A bag contains 75 marbles:35 are blue and 25 of these blue marbles are swirled. The rest of them are red, and 30 of the red ones are swirled. The marbles that are not swirled are clear. What is the probability of drawing? (a) A blue marble (b) A blue swirled marble (c) A red clear marble.
Answers
Answer:
a) 35/75
b)25/75
c)10/75
Step-by-step explanation:
Related Questions
I need help! 25 brainly points!
Answers
The surface areas for each figures are:
220 ft² 410 cm²596 cm²360 cm²Surface area of cylinders include: 132π mm²22π ft²396π square inches.How to calculate surface areas?1. The surface area of the cuboid is:
Top and bottom: 2(10 ft x 4 ft) = 80 ft²
Front and back: 2(10 ft x 5 ft) = 100 ft²
Sides: 2(4 ft x 5 ft) = 40 ft²
Total surface area = 80 + 100 + 40 = 220 ft²
2. The surface area of the cuboid is:
Top and bottom: 2(18 cm x 5 cm) = 180 cm²
Front and back: 2(18 cm x 5 cm) = 180 cm²
Sides: 2(5 cm x 5 cm) = 50 cm²
Total surface area = 180 + 180 + 50 = 410 cm²
3. The surface area of the prism is:
Top and bottom: 2(5 cm x 14 cm) = 140 cm²
Front and back: 2(5 cm x 12 cm) = 120 cm²
Sides: 2(12 cm x 14 cm) = 336 cm²
Total surface area = 140 + 120 + 336 = 596 cm²
4. The surface area of the stacked cuboids is:
Top and bottom of first cuboid: 2(6 cm x 7 cm) = 84 cm²
Front and back of first cuboid: 2(6 cm x 2 cm) = 12 cm²
Sides of first cuboid: 2(7 cm x 2 cm) = 28 cm²
Front and back of second cuboid: 2(7 cm x 2 cm) = 28 cm²
Sides of second cuboid: 2(2 cm x 4 cm) = 8 cm²
Front and back of third cuboid: 2(2 cm x 10 cm) = 40 cm²
Sides of third cuboid: 2(10 cm x 8 cm) = 160 cm²
Total surface area = 84 + 12 + 28 + 28 + 8 + 40 + 160 = 360 cm²
5. The surface area of the cylinder is:
Top and bottom: 2π(6 mm)² = 72π mm²
Side: 2π(6 mm)(5 mm) = 60π mm²
Total surface area = 72π + 60π = 132π mm²
6. The surface area of the cylinder is:
Top and bottom: 2π(1 ft)² = 2π ft²
Side: 2π(1 ft)(10 ft) = 20π ft²
Total surface area = 2π + 20π = 22π ft²
7. The surface area of the cylinder stacked on a cube is:
Top and bottom of cylinder: 2π(5 m)² = 50π m²
Side of cylinder: 2π(5 m)(8 m) = 80π m²
Surface area of cube: 6(10 m x 13 m) = 780 m²
Total surface area = 50π + 80π + 780 = (130π + 780) m²
8. The surface area of the cylinder is:
Top and bottom: 2π(9 in)² = 162π in²
Side: 2π(9 in)(4 in) = 72π in²
Therefore, the total surface area of the cylinder is:
2(162π in²) + 72π in² = 396π in²
So the surface area of the cylinder is 396π square inches.
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Image transcribed:
Find the surface area of each figure.
10 ft
18 cm
5 cm
4 ft
5 ft
3.
4.
6 cm
7 cm
2 cm
5 cm
12 cm
14 cm
4 cm
10 cm
8 cm
Find the surface area of each cylinder. Leave your answer in terms of π.
5.
6 mm
6.
1 ft
5 mm
10 ft
7.
5 m
8.
4 in.
8 m
10 m
9 in.
13 m
11 m
247
Journal and Practice Workbook
Geometry
Find two solutions of y = 2x +5 (Use x= 0 and x=1 to find your solutions) *
A (0,7) (1,7)
B(0,5) (1,7)
C (0,7) (1,5)
D (-1,3) (2,9)
Answers
Suppose a life insurance company sells a
$280,000
1-year term life insurance policy to a
20-year-old
female for
$270.
According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is
0.999544.
Compute and interpret the expected value of this policy to the insurance company.
Answers
Answer:
$142.32, profit on sale of the policy
Step-by-step explanation:
You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.
CostThe insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...
0.000456 × $280,000 = $127.68
ProfitThe company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...
$270 -127.68 = $142.32
The expected value of the policy to the company is $142.32.
This represents its profit from sale of the policy.
__
Additional comment
Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."
<95141404393>
Timmy is helping his grandpa on his chicken farm. Timmy has to pack 66 eggs into cartons, minimizing the packing cost. He can use 12-egg cartons and 6-egg cartons. Two 12-egg cartons cost as much as three 6-egg cartons.
Answers
Or 11 6 egg cartons.
I’d say 12-egg cartons. Although you don’t want to use half an egg carton, there will be more eggs. Also they are cheaper. You can pack 24 eggs for the same price you can package 18. Therefore Timmy should use the 12-egg cartons.
please help me i’ll give you brainlist!
Answers
X intercept: 10/5
Y intercept: 0
How to find intercept of a linear equation?To find the intercepts of a linear equation, you need to set either the X or Y variable to 0 and then solve for the other variable.
For example, if you have the equation 5x - 2y = 10, you can set X equal to 0 and solve for Y to find the Y intercept, or you can set Y equal to 0 and solve for X to find the X intercept.
X Intercept:
To find the X intercept, set Y equal to 0 and solve for X.
5x - 2(0) = 10
5x = 10
x = 10/5
X intercept = 10/5
Y Intercept:
To find the Y intercept, set X equal to 0 and solve for Y.
5(0) - 2y = 10
-2y = 10
y = -10/2
Y intercept = 0
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Find the value of x in the rhombus
Answers
Answer:
Your answer is.....
37
Mark it as brainlist answer . follow me for more answer.
Step-by-step explanation:
Fred is standing at a point looking north. He walks on a bearing 056° for 9.8km before stopping. He then walks an additional 3.5 km on a bearing of 112° before stopping to rest. (a) Find out how far he is away from his start point using sine or cosine rule (b) Determine the area of the enclosed shape (c) Draw neat labeled scale diagram of the same
Answers
The area of the enclosed shape is about 14.47 km^2.
We are given that;
056° for 9.8km and 3.5 km on a bearing of 112°
Now,
We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:
y = 180° - 56° - 112°
y = 12°
Now we can use the cosine rule to find z:
z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)
z^2 ≈ 101.87
z ≈ 10.09
Therefore, Fred is about 10.09 km away from his start point.
To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:
sin(56°) = x/9.8
x = 9.8 sin(56°)
x ≈ 8.27
The area of a triangle is given by half the base times the height, so:
A = (1/2)(3.5)(8.27)
A ≈ 14.47
Therefore, by trigonometric ratios the answer will be 14.47 km^2.
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The average daily balance of a credit card for the month of November was $700, and the unpaid balance at the end of the month was $1400. If the monthly interest rate is 1.3% of the average daily balance, what is the total balance on the next billing date December 1? Round your answer to the nearest cent. Do not use commas to separate numbers or dollar signs. For example, $5,678.00 should be entered as 5678.00.
Answers
9514 1404 393
Answer:
$1409.10
Step-by-step explanation:
The interest is added to the unpaid balance to obtain the total balance.
$700×1.3% + 1400 = $9.10 +1400 = $1409.10
simplify the polynomial
(3х^3+ 4х^2 + 1) + (2х^2 + 10)
Answers
Answer:
Step-by-step explanation:
8
Johnny ran a race in 15 seconds, Malik ran the race in 4,92 seconds less
then Johnny, How long did it take Malik to run the race?
Answers
Answer:
10.08 seconds
Step-by-step explanation:
15-4.92=10.08
What is the central angle(pic included)
Answers
Answer:
72
Step-by-step explanation:
circumference = 20
arc = 4
4/20 =1/5
a circle = 360°
1/5 * 360 = 72
different equation dy÷dx+ytanx=secx
Answers
Answer:
First, we rearrange the equation to isolate the y-term on one side:
dy/dx + ytanx = secx
Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1
Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1
Integrating both sides with respect to x, we get: y |secx| = x + C
where C is the constant of integration. Solving for y, we have:
y = (x + C)/|secx|
Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined
(HELP!!!!!!!!!!!!!!!!!) Vector v has an initial point at (5, 2) and a terminal point at (−15, 10). What is negative one half times vector v?
open angled bracket 10 comma 4 close angled bracket
open angled bracket negative 10 comma negative 4 close angled bracket
open angled bracket negative 10 comma 4 close angled bracket
open angled bracket 10 comma negative 4 close angled bracket
Answers
negative one half times vector v can be represented as \(< 10, -4 > ,\) which is equivalent to the option: open angled bracket negative \(10\) comma 4 close angled bracket. Thus, option B is correct.
What is the negative one half times vector?To obtain the negative one half times vector v, we need to multiply each component of vector v by \(-1/2\) . Given that vector v has an initial point at \((5, 2)\) and a terminal point at \((-15, 10)\) , we can calculate the components of vector v as follows:
x-component of vector v = terminal x-coordinate - initial x-coordinate
\(= -15 - 5\)
\(= -20\)
y-component of vector v = terminal y-coordinate - initial y-coordinate
\(= 10 - 2\)
\(= 8\)
So, vector v can be represented as \(< -20, 8 > .\)
To find negative one half times vector v, we need to multiply each component by \(-1/2\) :
x-component of negative one half times vector \(v = -1/2 \times -20= 10\)
y-component of negative one half times vector \(v = -1/2 \times 8= -4\)
Therefore, negative one half times vector v can be represented as < 10, -4 >, which is equivalent to the option: open angled bracket negative 10 comma 4 close angled bracket.
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Can anyone please help?
Q: A baseball is hit into the air by the Blue Jays' batting coach.
It's height h, in meters, after t seconds is h = - 4.9t² + 27.44t + 0.584
(a) write the equation in vertex form by completing the square
b) How high off the ground was the ball when it was hit?
c) When does the ball reach it's maximum height? what is it's maximum height?
d) For how long is the ball in the air ? Round answer to 1 decimal place
Answers
The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.
The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:
h = -4.9(t² - 5.6t) + 0.584
Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:
h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584
Simplifying, we get:
h = -4.9((t - 2.8)² - 2.8²) + 0.584
Expanding further:
h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584
Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328
b) The ball's height when it was hit can be found by evaluating the equation at t = 0:
h = -4.9(0 - 2.8)² + 34.328
h = -4.9(-2.8)² + 4.328
h = -4.9(7.84) + 34.328
h ≈ 0.784 meters
To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.
The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:
0 = -4.9(t - 2.8)² + 34.328
4.9(t - 2.8)² = 34.328
(t - 2.8)² ≈ 7
t - 2.8 ≈ ±√7
t ≈ 2.8 ± √7
Since time cannot be negative in this context, we can ignore the negative value.
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Are the following figures similar?
Trapezoids ABCD and EFGH are shown. Angle A equals 137 degrees, Angle B equals 90 degrees, Angle C equals 90 degrees, Angle D equals 43 degrees, Angle E equals 136 degrees, Angle F equals 90 degrees, Angle G equals 90 degrees, Angle H equals 44 degrees.
Answers
No, the trapezoids are not similar because their corresponding angles do not have the same measures.
The given trapezoids ABCD and EFGH can be analyzed to determine if they are similar. Similarity in geometric figures implies that their corresponding angles are congruent, and their corresponding sides are proportional.
Let's examine the angles of the trapezoids:
In trapezoid ABCD:
Angle A = 137 degrees
Angle B = 90 degrees
Angle C = 90 degrees
Angle D = 43 degrees
In trapezoid EFGH:
Angle E = 136 degrees
Angle F = 90 degrees
Angle G = 90 degrees
Angle H = 44 degrees
By comparing the angles, we can observe that angles B and F are both right angles (90 degrees) in both trapezoids. Additionally, angles C and G are also right angles (90 degrees) in both trapezoids.
However, angles A and E, as well as angles D and H, do not have the same measures. Angle A measures 137 degrees in trapezoid ABCD, while angle E measures 136 degrees in trapezoid EFGH. Similarly, angle D measures 43 degrees in trapezoid ABCD, while angle H measures 44 degrees in trapezoid EFGH.
Since the corresponding angles in the two trapezoids do not have the same measures, we can conclude that trapezoids ABCD and EFGH are not similar.
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Help thank you so very much
Answers
Hope it helps ya!
Answer:
x-0 12
Step-by-step explanation:
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The cross-section of a prism is an equilateral triangle of side 6cm. The length of the
prism is 20 cm. Calculate the total surface area of the prism
Answers
Answer:
the total surface area of the prism is 374.8 cm^2.
Step-by-step explanation:
Since the cross-section is an equilateral triangle of side 6 cm, the area of the triangle is:
A = 1/2 * base * height = 1/2 * 6 cm * 5.2 cm = 15.6 cm^2
where 5.2 cm is the height of the equilateral triangle.
The total surface area of the prism consists of the area of the two equilateral triangles and the area of the three rectangular faces. The area of each rectangular face is the product of its length and width.
The length of the prism is 20 cm and the width of each rectangular face is 6 cm, so the area of each rectangular face is:
A_rect = length * width = 20 cm * 6 cm = 120 cm^2
Therefore, the total surface area of the prism is:
A_total = 2 * A_tri + 3 * A_rect
= 2 * 15.6 cm^2 + 3 * 120 cm^2
= 374.8 cm^2
Hence, the total surface area of the prism is 374.8 cm^2.
The graph of � = ∣ � ∣ y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right by 4 44 units. What is the equation of the new graph? Choose 1 answer: Choose 1 answer: (Choice A) � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 A � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 (Choice B) � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 B � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 (Choice C) � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 C � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 (Choice D) � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4y, equals, vertical bar, x, minus, 9, vertical bar, plus, 4 D � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4
Answers
An equation of the new graph is: A. y = ∣x - 4∣ - 9.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:
g(x) = f(x - N)
Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:
g(x) = f(x) + N
Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:
y = ∣x - 4∣ - 9
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A software development company is voting to elect a president, a secretary, a treasurer, and three directors. If a total of 11 qualified candidates applied for these positions, in how many ways can the positions be filled?
Answers
The ways to elect the candidates from the total is 462
How to determine the ways of selection?From the question, we have
Total number of candidate, n = 11Numbers to selection, r = 6 i.e. the president, a secretary, a treasurer, and three directorsThe number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 11 and r = 6
Substitute the known values in the above equation
Total = ¹¹C₆
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 11!/5!6!
Evaluate
Total = 462
Hence, the number of ways is 462
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Each of the 39 students in the eighth grade at Lincoln Middle School has one dog or one cat or both a dog and a cat. Twenty students have a dog and 26 students have a cat. How many students have both a dog and a cat?
Answers
Number of 7 students have both a dog and a cat, out of the 39 eighth grade students at Lincoln Middle School.
Total number of 8th grade students: 39
Number of students with a dog: 20
Number of students with a cat: 26
Number of students with both a dog and a cat: 20 + 26 - 39 = 7. Therefore, 7 have both a dog and a cat.
There are 39 students in the 8th grade at Lincoln Middle School. Of those students, 20 have a dog, 26 have a cat, and 7 have both a dog and a cat. To calculate this number, we added the number of students with a dog (20) and the number of students with a cat (26) and then subtracted the total number of students (39). The result of this calculation, 7, is the number of students who have both a dog and a cat. This means that 7 out of 39 8th grade students at Lincoln Middle School have a dog and a cat.
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The electric cooperative needs to know the main household usage of electricity by it’s non commercial customers in KWH per day. They would like the estimate to have a maximum error of 0.1 3 KWH. A previous study found that for an average Family the standard deviation is 2.1 KWH and the mean is 15.8 KWH per day. If they’re using a 99% level of confidence how large of a sample is required to estimate the mean usage of electricity. Round your answer to the next integer
Answers
ANSWER:
1737
STEP-BY-STEP EXPLANATION:
Given:
standard deviation (σ) = 2.1
Margin of error = E = 0.13
At 99% confidence level the z is:
\(\begin{gathered} \alpha=1-99\% \\ \\ \alpha=1-0.99=0.01 \\ \\ \alpha\text{/2}=\frac{0.01}{2}=0.005 \\ \\ \text{ The corresponding value of z is the following:} \\ \\ Z_{\alpha\text{/2}}=2.58 \end{gathered}\)We can calculate the sample size using the following formula:
\(\begin{gathered} n=\left(\frac{Z_{\alpha \text{/2}}\cdot \sigma }{E}\right)^2 \\ \\ \text{ We replacing:} \\ \\ n=\:\left(\frac{2.58\cdot2.1}{0.13}\right)^2 \\ \\ n=1736.97\approx1737 \end{gathered}\)The sample size is 1737
Solve for x:-
2^x=32
Answers
Answer:
x=5
Step-by-step explanation:
2^x= 32
2^x=2^5
(comparing, common denominator)
therefore x=5.
if p(e and f)=.392, p(e/f)=.56 and p(f/e)=.7, then p(e)=
Answers
On solving the provided question, we can say that Probability(A and B) = P(A)P(B|A) and P(E or F) = P(E) + P(F) - P(E and F)
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
Probability(A and B) = P(A)P(B|A).
P(A and B) = P(B and A), this may also be written as P(A and B) = P(B)P(A|B).
Using the general multiplication rule, we have
P(E and F) = P(E)P(F|E)
.392 = P(E)(.7)
P(E) = .56
P(E and F) = P(F)P(E|F)
.392 = P(F)(.56), so
P(F) = .7
P(E or F) = P(E) + P(F) - P(E and F)
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5 plus the product of 39 and a number e
Answers
The required solution is 5+39e.
What is arithmetic?
The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications
Given :
Write down the question as an algebra problem, with the unknown as X
The unknown is a number plus 5, so we write it as (X+5). The product is four times (X+5), so we write it as 39(X+5). Set it equal to e, as per the question, 5+39e
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what is the product of mixed number 2 x 2 7/8?
Answers
Answer:
\(5\frac{3}{4}\)
----------------------------------------------------------------------------------------------------------
Since we have to convert mixed numbers to fractions, \(2\frac{7}{8}\) becomes \(\frac{23}{8}\)
And for whole number, add a 1 as the denominator.
\(\frac{2}{1}\)
Now, the equation becomes...
\(\frac{2~*~23}{1~*~8}\)
\(2 * 23 = 46\)
\(1 * 8 = 8\)
Convert these two numbers to a fraction.
\(46~and~8~-- > ~\frac{46}{8}\)
Simplify 46 over 8 and make it a mixed number.
\(\frac{46}{8} -- > 5\frac{3}{4}\)
why is the denominator 4? we had to simplify 8 using its GCF along with 46
the GCF is 2, so simplify using 2. to simplify, divide the number by its GCF.
\(\frac{46}{2} = 23\\\\\frac{8}{2} = 4\)
now you have \(\frac{23}{4}\)
and that, in mixed number, translates to \(5\frac{3}{4}\)
________________________________________________________
Questions?Ask in comments.
how to calculate area when you are given volume of 182m3 and height of 2.8m
Answers
Hey there!
We simply have to do 182/2.8, and you will get the area (65m^2).
We know that the formula for area is length x width, and the formula for volume is length x width x height. In the volume formula, we can see it can also be area x height to get volume. So, we know that area x height = volume, right? And in this equation, we are given volume and height. If V = ha, with V = volume; h = height; a = area, we can divide "h" on both sides, and we get V/h = a, or volume divided by height is area. To solve for the above equation, we can plug the numbers in the formula: 182/2.8 = a, or 65 = a.
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PLZ HELP
Draw a non-square rectangle or parallelogram or an isosceles trapezoid in the coordinate
plane so that portions of the shape are in each of the four quadrants. Explain what would
happen to your shape if you transformed it using each of the given rules.
2. (-x, -y)
1. (x, y)
4. (x, y + 3)
3. (x - 4, y)
6. (4x, 4y)
5. (r - 1, y + 4)
8. (2x, y-1)
Answers
Answer:
Step-by-step explanation:
Following changes will be there when the figure is transformed by the given rules.
1). Rule for transformation has been given as,
(x, y) → (x, -y)
Reflection across x axis.
2). (x, y) → (-x, -y)
Rotation of 180° about the origin.
3). (x, y) → (x - 4, y)
Shifted 4 units left horizontally.
4). (x, y) → (x, y + 3)
Shifted vertically up by 3 units
5). (x, y) → (x - 1, y + 4)
Shifted 1 units left horizontally and 4 units up vertically.
6). (x, y) → (4x, 4y)
Dilated by 4 units.
A television transmission tower casts a shadow 1130 feet long. The angle formed by the ground and a line from the top of the tower to the tip of the shadow is 48.3 degrees. How tall is the tower? Round your answer to the nearest foot.
Answers
The height of the television transmission tower is approximately 1298 feet.
The height of the television transmission tower, we can use trigonometry and the concept of tangent.
Let's denote the height of the tower as h.
We know the length of the shadow is 1130 feet and the angle formed by the ground and the line from the top of the tower to the tip of the shadow is 48.3 degrees.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
The height of the tower is the opposite side and the length of the shadow is the adjacent side.
Using the tangent function, we can set up the following equation:
tan(48.3°) = h / 1130
To solve for h, we can multiply both sides of the equation by 1130:
1130 × tan(48.3°) = h
Using a calculator, we find:
h ≈ 1130 × 1.1477
≈ 1297.601 feet
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Use the properties of exponents to generate an expression equivalent to each expression.
\((x^3y^7)^2\)
\((144^3)^\frac{1}{6}\)
\(2^(3t+4)\)
Answers
x⁶y¹⁴ is the expression equivalent to (x³y⁷)², 12 is the equivalent expression of \((144^{3}) ^{\frac{1}{6} }\) and 6t+8 is equivalent expression of 2(3t+4).
What is Expression?An expression is combination of variables, numbers and operators.
Equivalent expressions are expressions that work the same even though they look different.
The given expression is (x³y⁷)²
(x³)²(y⁷)²
x⁶y¹⁴
x⁶y¹⁴ is the expression equivalent to (x³y⁷)²
Expression is \((144^{3}) ^{\frac{1}{6} }\)
\(144^{\frac{3}{6} }\)
\(144^{\frac{1}{2} }\)
√144
12
12 is the equivalent expression of \((144^{3}) ^{\frac{1}{6} }\)
Expression is 2(3t+4)
Apply distributive property
6t+8
6t+8 is equivalent expression of 2(3t+4).
Hence, x⁶y¹⁴ is the expression equivalent to (x³y⁷)², 12 is the equivalent expression of \((144^{3}) ^{\frac{1}{6} }\) and 6t+8 is equivalent expression of 2(3t+4).
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Express the following expression in the form of a + bi: (39 + 34i) + (76 + 89i) - (47 +26i).
Answers
Answer:
68+97i
Step-by-step explanation:
work shown and pictured
Answer:
68+97i
Step-by-step explanation:
(39 + 34i) + (76 + 89i) - (47 +26i).
Distribute the minus sign
(39 + 34i) + (76 + 89i) + (-47 -26i)
Combine like terms
(39+76-47)+(34i+89i-26i)
68+97i