Using trigonometric ratio, the length of the ladder that reached the window is 20.03 feet
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let l represent the length of the ladder, using trigonometric ratio:
sin(64) = 18/l
l = 20.03 feet
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For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio $1:2:3:4:5:6$. What is the probability of rolling a total of 7 on the two dice
Step-by-step explanation:
$ 1: 2: 3: 4: 5: 6: 7: 7: in ratio
probability on two dice
1, 2, 3, 4, 5, 6, 7, 7.
The probability of rolling a total of 7 on the two dice is 8/63 if in the particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.
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.
Let x be the probability of rolling a 1.
Ratios are 1:2:3:4:5:6
Then,
x + 2x + 3x + 4x +5x + 6x = 1
21x = 1
x = 1/21
The possible combinations of two rolls that total 7 are:
{(1,6) ; (2,5) ; (3,4) ; (4,3) ; (5,2) ; (6,1)}
The probability P of rolling a total of $7$ on the two dice is equal to the sum of the probabilities of rolling each combination.
[tex]\rm P = \dfrac{1}{21}\cdot\dfrac{6}{21}+\dfrac{2}{21}\cdot\dfrac{5}{21}+\dfrac{3}{21}\cdot\dfrac{4}{21}+\dfrac{4}{21}\cdot\dfrac{3}{21}+\dfrac{5}{21}\cdot\dfrac{2}{21}+\dfrac{6}{21}\cdot\dfrac{1}{21}\\\\=\dfrac{8}{63}[/tex]
Thus, the probability of rolling a total of 7 on the two dice is 8/63 if in the particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6 on each die are in the ratio 1:2:3:4:5:6.
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Rick went on a hike with his family in Big Bend National Park. During the hike, he saw 6 lizards, 1 scorpion, 2 foxes, 3 jackrabbits, 6 deer, and 2 snakes.
Rick has a pet snake, so he was most excited to see the snakes. What percent of the animals were snakes?
During the hike, Rick saw 20 animals and 10% of the animals were snakes.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
During the hike, he saw 6 lizards, 1 scorpion, 2 foxes, 3 jackrabbits, 6 deer, and 2 snakes.
Total number of animals = 6 + 1 + 2 + 3 + 6 + 2 = 20 animals
Percentage of animals that were snakes = (2 / 20) * 100% = 10%
During the hike, Rick saw 20 animals and 10% of the animals were snakes.
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Two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
Create an organized list showing all the possible outcomes after both spinners are spun. Use R to represent red, G to represent green, W to represent white, and B to represent blue. Explain how to find the total number of outcomes from the list.
The total number of outcomes is 16 if the two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
What are permutation and combination?A permutation can be defined as the number of ways a set can be arranged, order matters, but in combination, the order does not matter.
Total number of outcomes on the first spinners = 4 (red, green, white, blue)
Total number of outcomes on the second spinners = 4 (red, green, white, blue)
Total number of outcomes = 4×4 = 16
Total outcomes:
RR RG RW RB
GR GG GW GB
WR WG WW WB
BR BG BW BB
Thus, the total number of outcomes is 16 if the two spinners are used in a game. Each spinner has four equal sections: red, green, white, and blue.
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11. Find the equation for the circle with center (−2,4) and passing through (5,−3).
Answer:
In standard form: (x+2)² + (y-4)² = 98
Use the distance formula to find radius:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
where (x1, y1), (x2, y1) are points
[tex]\rightarrow \sf d = \sqrt{(-2 - 5)^2 + (4-(-3))^2}[/tex]
[tex]\rightarrow \sf d = \sqrt{(-7)^2 + (7)^2}[/tex]
[tex]\rightarrow \sf d = 7\sqrt{2}[/tex]
Equation of circle:
(x-h)² + (y-k)² = r²(x-(-2))² + (y-4)² = (7√2)²(x+2)² + (y-4)² = (7√2)²(x+2)² + (y-4)² = 98The number of 9th graders attending the
high school in 2014 is expected to be 20%
greater than the 2012 total. How many 9th
graders are expected to be at the high school
in 2014?
Answer:
432 9th grade a students
Step-by-step explanation:
so In 2012 there the percentage was 11th grade 11% and 12th grade 12% and 9th grade 30% and 10th grade 47%
total is 1200
in 2014 their is 1.2*1200 students as that is adding on 20%
which is 1440
so then do 0.3*1440=432 9th grade a students as that give your 30%
216−−−√3 radical?? a little lost (Lol)
[tex]\sqrt[n]{3}[/tex] is 216−−−√3 radical: Yes because of the √
Meaning of RadicalA radical in mathematics can be defined as the square root of a number. It can also be said to be the opposite of exponent.
The symbol of a radical is √ also known as the square root.
Radicals are really important in mathematics as they help us find the nth term of any number.
We can conclude by saying that 216−−−√3 is a radical, because the radical sign is carried by 3.
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You must really like math to want to answer this ngl
Answer:
a) 2/10
b) 3/20
c) option 2
Step-by-step explanation:
On a number line, the directed line segment from q to s has endpoints q at –14 and s at 2. point r partitions the directed line segment from q to s in a 3:5 ratio. which expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r? (startfraction 3 over 3 5 endfraction) (2 minus (negative 14)) (negative 14) (startfraction 3 over 3 5 endfraction) (negative 14 minus 2) 2 (startfraction 3 over 3 5 endfraction) (2 minus 14) 14 startfraction 3 over 3 5 endfraction (negative 14 minus 2) minus 2
The mathematical expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r is:
" (startfraction 3 over 3 5 endfraction) (2 minus (negative 14)) (negative 14)" (Option A)
What is a mathematical expression?A mathematical expression is a statement that contains numbers, variables, functions, etc that are related to one another in a very logical way.
It can also be defined as a mathematical phrase that comprises:
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Answer:
A
Step-by-step explanation:
Write inequalities to represent the situations below.
1.
At the airport, each piece of luggage to be checked in must not weigh more than 40 pounds.
Use w to represent the weight (in ponds) of a piece of luggage that can be checked in.
2. The distance to the nearest exit door is at most 200 ft.
Use d to represent the distance (in feet) to the nearest exit door
In a pet store, the small fishbowl holds up to 2 2/5 gallons
of water. the large fishbowl holds up to 2 1/3 times as
much water as the small fishbowl.
eloise draws this model to represent the number of
gallons of water the large fishbowl will hold.
how many gallons of water does the large fishbowl
hold?
enter your answer as a mixed number in simplest form
by filling in the boxes.
The large fishbowl hold 5.6 gallons of water. The volume of the large. fishbowl is denoted by y in the given problem.
What is volume?The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
The volume of the small fishbowl is x
The volume of the large fishbowl is y
From the problem, the large fishbowl holds up to [tex]\rm 2\frac{1}{3}[/tex] times as much water as the small fishbowl.
[tex]\rm y = 2\frac{1}{3} x\\\\\ x= 2\frac{2}{5} =2.4\\\\ y= 2.333\times 2.4 \\\\\ y=5.6 \ gallon[/tex]
Hence, the large fishbowl hold 5.6 gallons of water.
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proportional relationship between 4y and 2x??
Answer:
This is proportional since rearranging it would get x/y = 2, which is an example of direct proportionality.
Step-by-step explanation:
Type the correct answer in the box. polygon abcde is reflected across the x-axis to form polygon a′b′c′d′e′. then polygon a′b′c′d′e′ is dilated by a scale factor of 0.5 about d′ to form polygon lmnop. vertices a and b correspond to l and m, respectively. if the length of is 2.20 units, the length of is units. write your answer as a decimal number to two decimal places.
Based on the calculations, the length of LM is equal to 1.10 units.
Given the following data:
Scale factor = 0.5.
Length of AB = 2.20 units.
The types of transformation.In Mathematics, there are different types of transformation and these include the following:
ReflectionRotationTranslationDilationHow to determine the length of LM?Since polygon A'B'C'D'E' is dilated by using a scale factor of 0.5 about D', so as to form polygon LMNOP. Thus, the length of LM is given by:
LM = A'B' × scale factor
LM = 2.20 × 0.5
LM = 1.10 units.
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The square below represents one whole.
What percent is represented by the shaded area?
Answer:
0.85.Step-by-step explanation:
We know that:
this grid is 1 whole.We don't know:
how much is shaded in.Let's count up by tenths:
0.10.20.30.40.50.60.70.8It suddenly stops at 0.8.
Let's count up by hundredths:
0.810.820.830.840.85It stops at 0.85.
0.85 is your answer.
what is the surface area
Which expressions are equivalent to the given expression?
√80
80²
☐ 4√10
160²
8√5
4√5
Answer:
4 root 5
Step-by-step explanation:
√80 = √ 16 X √5
√16 = 4
so 4√5
Which graph shows a dilation?
The graph that shows a dilation would show the reduction or enlargement of the original figure (see attachment).
What is a Dilation?Dilation is defined as a form of transformation where a figure is enlarged or reduced by scale factor. Simply put, a dilation is a process of resizing an original image.
The image containing the referenced graphs is missing. However, the image below shows what a dilation is.
Thus, the graph that shows a dilation would show an enlargement or reduction.
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Which could be the dimensions of a rectangular prism whose surface area is less than 160 square feet? Select two
options.
8 feet by 4 feet by 3 feet
17 feet by 6 feet by 4 feet
3 feet by 7 feet by 8 feet
3 feet by 6 feet by 7 feet
3 feet by 5 feet by 7 feet
Answer:
Option 3 and 4 are the most reasonable answers
Step-by-step explanation:
In the figure below lines p and q are are parallel. What do you notice?
35 points
Answer:
∠1 and ∠8 are alternate exterior angles which is when two parallel lines are intersected by a transversal, then the exterior angles formed on either side of the transversal are (their measures are) equal.
Simple terms: 1 and 8 are the same angle
A rectangle and an equilateral triangle have the same perimeter
The perimeter of the rectangle is 2x+2(3x-1) inches
The perimeter of the equilateral triangle is 3(x+1) inches
Solve the value of x and the perimeter of each figure
Answer:
A rectangle and an equilateral triangle have the same perimeter
The perimeter of the rectangle is 2x+2(3x-1) inches
The perimeter of the equilateral triangle is 3(x+1) inches
Solve the value of x and the perimeter of each figure
Which equation matches the graph?
y=-2x
Step-by-step explanation:
it can't be y=2x and y=-½ because it passes by the opposite side of the given graph
..................................
Answer:
..................................
Step-by-step explanation:
Answer:
..................................
Step-by-step explanation:
No clear question so the answer is the question
Using polynomial long division how can you determine if x-3 is a factor of x^3+4x^2-12x+24
When the remainder of the polynomial is 0, it is a factor and when it is not zero, then it is not a factor.
What is a polynomial?A polynomial is an algebraic equation with at least the power of its being 2.
When the power of the variable is 2, it is called a quadratic equation.
Analysis:
If [tex]x^{3}[/tex] + 4[tex]x^{2}[/tex] -12x + 24 is divided by x -3, quotient is [tex]x^{2}[/tex]
remainder 7[tex]x^{2}[/tex]-12x+24
7[tex]x^{2}[/tex]-12x+24 divided by x-3, quotient is 7x, remainder 10x + 24
10x+24 divided by x-3, quotient is 10, remainder is 54
In conclusion, since it has a non zero remainder, then x - 3 is not a factor of the polynomial.
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find the perimeter of the figure below, in centimeters
Answer:
73
Step-by-step explanation:
(7.7 * 2) + (9.6 * 6) = 74
A 90% confidence interval is centered at a _____ and is 90% sure to contain the _______.
a) statistic, variable
b) parameter, statistic
c) statistic, parameter
d) parameter, variable
e) variable, parameter
Answer:
See below
Step-by-step explanation:
A 90% confidence interval is centered at a parameter and is 90% sure to contain the statistic.
When you are running a statistical test, you can create a confidence interval centered at the appropriate parameter (such as the mean) to see if the statistic stated in your null hypothesis is true if it's contained in the interval. Whatever the confidence level is determines how wide the interval will be, and as such, will determine how likely the interval will catch the statistic in question.
PLEASE HELPPPPPP TYSMMMM
Answer:
292<298xj=158
Hope this helps!
(6ƒ² − 9ƒ + 10) − (− 2ƒ² − ƒ+3)
Answer:
Step-by-step explanation:
6f^2 - 9f + 10 + 2f^2 + f - 3
8f^2 - 8f + 7
What is 3.9047 rounded to the nearest thousandth?
Answer: 3.905 rounded
Step-by-step explanation: The thousandth in this number is 4.
Round it up since when its 5 or more you add 1 more/raise the score
The answer is 3.905
Rezultatul calculului 22 grade 45 minute+27 grade 35 minute este egal cu
Answer:
49 grade 80 minutes
Step-by-step explanation:
Zora owns an online fashion boutique. She launched a promotion where followers of her social media account who tag a friend are entered into a giveaway. The linear relationship between the hours since launching the promotion and her total number of followers on social media is shown on the graph below. a. Find the rate of change and explain its meaning. mt
An equation is formed of two equal expressions. The equation that can be used to represent the graph is y=50x+300.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
A.) The rate of change, in this case, signifies the number of followers Zora is gaining per hour. It can be found using any two coordinates of the line.
(x₁ , y₁) = (0,300) = coordinate of point 1,
(x₂ , y₂) = (2,400) = coordinate of point 2,
Now, the rate of change or the slope will be equal to,
[tex]m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{400-300}{2-0} = 50[/tex]
Hence, the rate at which Zora will gain followers is 50 followers/hour.
B.) The y-intercept is the value of y when the value of x is 0. Therefore, the y-intercept of the function is 300.
The y-intercept of the graph is 300, which means at the very initial stage Zora will have 300 followers.
C.) The graph is represented by a line, and the general equation of a line is represented by y=mx+c. To know the value of the constant c, substitute the value of the slope and any coordinate in the equation.
[tex]y=mx+c\\300=50(0)+c\\c=300[/tex]
Hence, the equation that can be used to represent the graph is y=50x+300.
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Solve the equation. - x^2 + 5x + 9 = 0
Answer:
x(1,2) = -5 ± √61) / (-2)
Step-by-step explanation:
The ABC formula of quadratic equation states
x(1,2) = (-b ± √b^2 - 4ac) / 2a
-x^2 + 5x + 9 = 0
a = -1
b = 5
c = 9
Thus x(1,2) = (-b ± √b^2 - 4ac) / 2a
= (-5 ± √(-5)^2 - 4*(-1)*9) / 2*(-1)
= (-5 ± √25+36) / (-2)
= (-5 ± √61) / (-2)
