal's present age is calculated as:
= 5 + Rui feng's age
= 5 + 3 = 8 years
• Vishal is thrice as old as Micheal
Vishal's present age is calculated as
= 3(Micheal age)
= 3(8)
= 24 years.
The sum of their ages in six years time
= ( 3 + 6) +( 8 + 6) + ( 24 + 6)
= 18 + 15 + 30
= 63 years
Therefore, a) Micheal's present age = 8 years old
b) The sum of their ages in 6 years time = 63 years.
Find the probability of rolling a three first and then a ten when a pair of dice is rolled twice
Answer: 0.0046
Step-by-step explanation:
First, let's calculate the total number of outcomes that you can see from a pair of dice.
Each dice has 6 options, so the total number of combinations is:
6*6 = 36.
Now, the combinations that are equal to 3 are:
3 and 1
1 and 3
2 combinations.
So the probability is equal to the quotient between the number of combinations that are equal to 3, and the total number of combinations:
P = 2/36 = 0.055
Now, the combinations that are equal to 10 are:
5 and 5
4 and 6
6 and 4.
3 combinations.
Then the probability is:
P = 3/36 = 0.0833
Now, the probability of both events happening is equal to the product of the probabilities for each event, so the total probability is equal to:
P = ( 0.0833)*( 0.055) = 0.0046
In a bag containing 3 red balls,and 2 blue balls,one of which is drawn at random.
Find the probability that its a red ball
Step-by-step explanation:
Given:
Successful outcome
Red=3
Blue=2
Possible outcome
Total=5 balls
Required:
The probability of drawing red ball
Formula:
Probability= Successful outcome ÷ Possible outcome
Solution:
Probability= Successful outcome ÷ Possible outcome
Probability=3÷5
Probability=3/5 or 0.6
Hope this helps ;) ❤❤❤
What is 5,000 - 245( 30/2))?
Answer:
1,325
Step-by-step explanation:
30 /2
= 155,000 - 245(15)
= 5,000 - 3,675
= 1,325
Answer:
1,325
Step-by-step explanation:
The cell cycle is the process by which a single cell replicates itself. A student investigates whether cell growth during the cell cycle is linear or exponential. The table at left gives the length, in micrometers, of an S. pombe (yeast) cell at different times after the cell cycle begins. Which of the following best describes the relationship between time and length of this cell?
The question is incomplete. the complete question is as follows:
The cell cycle is the process by which a single cell replicates itself. A student investigates whether cell growth during the cell cycle is linear or exponential. The table at the left gives the length, in micrometers, of an S. pombe (yeast) cell at different times after the cell cycle begins. Which of the following best describes the relationship between time and length of this cell?
A. It is linear because the length increases by the same factor every 10 minutes.
B. It is linear because the length increases by the same number of micrometers every 10 minutes.
C. It is exponential because the length increases by the same factor every 10 minutes.
D. It is exponential because the length increases by the same number of micrometers every 10 minutes.
Answer:
C. It is exponential because the length increases by the same factor every 10 minutes.
Step-by-step explanation:
According to the data shown, the relationship between time and length of this cell is exponential.
The relationship is exponential because the length increases by the same factor every 10 minutes.
The growth of the cell is exponential it means the optimal conditions are provided to the cell for their growth.
Hence, the correct answer is "C. It is exponential because the length increases by the same factor every 10 minutes."
The researcher is interested to know if policy A (new) is more effective than policy B (old). Frame the hypothesis and describe what each error would represent in terms of reality and conclusion.
Answer:
Null hypothesis: Policy B remains more effective than policy A.
Alternate hypothesis: Policy A is more effective than policy B.
Step-by-step explanation:
Remember, a hypothesis is a usually tentative (temporary until tested) assumption about two variables– independent and the dependent variable.
We have two types of hypothesis errors:
1. A type I error occurs when the null hypothesis (H0) is wrongly rejected.
That is, rejecting the assumption that policy B remains more effective than policy A when it is actually true.
2. A type II error occurs when the null hypothesis H0, is not rejected when it is actually false. That is, accepting the assumption that policy B remains more effective than policy A when it is actually false.
HIJ has coordinates H(-4,3), I7(-2, 0), and J (-4,1). Graph the triangle and its
translation 3 units to the right and 2 units down. What are the coordinates of J'?
Answer:
J'(-1; -1)Step-by-step explanation:
Look at the picture.
x - horizontal
y - vertical
left, right - horizontal
n units to the right: x + n
n units to the left: x - n
up, down - vertical
n units up: y + n
n units down: y - n
J(-4; 1)
3 units to the right: -4 + 3 = -1
2 units down: 1 - 2 = -1
J'(-1; -1)
ASAP!! I will not accept nonsense answers, but will give BRAINLIEST if you get it correct with solutions:)
Answer:
Third option is the correct answer (1/2 = e^{2k})
Step-by-step explanation:
Since, N =1/2 Nt
Therefore, 2N = Nt.... (1)
We are given that:
N= Nt e^{kt}
N = 2N e^{2k} (since, 2N =Nt and t =2)
N/2N = e^{2k}
1/2 = e^{2k}
What is the slope-intercept equation for the line below?
Answer: D
Step-by-step explanation:
If we look at the graph we can see that the line intercepts the y-axis at (0,-4), so the intercept must be -4.
If we use the rise-over-run formula for (0,-4) and (4,1) we would get:
[tex]\frac{1--4}{4} \\\\=\frac{5}{4}[/tex]
Since the line is going upwards, the equation must be positive.
Therefore, the equation in slope-intercept form is y=5/4x-4.
30. A rectangular prism has a volume of
285.6 cubic feet. The prism is
12 feet long and 3.4 feet wide. What is
the height of the prism?
A 7 ft
C 19 ft
B 15 ft
D 22 ft
Answer:
The answer is a
Step-by-step explanation:
my brother is very smart
Find the equation of the line below. Arrange your answer in the form y = mx + b, where b is the constant. (Note: in this answer make sure your x has a coefficient) (2,1) (-2,-1)
Which equation represents the graphed function?
Answer:
y=-1/2x+3
Step-by-step explanation:
To get the equation you do y=mx+b. Which is y=slope+y-intercept
The step function g(x) is defined as shown. g(x) = StartLayout Enlarged left-brace 1st row 1st column negative 3, 2nd column x less-than-or-equal-to 0 2nd row 1st column 2, 2nd column 0 less-than x less-than-or-equal-to 4 3rd row 1st column 5, 2nd column 4 less-than x less-than-or-equal-to 10 EndLayout
Answer:
{–3, 2, 5}
Step-by-step explanation:
The range refers to the values for the axis i.e to be dependent when there is a defined function
And the range is the combination of the integer i.e to be compounded by these three values
Data provided in the question
-3 , x ≤ 0
2, 0 < x ≤ 4
5, 4 < x ≤ 10
Based on the above information, the range of g(x) is {-3,2,5}
Hence, the correct option is c.
Answer:
C
Step-by-step explanation:
The batting Wang Xiu Ying uses to fill quilts has a thermal conductivity rate of 0.030.030, point, 03 watts (\text{W})(W)left parenthesis, start text, W, end text, right parenthesis per meter (\text{m})(m)left parenthesis, start text, m, end text, right parenthesis per degree Celsius (^\circ\text{C})( ∘ C)left parenthesis, degrees, start text, C, end text, right parenthesis. What is the batting's thermal conductivity value in \dfrac{\text{W}}{\text{cm}\cdot^\circ\text{C}} cm⋅ ∘ C W start fraction, start text, W, end text, divided by, start text, c, m, end text, dot, degrees, start text, C, end text, end fraction?
Answer:
0.0003W/cm°C
Step-by-step explanation:
The question is not properly written. Here is the correct question.
The batting wang xiu ying uses to fill quilts has a thermal conductivity rate of 0.03 watts (W) per meter(m) per degree celsius. what is the batting thermal conductivity when w/cm•c
Given the thermal conductivity in W/m°C to be 0.03W/m°C
We are to rewrite the value in W/cm°C
The difference is the unit. The only thing we need to do is to simply convert the unit (metres) in W/m°C to centimeters (cm)
Since 100cm = 1m, 0.03W/m°C can be expressed as shown below;
= 0.03W/m°C
= 0.03 × W/1m×°C
Note that 1m = 100cm, substituting this conversion into the expression, it will become;
= 0.03 × W/100cm × °C
= 0.03/100 × W/cm°C
= 0.0003W/cm°C
Hence the battling thermal conductivity in W/cm°C is 0.0003W/cm°C
Answer:
0.0003W/cm°C
Step-by-step explanation:
Use the rationalized expression from the previous question to
calculate the time, in seconds, that the cliff diver is in free fall.
Assume the acceleration due to gravity, a, is -9.8 m/s2, and the
dive distance, d, is -35 m. The negative numbers indicate the
direction is downward. Round the answer to two decimal places.
Answer:
Time taken (t) = 2.67 s (Approx)
Step-by-step explanation:
Find:
Time taken (t)
Given:
Initial velocity (u) = 0 m/s
Acceleration due to gravity(a) = -9.8 m/s²
Distance (d) = -35 m
Computation:
Using 2nd equation of motion,
d = ut + (1/2)at²
-35 = (0)t + (1/2)(-9.8)t²
-35 = -4.9 (t²)
t² = 7.1428
t = 2.6726
Time taken (t) = 2.67 s (Approx)
Kickboxing it's found the force needed to break a board varies inversely with the length of the board it takes 9 pounds of pressure to break a board that is 3 feet long how long is the board that requires 5 pounds of pressure to break
Answer:
If f=5 pounds of pressure, l=5.4 feet long
Step-by-step explanation:
Force needed to break a board varies inversely with the length of the board
Let
Force to break the board=f
Length of the board=l
f=k/l
Where k is a constant
If f=9 pounds of pressure and l=3 feet long
f=k/l
9=k/3
Cross product
9*3=k
27=k
If k=27, f=5 pounds of pressure. Find l?
f=k/l
5=27/l
Cross product
5l=27
l=27/5
=5.4
l=5.4 feet long
Using proportions, it is found that the board that requires 5 pounds of pressure to break is 1.67 inches long.
Proportions:This question is solved by proportions, using a rule of three.It takes 9 pounds to break a board that is 3 feet long, what is the length of a board that takes 5 pounds?The rule of three is:
9 pounds - 3 feet
5 pounds - x feet
Applying cross multiplication:
[tex]9x = 3(5)[/tex]
[tex]x = \frac{15}{9}[/tex]
[tex]x = 1.67[/tex]
The board that requires 5 pounds of pressure to break is 1.67 inches long.
To learn more about proportions, you can take a look at https://brainly.com/question/24372153
Graph y=-x2-170! Help.pllss
I have included a picture of the graph (click/tap on it to see the full picture.) I hope this helps! If there's anything else I can do please comment on this answer! If this did help please rate, thanks, and mark brainliest :)
please help ASAP. Which statement below is NOT true for the graph of a quadratic function? a) the axis of symmetry intersects the parabola at the vertex b) when the coefficient of x^2 is positive, the vertex of the parabola is a minimum point c)The vertex of a parabola is its highest or lowest level d) the parabola is symmetrical about the y-axis
Answer:
Step-by-step explanation:
All of these statements about a vertical parabola with known vertex are true.
The statement which is not always true about the graph of a quadratic function is option d) the parabola is symmetrical about the y-axis.
What is Parabola?A parabola is a open U shaped curve on a plane where all the points on the curve will be at an equal distance from a fixed point called focus and a fixed line called directrix.
Vertex of a parabola is the point where the parabola intersects with it's line of symmetry. So the vertex will always lie at the maximum point or the minimum point.
Axis of symmetry is the line that passes through the vertex of a parabola.
Graph of the quadratic equation will always be a parabola.
When the coefficient of x² is positive, then the vertex of the parabola will be at a minimum point and if the coefficient is negative, then the vertex will be at a maximum point.
The parabola is symmetrical to y axis only if the vertex of the parabola lies on the Y axis. So it will not be always true.
Hence the statement the parabola is symmetrical about the y-axis is not always true.
Learn more about Parabola here :
https://brainly.com/question/1440592
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[5 points] Each size of tile is named for its area. The smallest tile, called the “unit tile”, has sides that measure exactly 1 unit. Therefore, the area of the unit tile is 1 unit 1 unit=1 unit2. Can you use the unit tile to find the exact area of the other tiles? Explain.
Answer:
Yes you can, it’s 1010
Step-by-step explanation:
the reason is to 101 the number for its to become the one for the unit which is 1010
Yes, you can use the unit tile to find the exact area of the other tiles.
What are units and measurements?The fundamental units are the units defined for the fundamental quantities. The derived units are the units of all other physical quantities that are derived from the fundamental units.
Given :
The unit tile has 1 unit length and 1 square unit of area.
Yes, you can use the unit tile to determine the length of the other rectangle and square.
You can place tiles along the length of the rectangle and count them so that the number of tiles equals the length of the rectangle, and then use the same method to find the side of the squares.
As shown in the given diagram below :
Therefore, you can use the unit tile to find the exact area of the other tiles.
To learn more about units and measurements refer to :
https://brainly.com/question/9606366
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A linear inequality in one variable is a linear equation in one variable with the equals symbol replaced by an inequality symbol. True or False?
Answer:
True
Step-by-step explanation:
Example:
8 = 3 x - 5 is the equation in one variable
an associated linear inequality in one variable is for example:
8 < 3 x - 5
PLEASE HELP! BRAINLIEST! ASAP!
Answer:
x = -5
I hope this helps!
Answer:
x = - 5
Step-by-step explanation:
The equation of a vertical line parallel to the y- axis is
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (- 5, 7 ) with x- coordinate - 5 , thus
x = - 5 ← equation of vertical line
Which of the following describes the graph of 2x + 4y < 16? a:solid line, shaded below b:dashed line, shaded above c:dashed line, shaded below d:solid line, shaded above
Answer: C
Step-by-step explanation:
[tex]2x+4y<16\\=4y<-2x+16\\=y<-\frac{1}{2} x+4[/tex]
Since we are not dividing by a negative at any point during the simplification, the inequality sign won't change.
"<" means that the line will be dashed and shaded below.
Hope this helps!
The description of the inequality is (c) dashed line, shaded below
The inequality is given as:
2x + 4y < 16
The inequality is represented as less than (<)
When the less than sign is used in an inequality, the graph of the inequality would be a dashed line shaded below
Hence, the true statement is (c) dashed line, shaded below
Read more about inequalities at:
https://brainly.com/question/11234618
Figure A is a scale image of Figure B. What is the value of x?
Answer:
x = 5.4
Step-by-step explanation:
Multiply 7.2 by 3/4 to find the equivalent ratio.
Answer:
5.4Step-by-step explanation:
[tex] \frac{7.2}{x} = \frac{4}{3} [/tex]
Apply cross product property
[tex]4x = 7.2 \times 3[/tex]
Multiply the numbers
[tex]4x = 21.6[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{21.6}{4} [/tex]
Calculate
[tex]x = 5.4[/tex]
Hope this helps..
best regards!!
express each of the following decimal number in the p/q form (1)0.5 (2)3.8
Answer:
see explanation
Step-by-step explanation:
(1)
0.5 = [tex]\frac{5}{10}[/tex] = [tex]\frac{1}{2}[/tex]
(2)
3.8 = 3 [tex]\frac{8}{10}[/tex] = [tex]\frac{10(3)+8}{10}[/tex] = [tex]\frac{30+8}{10}[/tex] = [tex]\frac{38}{10}[/tex] = [tex]\frac{19}{5}[/tex]
Carter is choosing clay for his pottery class. Clay is sold in three different-shaped solids at the craft store. The dimensions of each of these shapes is shown below.
Answer:
[tex]\boxed{V_{cone} = 1017.36\ in.\³}[/tex]
[tex]\boxed{V_{cylinder} = 3052.08\ in.\³}[/tex]
[tex]\boxed{V_{sphere} = 3052.08\ in.^3}[/tex]
Step-by-step explanation:
Volume of Cone:
[tex]\sf V = \frac{1}{3} \pi r^2 h\\Where\ r = 9 , h = 12\\ V = \frac{1}{3} (3.14)(9)^2(12)\\V = \frac{1}{3} (3.14)(81)(12)\\V = \frac{1}{3} 3052.08\\[/tex]
V = 1017.36 in.³
Volume of Cylinder:
[tex]\sf V = \pi r^3h\\V = (3.14)(9)^2(12)\\V = (3.14)(81)(12)[/tex]
V = 3052.08 in.³
Volume of Sphere:
[tex]\sf V = \frac{4}{3} \pi r^3\\Where \ r = 9 \ in\\V = \frac{4}{3} (3.14)(9)^3\\V = \frac{4}{3} (3.14)(729)\\V = \frac{9156.24}{3}[/tex]
V = 3052.08 in.³
Answer:
[tex]\boxed{\sf V_{cone} = 1017.36\ in \³}\\\boxed{\sf V_{cylinder} = 3052.08\ in\³}\\\boxed{\sf V_{sphere} = 3052.08\ in^3}[/tex]
Step-by-step explanation:
[tex]\frac{1}{3} \pi (9)^2 (12)\\324 \times 3.14 \\ 1017.36[/tex]
[tex]\pi (9)^2 (12)\\972 \times 3.14\\ 3052.08[/tex]
[tex]\frac{4}{3} \pi (9)^3\\972 \times 3.14\\3052.08[/tex]
A school has 6 3/4 kg of detergent in stock. During ' Use Your Hands ' campaign, each class will be given 3/8 kg of detergent. There are 28 classes in the school.
(a) What fraction of the school will be supplied with the detergent in stock?
(b) How much detergent will be required altogether for the whole school?
(c) How much more detergent does the school need to order?
(d) If the school gives out the detergent in stock to the 15 lower secondary classes first,
(i) how much detergent will be given out;
(ii) how much detergent in stock will be left?
Answer:
Step-by-step explanation:
Total stock available = 6 x 3/4 = 18/4
Detergent given to each class=3/8
Total number of classes in the school = 28
Total detergent required by the school=3/8*28
=42/4
a. Fraction if the school who will get the detergent=18/42
b. Total required detergent for the whole school= 42/4
c. School needs to order = 42/4 - 18/4
= 24/4
= 6
d. i. Detergent given out to 15 classes = 15 x 3/8
= 45/8
ii. There will be no detergent left in stock
3x - 5y+5=0
4x+ 7y+8=0
Please help
Answer:
Y= -4. X=5
Step-by-step explanation:
This is a simultaneous equation
3x+5y= -5 ------------(1)
4x+5y= -8 ------------(2)
Using elimination method
Eliminate x
×4. 3x+5y= -5
×3. 4x+7y= -8
12x+20y= -20
-(12x+21y= -24) Minus
-y=4 therefore y= -4
Substitute x into equation 1
3x+5(-4)= -5
3x-20= -5
3x= -5+20
3x= 15
x=5
Which represents the solution to 7x > 21 or 6x - 9 < 21?
Answer:
1) The correct option is the third line
2) The correct option is the third line please see attached graph
Step-by-step explanation:
For the system of inequalities,
7·x > 21 or 6·x -9 < 21 we have;
7·x > 21
x > 21/3 = 3
x > 3
Also we have for 6·x -9 < 21 we have;
6·x -9 < 21
6·x < 21 + 9
6·x < 30
x < 30/6 = 5
x < 5
The representation of the region x > 3 and the region x < 5 on the number line consists of indicating points 3 and 5 with circles not filled to represent less than < and not less than or equal to ≤ and shading the potion of the number line in between the two points
Which gives the correct option as the third line which has an open circle at point 3 and 5
b) To graph the inequality v + 4 > 2 and 8·v - 20 ≤ 36
For the inequality v + 4 > 2, we have;
v > 2 - 4
v > - 2
For the inequality 8·v - 20 ≤ 36, we have;
8·v - 20 ≤ 36
8·v ≤ 36 + 20
8·v ≤ 56
v ≤ 56/8
v ≤ 7
The region representing v > -2 or v ≤ 7 on the number line consists of indicating points -2 with a circle (not filled) to represent less than < and point 7 with a filled circle to represent less than or equal to ≤ and shading the potion of the number line in between the two points
Which gives the correct option is the third line which has a closed circle at point -2 and an open circle at point 7