What is the length of CD? round to the nearest tenth
Answers
Answer: it is c. 10.7 cm
Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.
To find the length of CD in a right triangle ABC where:
BA = 10 cm (the side adjacent to angle B)
angle B = 30 degrees
angle C = 90 degrees (a right angle)
angle D = 25 degrees
We can use the trigonometric ratio for tangent (tan) since we know the measure of angle B and the length of side BA. The tangent of an angle in a right triangle is the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.
In this case, we want to find CD, which is the side opposite to angle B. So, we can use the following relationship:
tan(B) = CD / BA
First, find the tangent of angle B (30 degrees):
tan(30 degrees) ≈ 0.5774 (rounded to four decimal places)
Now, we can solve for CD:
CD = tan(B) * BA
CD ≈ 0.5774 * 10 cm
CD ≈ 5.774 cm
Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.
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Related Questions
Can someone pls help me
Answers
Answer:
behaviour
Step-by-step explanation:
Harry Potter is at Ollivanders Wand Shop. As we all know, the wand must choose the wizard, so Harry cannot make the choice himself. He interprets the wand selection as a random process so he can determine the probabilities of different outcomes.
The wood types available are holly, elm, maple, and wenge. The core materials on offer are phoenix feather, unicorn hair, dragon scale, raven feather, and thestral tail.
Let A be the event that Harry is chosen by a wand made of holly and B be the event that he is chosen by a wand with a dragon scale core.
Answers
Answer: The probability of being chosen by a wand made of holly or a wand made of dragon scale core is 0.4 or 40%
Step-by-step explanation: What we have are probabilities of two events. The first is the probability that Harry Potter is chosen by a wand made of Holly which is P(A). The other event is the probability that Harry is chosen by a wand with a dragon scale which is P(B).
In other to calculate P(A), there is a total of four possibilities, (that is holly, elm, maple and wenge). Therefore, the probability is derived as;
P(A) = Number of required outcomes/Number of all possible outcomes
P(A) = 1/4 or (0.25)
To calculate P(B), there is a total of five possibilities (that is phoenix feather, unicorn hair, dragon scale, raven feather and thestral tail). Therefore the probability is derived as;
P(B) = Number of required outcomes/Number of all possible outcomes
P(B) = 1/5 or (0.20)
However, the question requires the probability of P(A or B).
First we derive the probability of being chosen by a wand made of holly AND one made of a dragon scale core. In other words we shall calculate the probability of P(A and B) which is derived as;
P(A and B) = P(A) x P(B)
P(A and ) = 1/4 x 1/5
P(A and B) = 1/20 (0.05)
The probability of P(A or B) can now be calculated as follows;
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = (0.25 +0.20) - 0.05
P(A or B) = 0.45 - 0.05
P(A or B) = 0.40
Therefore the probability that Harry Potter is chosen by a wand made of Holly or a wand with Dragon scale core is 0.4 or 40%
Answer: P( A or B) = 2/5
Step-by-step explanation:
Suppose you drop a ball from a height of 10 feet. After the ball hits the floor, it rebounds to a height defined by the recursive formula an = 0.85an – 1. What is a1?
Answers
Answer:
10 feet
Step-by-step explanation:
The height of the ball after it hits the floor and rebound is defined by the recursive formula:
[tex]a_n = 0.85a_{n-1}[/tex]
This is an example of a geometric sequence in which the next term is gotten by multiplication of the previous term by 0.85.
If the ball is dropped from a height of 10 feet, the first term is 10.
Its Initial height, [tex]a_1=10 \:feet[/tex]
Which three statements are true as they relate to supply and demand? As supply rises, prices generally decrease. As demand decreases, costs generally increase. As supply decreases, prices increase. The average rate of change describes how much a quantity changes as price increases. As demand rises, the price of the product decreases.
Answers
As supply rises, prices decrease.
And The average rate of change describes how much a quantity changes as prices increases
As supply decreases, prices increase. It seems logical but I'm not 100% positive on the last one. I know the first 2 are right.
The statements that are true as they relate to supply and demand are: as supply rises, prices generally decrease; as demand decreases, prices generally increase; as supply decreases, prices increase.
Explanation:Supply and demand are fundamental concepts in economics. The law of supply states that as supply increases, prices generally decrease. This is because when there is a higher quantity supplied, producers compete to sell their products, leading to lower prices. On the other hand, the law of demand states that as demand decreases, prices generally decrease. When there is lower demand for a product, sellers may lower prices to attract more buyers.
Additionally, the statement that as supply decreases, prices increase is also true. When the quantity supplied decreases, the scarcity of the product can drive up prices as buyers are willing to pay more for limited supply. The average rate of change refers to how much a quantity changes as the price increases. It is not directly related to supply and demand dynamics, but rather focuses on the relationship between quantity and price. As demand rises, the price of a product generally increases. This is because as more people want to buy a product, sellers can charge higher prices since there is higher demand.
There are 4 blueberry, 6 raisins, and 2 plain bagels in a bag. Mike randomly selects two bagels without replacing the first bagel. Find the probability that he selects a raisin bagel and then a plain bagel
Answers
Answer:
The probability that he selects a raisin bagel and then a plain bagel is [tex]\frac1{11}[/tex].
Step-by-step explanation:
Probability:
The ratio of the number of outcomes of favorable event to total number of all possible outcomes is called probability of the favorable event.
[tex]Probability=\frac{\textrm{The number of favorable outcomes}}{\textrm{Total number of all possible}}[/tex]
Given that, there are 4 blueberry, 6 raisins and 2 plain bangles in a bag.
Total number of bangles= (4+6+2)
= 12
The probability that he selects a raisin
[tex]=\frac{\textrm{Number of raisin bangles}}{\textrm{Total number of bangles}}[/tex]
[tex]=\frac{6}{12}[/tex]
[tex]=\frac12[/tex]
Total number of remaining bagels is =(12-1)=11
After selecting a raisin bagel,the probability that he selects a plain bangle is
[tex]=\frac{\textrm{Number of plain bangles}}{\textrm{Total number of bangles}}[/tex]
[tex]=\frac{2}{11}[/tex]
Selecting of a raisin bangle and a plain bangle are both independent event.
The probability that he selects a raisin bagel and then a plain bagel is
[tex]=\frac{1}2\times\frac{2}{11}[/tex]
[tex]=\frac1{11}[/tex]
Mr. Ishimoto needs to replace the grass in the section of his lawn that is shown below.
A grass section can be broken into 2 rectangles. 1 rectangle has a base of 7 feet and height of 3 feet. The other rectangle has a base of 2 feet and height of 7 feet.
If the new grass costs $0.40 per square foot, how much will the grass cost Mr. Ishimoto?
$14.00
$16.40
$35.00
$41.00
Answers
Answer:
The replacing the grass will cost Mr. Ishimoto $14.00.
Step-by-step explanation:
The area of a rectangular field is:
[tex]\text{Area}=\text{height}\times \text{base}[/tex]
It is provided that Mr. Ishimoto needs to replace the grass in the section of his lawn.
The grass section can be broken into 2 rectangles.
First rectangle: Base = 7 feet and Height = 3 feet.
Second rectangle: Base = 2 feet and Height = 7 feet.
Compute the area of both the rectangles as follows:
[tex]\text{Area}_{1}=\text{height}_{1}\times \text{base}_{1}\\=3\times 7\\=21[/tex] [tex]\text{Area}_{2}=\text{height}_{2}\times \text{base}_{2}\\=7\times 2\\=14[/tex]
Now the cost of the new grass is $0.40 per square foot.
Compute the cost of replacing the grass in the first rectangular section as follows:
[tex]\text{Cost of new grass for section 1}=\text{Area}_{1} \times\$0.40\\[/tex]
[tex]=21\times \$0.40\\=\$8.40[/tex]
Compute the cost of replacing the grass in the second rectangular section as follows:
[tex]\text{Cost of new grass for section 2}=\text{Area}_{2} \times\$0.40\\[/tex]
[tex]=14\times \$0.40\\=\$5.60[/tex]
The total cost of replacing the grass is:
[tex]\text{Total cost}=\text{Cost of new grass for section 1}+\text{Cost of new grass for section 2}[/tex]
[tex]=\$8.40+\$5.60\\=\$14.00[/tex]
Thus, the replacing the grass will cost Mr. Ishimoto $14.00.
Answer
14.00
Step-by-step explanation:
In a computer catalog, a computer monitor is listed as being 27 inches. This distance is
the diagonal distance across the screen. If the screen measures 15 inches in height, what
is the actual width of the screen to the nearest inch?
Answers
The width of the computer monitor is 22 inches
What is a Rectangle?
In a Rectangle
It is a four sided shape where every angle is a right angleThe alternative sides are equalTwo axes of symmetry bisect each otherDiagonals are equal in lengthThe diagonal equals the square root of the width squared plus the height squared
Given data ,
Let the Width of the rectangle be W
Diagonal of the rectangle = 27 inches
Height of the rectangle = 15 inches
D² = L² + W²
W² = D² - L²
W² = ( 27 )² - ( 15 )²
= 729 - 225
= 504
Therefore , Width W = √504
≈ 22.45 inches
≈ 22 inches
Hence , the width of the computer monitor is 22 inches
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A shipping clerk will ship an order of 200 batteries so long as three randomly selected batteries work. Past data has shown that five out of 200 batteries are defective. What is the probability that the clerk will ship the order?
Answers
Answer:
0.9264999239
Step-by-step explanation:
chance that first battery that is being checked works is 195/200
chance that second battery that is being checked works is 194/199
chance that third battery that is being checked works is 193/198
propabilty that the clerk ships the order is (195/200)×(194/199)×(193/198)
=0.9264999239
True or false: y=x3−4 is a linear equation. A true B false
Answers
false because it is formed wrong
Final answer:
The equation y = x^3 - 4 is not a linear equation because it contains a cubic term (x^3), which means the graph is a curve, not a straight line. Therefore, the correct answer is false.
Explanation:
The equation y = x3 − 4 is not a linear equation. A linear equation is one in which every term is either a constant or the product of a constant and the first power of a variable. In the given equation, the term x3 indicates that it is a cubic term because the value of x is raised to the power of three, suggesting that the graph of this equation would be a curve, not a straight line. Therefore, the correct answer is false.
Linear equations have the general form y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Examples of linear equations include y = −3x, y = 0.2 + 0.74x, and y = −9.4 − 2x, which can all be graphed as straight lines. In contrast, an equation like y = x3 − 4 does not fit this form and therefore is not considered linear.
find the value of each variable
Answers
Answer:
x = 12[tex]\sqrt{2}[/tex]
y = 12
z = 12[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The triangle with z as one of it's sides is a 30, 60, 90 triangle where the longest side of the triangle is 2x, the shortest side as x, and the middle side as x*sqrt of 3.
The shared line between the two triangle is 12 and z is 12*sqrt of 3
The left triangle is a 45, 45, 90 triangle where the 2 sides that look the same are the same and the hypotenuse is x sqrt of 2 so y is 12 and x is 12 sqrt of 2
Answer:
x = [tex]12\sqrt{2}[/tex] units
y = 12 units
z = [tex]12\sqrt{3}[/tex] units
Step-by-step explanation:
Notice that the biggest triangle is broken up into a 45-45-90 isosceles triangle with hypotenuse x and leg y, as well as a 30-60-90 triangle with hypotenuse 24 and long leg z.
Let's focus on finding z first. Remember that in a 30-60-90 triangle, the ratio of the short leg to the long leg to the hypotenuse is: [tex]1:\sqrt{3} :2[/tex]. Here, the hypotenuse is 24 and z is the longest leg, so we have the proportion:
[tex]\frac{\sqrt{3} }{2} =\frac{z}{24}[/tex]
Cross-multiply:
[tex]24\sqrt{3} =2z[/tex]
z = [tex]12\sqrt{3}[/tex] units
Now, let's find the smallest leg of the 30-60-90 triangle; it is simply 24/2 = 12 units. Let's move onto x and y.
Remember that in a 45-45-90 triangle, the ratio of one leg to the second leg to the hypotenuse is: [tex]1:1:\sqrt{2}[/tex]. So, since y is a leg of this triangle and the smallest leg of the 30-60-90 triangle coincides with the second leg of the 45-45-90 triangle, y = 12 units.
Finally, x is found by multiplying 12 by [tex]\sqrt{2}[/tex]: 12 * [tex]\sqrt{2}[/tex] = [tex]12\sqrt{2}[/tex] units
Hope this helps!
A 3 cm x 10 cm rectangle sits inside a circle with radius of 12 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answers
Answer:
422.389 cm
Step-by-step explanation:
First you have to find the area of the circle then subtract it by the area of the rectangle. To find the area of the circle you have to square the radius then multiply it by 3.14.(12×12=144, 144× 3.14=452.389) Therefore 452.389 cm is the area of the circle. Area of the rectangle 30cm.
452.389 -30=422.389
Ortega is trying to fill three bags equally with sand. He wants the bags to weigh the same. If the bags currently weigh 55 pounds, 51 pounds, and 48 pounds. Can Ortega get each bag to weigh the same by moving the weight around?
Answers
Answer:
yes
Step-by-step explanation:
The average weight of the three bags is ...
(55 +51 +48)/3 = 154/3 = 51 1/3 . . . pounds
By removing 3 2/3 pounds of sand from the heaviest bag, adding 1/3 pound to the middle-weight bag, and the remaining 3 1/3 pounds to the lightest bag, Ortega can make all of the bags weigh the same: 51 1/3 pounds.
How are ridge transformations are congruent figures related ?
Answers
Answer:
uh im not in that grade yet so ye
Step-by-step explanation:
I need help graphing on this number line
Answers
Answer:
1 is c
2 is b
3 is d
4 is a
Step-by-step explanation:
Open circle is 'less than' or 'greater than'.
Closed (shaded) circle is 'less than or equal to' or 'greater than or equal to'.
If the mean of the data set is
4 bubbles, find the number of bubbles Hannah blew. khan academy
Answers
Answer: Hannah blew 1 bubble
Step-by-step explanation:
Mean * number of gum chewers= total bubbles
4*4=16
Let’s add up the numbers of bubbles that we do know.
4+5+6=15
16-15=1
Hannah blew 1 bubble
The number of bubbles Hannah blew can be expressed as 1
How can the number of bubbles Hannah blew be calculated?The study of variables and the formula manipulation principles is known as algebra. Its roots lie in the computation methods of ancient Babylonia, but now it is a mode of thinking that permeates practically all branches of mathematics.
Let number of bubbles Hannah blew =x
Then we can set up the equation as
[tex]\frac{1}{4} (4+5+6+x)=4[/tex]
15+x=16
x=16-15
x=1
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Write the number 7.748 x 10-5 in standard form.
OA. 0.0007748
OB. 774,800
OC. 0.000007748
D. 0.00007748
Answers
PLEASE HELP ITS URGENT
Answers
Lindsay used two points, (x 1, y 1) and (x 2, y 2), to find the equation of the line, y = mx + b, that passes through the points. First, she used the definition of slope and determined that the value of m is StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. Given this information, which expression must represent the value of b?
Answers
Answer:
tb i think its A
Step-by-step explanation:
Answer:
It is A
Step-by-step explanation:
Plz help! Question is in the picture! 10 point reward!
Answers
Answer:
1, 8.4
Unit rate: 8.4 feet per second
Step-by-step explanation:
To find the unit rate you divide the time by the distance, therefore with 8.4 it's easy to find the unit rate! :) Hope this helps! If it did, rate brainliest
A pet store makes a 60% profit on sales. The manager wants the store to make over $6,000 in profit each month. Describe the inequality and the graph of the solution to find the minimum amount of sales the store must have each month to reach the goal.
The inequality is .
The graph of the solution is .
Answers
The inequality is : 0.6x > 6000. The graph of the solution is : open circle at 10,000; arrow right
Thats the right answer it told me
Answer:
The inequality is
✔ 0.6x > 6000
.
The graph of the solution is
✔ open circle at 10,000; arrow right
Step-by-step explanation:
Only 3 years late ;)
It took a skydiver 5 seconds to drop 400 feet. What is the
rate (in feet per/second) of the skydiver's drop?
Answers
80 feet per second
Step-by-step explanation:
just divide the amount he fell by the amount of time it took so you would take 400/5 and get the answer
Answer:
80
Step-by-step explanation:
If it took him 5 seconds to drop 400 feet then you have to divide it by 5 to determine the rate he can drop a certain amount of feet per second.
In a scale drawing of a law office, 1/4 inch represents 4 1/2 feet. If the actual length of the conference room is 30 3 5 feet, what is the length of the conference room, in inches, on the scale drawing?
Answers
Answer:
tbh im not sure but i think the answer is 30 ft
Step-by-step explanation:
Tickets to the school dance cost $3.00 in advance or $5.00 at the
door. There were a total of 184 tickets sold, raising $688. How many tickets
were sold at the door?
Answers
Answer:
68 tickets
Step-by-step explanation:
This is a problem that involves a system of equations, the first step is to define your variables and write equations to represent the situation.
x = number of advance tickets
y = number of door tickets
x + y = 184
3x + 5y = 688
Next, you need to solve for one variable, based on how these equations are written, the best method would be to solve by multiplication.
-3(x + y = 184) (multiply equation by -3)
-3x - 3y = -552
Now we need to combine the two equations together
3x + 5y = 688
-3x - 3y = -552
From here we can eliminate the x variable when subtracting the equations, this results in:
2 y = 136
y = 68
Therefore, 68 tickets were sold at the door.
A smaller triangle is cut out of a larger triangle. The larger triangle is a right triangle with side lengths of 5 millimeters and 12 millimeters. The smaller triangle has side lengths of 4 millimeters and 3 millimeters.
What is the area of the shaded region?
21 mm2
24 mm2
42 mm2
48 mm2
Answers
Answer:
Sorry if this is late, but it's 24mm2
Step-by-step explanation:
i got a 100 on the quiz
The area of the shaded region, if a smaller triangle is cut out a larger triangle is 24 mm²
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
Area of the larger triangle = (1/2) * 5 mm * 12 mm = 30 mm²
Area of the smaller triangle = (1/2) * 4 mm * 3 mm = 6 mm²
Area of shaded region = 30 mm² - 6 mm² = 24 mm²
The area of the shaded region, if a smaller triangle is cut out a larger triangle is 24 mm²
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Please help me now please
Answers
Answer:
0.4444444
Step-by-step explanation:
2/3 x 2/3 = 0.4444 repeating!
Hope this helps!
Find: P (Red and Small)
Answers
Answer:
3/10
Step-by-step explanation:
Hey ya'll don't scroll please, just look at the attachment and answer every single question please- thank you very much.
I need this done in 15 minutes so it would really really help. Also I have made my 11th account this week regarding this question so just please answer it for me- thanks girlie.
Answers
B= 1 and a half
C= 11 and a half
The local newspaper has letters to the editor from
60
60 people. If this number represents
2
2% of all of the newspaper's readers, how many readers does the newspaper have?
Answers
Answer:
300 readers
Step-by-step explanation:
60/2=30
30X100=300
The total number of readers of a newspaper based on the percentage of people who wrote letters to the editor are 3000.
The number of readers the newspaper has is:
Number of readers = (60 / 0.02) = 3000 readers
Therefore, the newspaper has 3000 readers.
To factor a trinomial you must find the product of "a" and "b" and find the sum of "c"
True
False
Answers
Answer:
true
Step-by-step explanation:
Takumi started studying how the number of branches on his tree changes over time.
The relationship between the elapsed time, t, in years, since Takumi started studying his tree, and the total
number of its branches, N(t), is modeled by the following function:
N(t) = 63. 2
Complete the following sentence about the yearly rate of change in the number of branches.
Every year, the number of branches
grows/shrinks
by a factor of
Answers
Answer:
Grows, Factor of 2
Step-by-step explanation:
The relationship between the elapsed time, t, in years, since Takumi started studying his tree, and the total number of its branches, N(t), is modeled by the function:
[tex]N(t) = 63. 2^t[/tex]
For illustration, let us take the growth for the first three years after he started studying the number of branches.
[tex]When \:t=1, N(1) = 63. 2^1=126\\When \:t=2, N(2) = 63. 2^2=252\\When \:t=3, N(3) = 63. 2^3=504\\504\div 252=252\div 126=2[/tex]
We notice that for each subsequent year, the number of branches doubles.
Therefore:
Every year, the number of branches grows by a factor of 2.