Answers
The ratio table is given below:-
Oranges 3 4 8 10 12
Cost( in $) 3.75 5 10 12.5 15
What exactly is a ratio?
Fractions are frequently used to describe ratios and proportions. A ratio is shown when a fraction is stated as a:b, whereas a proportion implies that two ratios are equal. a and b can be any two numbers in this situation. The ratio and proportion are two fundamental ideas that lay the groundwork for comprehending other concepts in mathematics and science.
We use the concept of ratio and proportion in our daily lives, such as in business when dealing with money or in cooking.
As a result, the ratio defines the relationship between two values, such as a:b when b is higher than zero. For example, the 2:4 ratio is expressed as 2:4 = 1:2. And in this instance, the comment is deemed proportionate.
Now,
As given no. of oranges = 8
Cost of 8 oranges = 10
cost of 1 orange=10/8=1.25 rs/orange
then
The table will be as follow
Oranges 3 4 8 10 12
Cost( in $) 3.75 5 10 12.5 15
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Related Questions
Xx
Which equation models the rational function shown in
the graph?
2(x+2)
X-2
O f(x) =
O f(x) = x-2
x+2
2(x-2)
x+2
Of(x)=.
O f(x) = x+2
X-2
Answers
At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
From given graph we can see that
At x=2, the function in the graph is approaches to infinity.
It means function is not defined at x=2
We know that a rational function is undefined when denominator is equal to zero.
For equation 1:
f(x)= 2(x+2)/(x-2)
Equating the denominator:
x-2=0
x=2
It means function is not defined at x=2
The y-intercept is: y= -2
The function is passing through the point (1,-6).
When we substitute x=1
Hence, option 1 is true.
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Taking the earth to be the sphere of radius 6378000m, find the circumference of the equator of the earth. Give your answer in km and in terms of pi.
Answers
Answer:
12756pi km
Step-by-step explanation:
Circumference = pi * diameter
Diameter = radius * 2
kilometer = meter/1000
6378000*2= 12756000
diamter = 12756000 meters
12756000/1000 = 12756 kilometers
diameter = 12756 kilometers
12756pi km= circumference
HELPPPPPP
find each value
Answers
Answer: x=4, AB=19, ED=57
Step-by-step explanation:
Trapezoid midsegment formula: [tex]\frac{b1+b2}{2}[/tex]=Midsegment
Therefore, (4x+3+18x-15)/2=38
Multiply both sides by 2 in order to get rid of the fraction. (Multiplication property of equality)
4x+3+18x-15=76
Combine like terms.
22x-12=76
Add 12 to both sides. (Addition property of equality)
22x = 88
Solve for x
x = 4
Now, substitute x in for segment AB and ED
AB = 4(4)+3
AB= 16+3
AB= 19
ED=18(4) -15
ED=72-15
ED=57
Check your work:
(ED+AB)/2 = 38
(57+19)/2 = 38
76/2 = 38
38 = 38
Select the statement that correctly defines continuous and discrete quantitative variables. O A continuous variable has an infinite number of possible values, whereas a discrete variable always has a finite number of possible values. O A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units. O A continuous variable has a countable number of possible values, whereas a discrete variable has an uncountable number of possible values. O A continuous variable has numerical values, whereas a discrete variable serves to group items into categories.
Answers
The statement that correctly defines continuous and discrete quantitative variables is:
"A continuous variable can take on any real number value within some range, whereas a discrete variable come in countable units."
A variable is a quantity that may assume any one of a set of values.
This means that a continuous variable can take on any value within a certain range, which could be infinite, and that it can have decimal values. In contrast, a discrete variable has specific values that are separate and countable, such as integers or categories. For example, the height of individuals is a continuous variable, while the number of siblings someone has is a discrete variable.
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The cardiovascular system transports materials around the body, taking nutrients from the digestive system to the tissues, moving oxygen from the lungs to the cells, and taking wastes to the kidneys where they are filtered and excreted. What functions does the cardiovascular system share with the endoplasmic reticulum of the cell? select all that apply.
Answers
There are no shared functions between the cardiovascular system and the endoplasmic reticulum of the cell.
The endoplasmic reticulum is an organelle within cells that plays a role in protein synthesis, lipid metabolism, and other cellular processes. It does not transport materials around the body or filter wastes.
The endoplasmic reticulum is equipped with a complex network of pathways designed to meet the needs of the cell's secretory and integral membrane protein manufacturing processes. It also has adaptive responses prepared for the endoplasmic reticulum to rely on under stressful situations.
Because to the complexity and necessity of these pathways, a variety of conditions can result in a defective endoplasmic reticulum and a dysfunctional cell, which may advance disease.
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See attached image and answer questions.
Answers
The properties of the polynomial are
Degree = oddLeading coefficient = NegativeOdd multiplicity = 3Even multiplicity = 1How to determine the properties of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -5A root of multiplicity 1 at x = -2A root of multiplicity 2 at x = 1A root of multiplicity 1 at x = 4y-intercept = 2Using the above as a guide, we have the following:
Degree = sum of multiplicities
Degree = 1 + 1 + 2 + 1
Degree = 5
The leading coefficient is negative
This is so because the graph opens down
There are 3 zeros with odd multiplicities and 1 zero with even multiplicity
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V = 1/3 (3.14) (5²) X10
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{v = \dfrac{1}{3}(3.14) (5^2) \times 10}\\\\\mathsf{v = \dfrac{1}{3}(\dfrac{3.14}{1})(5\times5)(10)}\\\\\mathsf{v = \dfrac{1\times3.14}{3\times1}(25)(10)}\\\\\mathsf{v = \dfrac{3.14}{3}(25)(10)}\\\\\mathsf{v = 1.046667(25)(10)}\\\\\mathsf{v = 26.166667(10)}\\\\\mathsf{v = \dfrac{785}{3}}\\\\\mathsf{v = 261 \dfrac{2}{3}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{v = \dfrac{785}{3} \ or \ v = 261 \dfrac{2}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the surface area of the cube if s = 10?
Answers
The surface area of cube will be 600 square units.
What exactly is a cube?
A Cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges in geometry. It is also described as a regular hexahedron. You've probably seen the 3 3 Rubik's cube, which is the most prevalent example in real life and is useful for improving brain capacity. Similarly, you will come across several real-life instances, such as 6 sided dice, etc. Solid geometry is concerned with three-dimensional objects and figures with surface areas and volumes. Other solid forms include cuboid, cylinder, cone, and sphere.
Surface area of cube=6*side²
Volume of cube=side³
Now,
As Side of cube=10 units
and Surface area of cube=6*side²
=6*10*10
=600 square units.
Hence,
The surface area of cube will be 600 square units.
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Please help!
An object is dropped from the top of a tower with a height of 1170 feet. Neglecting air resistance, the height of the object at time
t seconds is given by the polynomial -16t² +1170. Find the height of the object at t=2 seconds.
The height of the object at 2 seconds is _____ feet.
Answers
The height of the object at a time of 2 seconds is given as follows:
1106 feet.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
h(t) = -16t² + 1170.
At a time of 2 seconds, the height is found replacing the lone instance of t by two, hence:
h(2) = -16(2)² + 1170
h(2) = 1106 feet.
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A researcher tested two groups (females and males) of rats on memory performance. The following scores are for the number of correct choices they made on the task:
Answers
The probability distribution does not add up to 1.0, in other words.
What is meant by probability?Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes.The study of events susceptible to probability is known as statistics. The probability is frequently stated as a ratio between the total number of outcomes in the sample space and the number of positive outcomes.This is how it is written: Number of Favorable Outcomes P(E) = Probability of an Event (Sample space).Probability can be divided into four main categories: axiomatic, axiomatic, classical, and empirical. The area of mathematics known as probability studies the likelihood that a random event will occur.The complete question is:
A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?
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Answer:
It is not accurate
Step-by-step explanation:
If the complete question is:
A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?
THEN:
To determine whether the probability distribution is accurate, we need to check two conditions:
The sum of the probabilities should be equal to 1.
All probabilities should be between 0 and 1.
Let's check these conditions:
Sum of probabilities:
p(0) + p(1) + p(2) + p(3) + p(4 or more) = 0.22 + 0.30 + 0.16 + 0.12 + 0.25 = 1.05
The sum of the probabilities is greater than 1, which violates the first condition. Therefore, this is not a valid probability distribution.
All probabilities should be between 0 and 1:
The probability of making 0, 1, 2, or 3 mistakes are all between 0 and 1, so they satisfy this condition.
However, the probability of making 4 or more mistakes is 0.25, which is a valid probability, but it implies that the probability of making 0, 1, 2, or 3 mistakes is negative, which is impossible. Therefore, this distribution does not satisfy this condition.
Since this probability distribution violates both conditions for a valid probability distribution, it is not accurate, and the researcher should revise their data.
RECAP NEED HELP STILL
Answers
Using trigonometric functions and Pythagoras' theorem, the x value of different right-angled triangles is found.
What is a right-angled triangle?
A right triangle, also known as a right-angled triangle, is a triangle with one right angle, or two perpendicular sides. The sum of the other two angles is 90 degrees.
In all of these figures, one of the angles is 90°. So we can use Pythagoras' theorem and trigonometric relations, to solve the questions.
1) Opposite side = 5
sin 27° = Opposite side/ hypotenuse
0.45 = 5/x
x = 11.11
2) Hypotenuse = 16
cos 63 = adjacent side/hypotensue
0.45 = x / 16
x = 7.2
3) Hypotenuse = 29
sin 67 = opposite side/hypotensue
0.92 = x/29
x = 26.68
4) Opposite side = 27
tan 39° = opposite side/ adjacent side = 27/x
0.81 = 27/x
x = 33.33
5) sin Q = opposite side / hypotensue = 14/50 = 7/25
sin R = opposite side / hypotensue = [tex]\sqrt{50^2 - 14^2}[/tex]/50 = 48/50 = 24/25
cos Q = PQ/ 50 = 48/50 = 24/25
cos R = PR/50 = 14/50 = 7/25
tan Q = sin Q/cos Q = 7/24
tan R = sin R/cos R = 24/7
Therefore using trigonometric functions and Pythagoras' theorem, the x value of different right-angled triangles is found.
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Consider the line 8x-5y=1
what is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line
Answers
Answer:
[tex]\frac{8}{5}[/tex] and - [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
8x - 5y = 1 ( subtract 8x from both sides )
- 5y = - 8x + 1 ( divide through by - 5 )
y = [tex]\frac{8}{5}[/tex] x - [tex]\frac{1}{5}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{8}{5}[/tex]
• Parallel lines have equal slopes
then the slope of a parallel line is m = [tex]\frac{8}{5}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{8}{5} }[/tex] = - [tex]\frac{5}{8}[/tex]
As part of a larger experiment, Dale (1992) looked at six samples of a wetland soil undergoing a simulated snowmelt. Three were randomly selected for treatment with a neutral pH snowmelt; the other three got a reduced pH snowmelt. The observed response was the number of Copepoda removed from each microcosm during the first 14 days of snowmelt Reduced pH Neutral pH 256 159 149 54 123 248 (a) [3 points Write two simple models: one model for the number of Copepoda in a neutral pH snowmelt and one model for the number of Copepoda in a reduced pH snowmel. Use mathematical notations. (b) 2 points We want to test whether the two treatments have equal average numbers of Copepoda. Write the n and the alternative hypotheses using the notations defined in the previous question (c) 5 points We want to perform a t-test. What assumptions are you making? Compute the corresponding test statistic. Give the critical value for a level of significance v = 0.05. What do you conclude? (d) 5 points) Using a randomization-based analysis, test the nul hypothesis that the two treatments have equal average numbers of Copepoda versus a two-sided alternative. Use a level of significance v = 0.05.
Answers
(a) The mathematical notations is (xₙ, yₙ)
(b) The alternative hypotheses using the notations defined in the previous question is t = (Xₙ - Yₙ) / SE
(c) The assumptions making is variances of the two populations are equal.
A hypothesis is a tentative explanation or prediction of a phenomenon, and it is essential in scientific research. In this study, we have two hypotheses:
Null Hypothesis: There is no significant difference in the average number of Copepod between the reduced pH and neutral pH snowmelt treatments.
Alternative Hypothesis: There is a significant difference in the average number of Copepod between the reduced pH and neutral pH snowmelt treatments.
Model:
A model is a mathematical representation of a phenomenon, and it is used to make predictions or explanations. In this experiment, we can create two simple models:
Model for Neutral pH Snowmelt:
Let Yₙ be the number of Copepod in a microcosm treated with neutral pH snowmelt. Then, Yₙ follows a normal distribution with mean µn and standard deviation σn.
Model for Reduced pH Snowmelt:
Let Yₙ be the number of Copepod in a microcosm treated with reduced pH snowmelt. Then, Yₙ follows a normal distribution with mean µr and standard deviation σr.
Assumptions:
Before conducting a t-test, we must ensure that the data satisfies the following assumptions:
The sample is a random and representative sample of the population.
The data is normally distributed.
The variances of the two populations are equal.
The test statistic for the t-test is:
t = (Xₙ - Yₙ) / SE
where Xₙ is the sample mean of neutral pH snowmelt, Yₙ is the sample mean of reduced pH snowmelt, and SE is the standard error.
Assuming a level of significance v = 0.05, we have a critical value of t = 2.306 for a two-tailed test with 4 degrees of freedom. If our calculated t-value is greater than 2.306 or less than -2.306, we reject the null hypothesis.
We can perform a randomization test as follows:
If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the average number of Cope pod between the reduced pH and neutral pH snowmelt treatments. If the p-value is greater than 0.05, we fail to reject the null hypothesis.
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Hassan finds the product of two multiples of 10 the answer is 6000 list 5 different calculations Hassan could write
Answers
The two ways of writing the number 6000 will be 10 x 600 and 100 x 60.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Multiplication is the process of determining the product of two or more numbers in mathematics.
Given that Hassan discovers that the result of two multiples of 10 is 6000.
The two ways can be calculated as:-
10 x 600 = 6000
100 x 60 = 6000
Hence, the two ways are 10 x 600 = 6000 and 100 x 60 = 6000.
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Use the formula V = Bh to calculate the volume of a cylinder that has a diameter of 6 centimeters and a height of 8 centimeters. Express your answer in terms of pi.
Answers
The volume of the cylinder is 72π cubic centimeters.
What is volume?
Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.
For solid objects, volume refers to the amount of space the object occupies in three-dimensional space.
The formula for the volume of a cylinder is:
V = Bh
where B is the area of the base of the cylinder, and h is the height of the cylinder.
In this problem, the cylinder has a diameter of 6 centimeters, which means the radius is 3 centimeters. The area of the base of the cylinder is therefore:
B = πr²
B = π(3 cm)²
B = 9π cm²
The height of the cylinder is given as 8 centimeters. Therefore, we can use the formula for the volume of a cylinder to find the volume V:
V = Bh
V = (9π cm²)(8 cm)
V = 72π cubic centimeters
Therefore, The volume of the cylinder is 72π cubic centimeters.
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NEED HELP ASAP PLEASE! The table below represents a linear function. What is the slope of the graph of this function?
Input x -2 -1 0 1 2
Output y -3 -1 1 3 5
A: 2
B: -1/2
C: 1/2
D: -2
Answers
The slope of the graph of this function is 1/2, the correct option is C.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
We are given that;
The x input and y output of function.
Input x -2 -1 0 1 2
Output y -3 -1 1 3 5
Now
m=y2-y1/x2-x1
m= 2-1/5-3
m=1/2
Also, m=-1+2/-1+3
m=1/2
Therefore, the slope of the function will be 1/2
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Luis compro un refrigerador de 7827.40 si va a pagar el 15%IVA ¿cuánto le cobraron en total?
Answers
Luego de el 15% de iva, el precio será 9001.51
¿Cuánto le cobraron en total?Si le aplicamos un incremento de un porcentaje x a un precio P, entonces el nuevo precio será:
P' = P*(1 + x)
Donde x es el porcentaje en forma decimal.
En este caso tenemos un 15% de IVA, entonces x = 0.15
Y el precio original es 7827.40
Entonces el nuevo precio será:
P' = 7827.40*(1 + 0.15) = 9001.51
Esa es la cantidad que Luis pago.
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Solve the triangle. Round to the nearest tenth.
Answers
In the given triangle, ∠F=29°, d>15 and e<15.
What exactly is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorised into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.
Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.
Equilateral Triangle - A triangle has three sides that are of the same length.
A triangle is categorised into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.
Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.
Triangle with a Right Angle - A triangle with one of its angles equal to 90°.
Now
As sum of all angles of triangle=180°
∠F+127°+24°=180°
∠F=180-151
∠F=29°
and In a triangle Largest angle is opposite to largest side and smallest angle is opposite to smallest side.
Then the sides e and d will be as following d>15 and e<15.
hence,
In the given triangle, ∠F=29°, d>15 and e<15.
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In-State tuition at UNCW is currently
$6,691. NC is raising tuition 1% each year for the next 4 years. What will be the new tuition 4 years from now?
Answers
The new tuition 4 years from now is $6962.68.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, principal =$6691, rate of interest=1% and time period=4 years.
Now, A=6691(1+1/100)⁴
=6691(1+0.01)⁴
=6691(1.01)⁴
= 6691×1.04060401
= $6962.68
Therefore, the new tuition 4 years from now is $6962.68.
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A total of 360 people voted in an election. The circle graph shows the results.
(a) How many people (number of people, not the percentage) voted for Goron?
Show your work.
(b) How many people (number of people, not the percentage) voted for Fishman
and Other? Show your work. PLEASE HELP
Answers
a. There were 126 people who voted for Goron.
b. There were 144 people who voted for Fishman.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The given circle graph shows the results.
There were 360 people who voted in the election.
According to the question, the required solution would be as:
number of people who voted for Goron = 35% of 360
15% is expressed as 15/100 in fractional form
number of people who voted for Goron = (35/100) × 360
number of people who voted for Goron = 126
number of people who voted for Fishman = 40% of 360
number of people who voted for Fishman = (40/100) × 360
number of people who voted for Fishman = 144
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The missing figure has been attached below
Find the sum of 4√5 and √5 in simplest form. Also, determine whether the result is
rational or irrational and explain your answer.
Answers
Answer:
See below
Step-by-step explanation:
[tex]4\sqrt{5}+\sqrt{5}=(4+1)\sqrt{5}=5\sqrt{5}[/tex]
This sum is irrational because [tex]\sqrt{5}[/tex] was irrational to begin with.
A company that makes golf balls needs to ship bags of balls that contain 690 balls, plus or minus 6 balls. Write an absolute value inequality that expresses the acceptable number of balls in each bag.
Answers
A recent conference had 850 people in attendance. In one exhibit room of 60 people, there were 46 teachers and 14 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 652 principals in attendance.
There were about 453 principals in attendance.
There were about 259 principals in attendance.
There were about 198 principals in attendance.
Answers
The predicted number of principals in attendance at the conference can be 161
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
A recent conference had 850 people in attendance.
In one exhibit room of 60 people, there were 46 teachers and 14 principals.
The predicated number of principals = ?
The ratio of teachers to principals = 60/14
= 30/7
In the same ratio there will be total teachers and principals:
Suppose, the number of teachers = x
the number of principals = y
x + y = 850
x/y = 30/7
x = (30/7)y
(30/7)y + y = 850
37y = 850 x 7
y = 161 (approx)
Hence, the number of principals cab be 161
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Answer:
D
Step-by-step explanation:
There were about 198 principals in attendance. EZ
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:15n + 3 = 153
Step-by-step explanation:
15n + 3 = 153
product of 15 and a number n is 15n, and 3 more gets the plus 3, and it said all of this is 153
n=10 also as subtract 3 both sides then get 15n=150 get n by itself by dividing both sides by 15 and get n=10
In Iceland, the temperature drops when the sun goes down. The temperature at 5:00 is 5°C. By 9:00, the temperature had dropped 24°. If the temperature dropped at a constant rate, how much did it drop per hour?
Answers
If the temperature dropped at a constant rate, it would have dropped 4°C per hour. This can be calculated by taking the difference in temperature (24°C) and dividing it by the number of hours that passed (4 hours).
Please help I am not sure how to solve this
Answers
m∠K = 59.09°. This can be solved by using the concept of SAS theorem.
What is SAS theorem?Triangles are congruent if their two sides and included angles are equivalent to those of another triangle's two sides and included angle. The SAS Theorem states that two triangles are congruent if their included angle and two of their sides are the same.
Here, ∠B = m∠K (consider it)
sin B /b = Sin A /a
sin B / 15 = sin 31° / 9
sin B / 15 = 0.5150 / 9
sin B / 15 = 0.057
sin B = 0.858
B = 59.09°
Thus, m∠K = 59.09°
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pls help with this
Find the length of side x in simplest radical form with a rational denominator.
Answers
The length of x is 6 in the given triangle.
What is Trigonometry?The branch of Mathematics which studies relationships between side lengths and angles of triangles.
We have to find the value of x in the given triangle.
We know that tan theta is the ratio of opposite side by adjacent side.
The opposite side is x and the adjacent side has √12
tan60=x/√12
√3=x/√12
x=√12√3
x=√36
x=6
Hence, the length of x is 6.
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a. Will he be able to make a right triangle with his fence? Why or why not?
Answers
Joel be not able to make a right triangle with his fence because the given dimensions are not satisfying for Pythagoras theorem.
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Dimensions of triangle he has to use for fencing are
15 feet, 8 feet, and 20 feet.
For making it a right triangle it must satisfy the "Pythagoras theorem" which states that
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
H²=B²+P²
20²=15²+18²
400=225+64
400≠289
No, it will not be able to make a right triangle.
Hence, Joel will be not able to make a right triangle with his fence because the given dimensions are not satisfying for pythagoras theorem.
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The complete question is given below:
Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 15 feet, 8 feet, and 20 feet long.
1. Will he be able to make a right triangle out of his fence? Why or why not?
Population increase in India India had one billion people in 2001. Its growth rate was 1.8% per year. By how many people did the population increase the first year?
Answers
The population increased by 18 million at the end of one year at the rate of 1.8%.
What is percentage?The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. Alternatively put, it is the relationship between a component and a whole in which the value of "whole" is always assumed to be 100.
For instance, if a student receives 15 out of 50 in math, one can determine the relevant percentage by expressing "marks earned" as a fraction of "total marks" and multiplying the result by 100. i.e., the percentage of marks is equal to 15 / 50 100, or 30%.
Given that, population of India is one billion.
The rate of increase is 1.8%.
After one year the population will be:
P = (1000000000)(1.8/100)
P = 18000000
Hence, the population increased by 18 million at the end of one year at the rate of 1.8%.
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Graph the linear inequality.
x < 2
