The integer representing the entrance of the cave is 14.
What is integer?An integer is a whole number from the set of negative, non-negative, and positive numbers. An integer is a number with no decimal or fractional part, and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes: Positive Numbers: A number is positive if it is greater than zero. or we can say an integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z o
Given that, The entrance of a cave is at an elevation of 14 meters. the lowest part of the cave is at an elevation of -86 meters.
We know that, the integer numbers or simply integers are sets of numerical signs that contain the natural numbers (positive numbers), the zero number "0" and the opposite numbers corresponding to the negative numbers of the natural numbers. The integer numbers have no decimal part, are not fractional, nor have imaginary part.
The entrance is at 14 meter, that means the entrance is represented by the integer 14.
Hence, The integer representing the entrance of the cave is 14.
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What is the vertex of â ABC?
The vertex of angle ABC is equal to point B.
Step by Step explanation :
Given angle is represented by ∠ABC
Angle is representation of two rays meeting at the same point.Initial point of both the rays is same known as vertex of the angle.In the given angle ABC , two different rays are BA and ray BC.Initial point of ray BA is B and initial point of ray BC is B.Ray BA and BC meet at point B.Initial point of ray BA and BC is point B.Point 'B' is known as the vertex of angle ABC.Therefore, the vertex of the given angle ABC is given point B.
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f(x)=-3x+5 find f(-2)
Answer:
f(-2) = 11
Step-by-step explanation:
f(-2) = -3 ( -2 ) + 5
f(-2) = 6 + 5
f(-2) = 11
Given that 7 x − 3 y = 23 Find x when y = − 2 Give your answer as an improper fraction in its simplest form.
for what value of x is the equation true 10x-2 (x + 6) =52
A x=5
B =5 3/4
C x=7 1/9
D =8
Answer:
The answer should be D.8
Three times the larger of two consecutive even integers is ten more than the smaller. Find the numbers
Answer:
The numbers are 2 and 4---------------------------
Let the integers be x and y.
Set equations:
y = x + 2 (consecutive even numbers are 2 apart)3y = x + 10Substitute the value of y into the second equation:
3(x + 2) = x + 103x + 6 = x + 103x - x = 10 - 62x = 4x = 2Find y:
y = 2 + 2 y = 4What number completes the prime factorization of 300?
2•2•3•5•___
Answer:
2 × 2 × 3 × 5 × 5 or 2² × 3 × 5²
Step-by-step explanation:
300
= 2 × 150
= 2 × 2 × 75
= 2 × 2 × 5 × 15
= 2 × 2 × 3 × 5 × 5
= 2² × 3 × 5²
The picture shows angles A and B. Explain why sin(B) = sin(A) and why cos(B) = -cos(A).
Answer:
Step-by-step explanation:
A = 45 degrees
B = 225 degrees
sin(225) = -√2/2
sin(45) = √2/2
-sin(45) = -√2/2
cos(225) = -√2/2
cos(45) = √2/2
-cos(45) = -√2/2
Al’ garden i 18 feet long and 30 feet wide. He want to put fence pot the ame ditance apart along all ide of the garden. What i the greatet ditance apart that Alcan place the fence pot? (Show your work)
6 feet is the greatest distance apart by using the greatest common factor that Al can place the fence post.
What is the greatest common factor?The greatest common factor (GCF) of a set of numbers is the largest factor that all of the numbers share.
Given:
The length of the garden is 18 feet.
The width of the garden is 30 feet.
We need to find the greatest common factor between 18 and 30. These numbers can be expressed as follows (using multiplication of prime numbers).
18 = 2*3*3
30 = 2*3*5
2*3 = 6 appears in both cases and is the greatest common factor.
Therefore, 6 feet is the greatest distance apart that Al can place the fence post
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In which coordinate of the point which divides the join of 1/7 and 4/3 in the ratio 2 3?
The coordinates of the point dividing the join of given points will be equal to (1, 3).
If we need to find the coordinates of a point P(x, y) dividing the join of points (x₁, y₁) and (x₂, y₂) in the ratio m:n then the formula is expressed as
P(x, y) = [(mx₂ + nx₁/m + n), (my₂ + ny₁/m + n)]
We have the values as m:n = 2:3 and
(x₁, y₁) = (-1, 7) and (x₂, y₂) = (4, -3)
On using the above formula we get
P(x, y) = [2(4) + 3(-1)/2 + 3, 2(-3) + 3(7)/2 + 3]
P(x, y) = [(8 - 3)/5, (-6 + 21)/5]
P(x, y) = (1, 3) which is the required coordinate.
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Complete Question:
Find the coordinates of the point which divides the join of (-1, 7) and (4, - 3) in the ratio 2 : 3.
Shelby is walking through her favorite store and sees a shirt she likes being sold for $80.00. She then notices the store is having a 45% off sale on all items. Excited to purchase the shirt, she grabs it and goes to the cash register. As she’s taking out her wallet, she finds a coupon for 25% off (that is applied after the store’s sale). What is the final price of the shirt that Shelby pays after the two discounts?
a. $9.00
b. $33.00
c. $28.00
d. $52.00
Answer:
B. $33
Step-by-step explanation:
First take off the initial 45% from 80 by multiplying it by .55
80x.55= 44
Then, take off the other 25% by multiplying the resulting 44 by .75
44x.75=33
what graph represents a liner function
Answer:
A linear function can be represented by a graph that is a straight line. The equation for a linear function is of the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). The slope of the line tells us how steep the line is, and whether it has a positive or negative slope. A positive slope means that the line is sloping upwards from left to right, while a negative slope means that the line is sloping downwards from left to right.
9w-10 help please i am so dum
Answer:
w=10/9
Step-by-step explanation:
Which choice is an equation of the line written in point-slope form?
HINT: Use the answer to help you with the next two questions. You will be using the same graph.
A: y+1=12(x−1)
B: y−1=12(x+1)
C: y−1=2(x+1)
D: y+1=2(x−1)D:
Answer: The answer is C
Step-by-step explanation: If y plus 1 is 2 then y is one which is the difference between the second number of the dots on the graph
Answer:
[tex]y-1=\frac{1}{2} (x+1)[/tex]
Step-by-step explanation:
Point slope formula:
[tex]y-y_{1} = m(x-x_{1} )[/tex]
Find the slope using
[tex]m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\m = \frac{2-1}{1--1} \\m = \frac{1}{2}[/tex]
Plug the slope and points into the point slope formula
[tex]y+1=\frac{1}{2} (x-1)[/tex]
The first side of a triangle is twice as long as the second side. The third
side is 12 inches long. The perimeter of the triangle is 36 inches. What is
the measure of the first side of the triangle?
A. 8 inches
B. 10 inches
C. 12 inches
D. 16 inches
Answer:
The measure of the first side of the triangle is 10 inches. This can be determined by using the given information to set up and solve a system of equations. We are given that the first side is twice as long as the second side, and that the third side is 12 inches long. Let's call the length of the first side x and the length of the second side y. We can then set up the following system of equations:
x = 2y
12 = x + y
We can then solve this system of equations by substituting the first equation into the second equation, which gives us:
12 = 2y + y
We can then solve for y by subtracting 2y from both sides of the equation and dividing both sides by 2, which gives us:
y = 4
We can then substitute this value of y back into the first equation to solve for x, which gives us:
x = 2 * 4
x = 8
Therefore, the measure of the first side of the triangle is 10 inches. This can be verified by calculating the perimeter of the triangle, which should be equal to 36 inches. When we do this, we get:
x + y + 12 = 10 + 4 + 12 = 36
Which confirms that the measure of the first side of the triangle is 10 inches.
Step-by-step explanation:
pls help me this is due now and can you explain how to do it
Answer:
D) -5
Step-by-step explanation:
-5 x -5 x -5= -125
Cube root means u multiply a number three times. Since it is negative, you’ll have to multiply with a negative number because if you multiply with a negative number 3 times youll get a negative number. A and C are a result of addition or square root.
Hope that was clear. Ask me any other questions to clarify!
Answer:
D. -5
Step-by-step explanation:
∛-125
= [tex](-125)^{\frac{1}{3} }[/tex]
= [tex]((-5)^{3} )^{\frac{1}{3} }[/tex]
[tex](a^{b} )^{c} = a^{b*c}[/tex]
= -5
What is the probability that a person chosen at random from this group has brown or green eyes?.
For the given table of different eyed colour people , the probability that a person chosen at random from this group has brown or green eyes is 0.6036..
We have given a table lists eye colour for a random sample of people as seen above.
Total number of people or possible outcomes
= 222
Total number of people have blue eye colour
= 38
Total number of people have green eye colour
= 13
total number of people have Amber eye colour
= 22
Total number of people have Hazel eye colour
= 28
Total number of people have Brown eye colour
= 121
A person chosen at random from this group.
Probability that the selected person has brown eye Colour , P(B)
= total brown eyed persons /total persons
=> P(B) = 121/222
Probability that the selected person has gren eye Colour , P(G) = total green eyed person/total persons
=> P(G) = 13/222
Now, probability that a person chosen at random from this group has brown or green eyes ,
P(G or B ) = P(G) + P(B)
= 13/222 + 121/222
= 134/222 = 0.6036
Hence, the required probability is 0.6036..
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Complete question:
The above-mentioned table lists the eye colors of a random sample of people. If a person is chosen at random, What is the probability that a person chosen at random from this group has brown or green eyes?
A group of 10 science club students is on a field trip. That number of students represent 20% of the total number of students in the science club. What is the total number of students in the science club?
A 20
B 30
C 50
D 80
The total number of students in the science club will be 50. Then the correct option is C.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
A gathering of 10 science club understudies is on a field trip. That number of understudies addresses 20% of the complete number of understudies in the science club.
The total number of students in the science club will be given as,
⇒ 10 / 0.20
⇒ 50
The total number of students in the science club will be 50. Then the correct option is C.
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Answer:
Step-by-step explanation:
When we add a whole number to another whole number we always get a whole number True or false?
True. When we add a whole number to another whole number, the result is always a whole number.
This is called the closure property of addition.
A whole number is a set of all positive integers from 0 to infinity. Also, these numbers in their simplest fractional form will have a denominator of 1. This means no numbers after decimal point.
Example 1 If we add 34 and 67
34 + 67
= 101
Hence 101 is a whole number.
Example 2- If we add 54 and 450
54 + 450
= 504
From the definition, we can say that 504 is a whole number.
This is the closure property.
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Find the Value of x and HE in the image below
Answer:
HE = 6
x = 2
Step-by-step explanation:
You found the right answer for what x was so the next step is to solve for HE using the expression they gave:
HE = 3x
HE = 3(2)
HE = 6
I need's da help I can get
Answer: c
Step-by-step explanation: 18/8=2.25
What is the slope of the line passing through 3 8 and (- 1 0?
The slope of the line passing through (3, 8) and (-1, 0) will be equal to 2.
Slope of the line is needed for the equation of the line and If we have two points (x₁, y₁) and (x₂, y₂) and we need the slope then the formula of finding the slope between these points is expressed as
m = (y₂ - y₁)/(x₂ - x₁)
where m is the slope between the points, y₂ - y₁ is difference between the y coordinates and x₂ - x₁ is the difference between the x coordinates.
Now the points given are (3, 8) and (1, 0), so the difference between the coordinates is expressed as
y₂ - y₁ = 0 - 8
y₂ - y₁ = -8
and
x₂ - x₁ = 1 - 3
x₂ - x₁ = -4
Now the slope will be equal to
m = -8/-4
m = 2
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solve 2(x+3)=x-4
solve 4(5x-2)=2(9x+3)
Answer:
2(x+3)=x-4 x = -10
4(5x-2)=2(9x+3) x = 7
Step-by-step explanation:
2x+6=x-4
Subtract 6 from both sides
2x=x-10
Subtract "x" from both sides
x=-10
20x-8=18x+6
You want to isolate the variable by dividing each side by factors that don't contain the variable
x=7
Answer: X=-10 and X=7
Step-by-step explanation: 2(x+3)=x-4 Distribute 2x+6=x-4 Subtract both sides by 6 SImplify x=-10
4(5x-2)=2(9x+3) Distribute 20x-8=2(9x+3) Add both sides by 8 x=7
Which of the correlation values represent a perfect linear relationship between x and y?
a. 0.5
b. 1
c. 100
d. -1
e. 0
The correlation values which represents a perfect linear relationship between x and y are:
b. 1 and d. -1
A perfect linear relationship is indicated by a correlation with a magnitude of 1. The sign of the correlation coefficient is the sign of the slope of the line describing the relationship. It may be positive or negative.
The appropriate choices are :
b. -1
d. 1
A perfect linear relationship (r=-1 or r=1) states that a linear function of one variable can perfectly describe the other.
A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.
Hence we get the required answer.
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The management of the local zoo wants to know if all of their animal exhibits are equally popular. If there is significant
evidence that some of the exhibits are not being visited frequently enough, then changes may need to take place within the
zoo. A tally of visitors is taken for each of the following animals throughout the course of a week, and the results are
contained in the following table. At a = 0.10, determine whether there is sufficient evidence to conclude that some exhibit
are less popular than others.
Number
of
visitors
Animal Exhibits at the Zoo
Elephants Lions/Tigers Giraffes Zebras Monkeys Birds Reptiles
133
172
163
165
134
155
148
Copy Data
Step 2 of 4: Calculate the expected value for the number of visitors for the lions and tigers exhibit. Enter your answer as a
fraction or a decimal rounded to three decimal places.
There is not sufficient evidence to conclude that some exhibits are less popular than others.
How to test the hypothesis?We are going to test if all the animals are equally as likely to be seen, or if some are more likely than another, hence a goodness of fit test is made, using the chi-square distribution.
The test statistic for the chi-square distribution is given as follows:
Chi-squared = sum ((O - E)²/E)
In which:
O is the observed measure.E is the expected measure.The total number of measures in this problem is given as follows:
133 + 172 + 163 + 165 + 134 + 155 + 148 = 1070.
There are seven types of animals, hence the expected value is obtained as follows:
E = 1070/7 = 152.86.
The critical value is obtained with a chi-square calculator, for a two-tailed test, with 7 - 1 = 6 df and a significance level of 0.1, hence it is of:
Chi squared = 10.64.
Hence the conclusion will be reached as follows:
Chi-squared < 10.64 -> not enough evidence to conclude that some exhibits are less popular than others.Chi-squared > 10.64 -> enough evidence to conclude that some exhibits are less popular than others.The test statistic is calculated as follows:
Chi-squared = 1/152.86 x [(133 - 152.86)² + (172 - 152.86)² + (163 - 152.86)² + (165 - 152.86)² + (134 - 152.86)² + (155 - 152.86)² + (148 - 152.86)²]
Chi-squared = 9.13.
Less than the critical value, hence there is not sufficient evidence to conclude that some exhibits are less popular than others.
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what kind of function can be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes
By using the concept of depreciation, it can be concluded that-
The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.
What is growth?
Growth is the exponential increase in the value of an asset or article or population at a certain rate over a certain period of time
EPA calculated that the air pollution should decrease by approximately 8% each year
The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.
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Complete Question
One function of the Environmental Protection Agency (EPA) is to reduce air pollution. After implementing several pollution reduction programs in a certain city, EPA calculated that the air pollution should decrease by approximately 8% each year. What kind of function could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes?
jody and jill are going on a road trip. they would like to make it 350 miles before stopping. if they keep a speed of 70 mph, how many hours will it take to reach their first stop?
It will take to reach their first stop in 5 hours 43 minutes.
How to solve word problems?
Establish a variable.Utilizing the variable, write an equation.Make the equation work.Use the variable to determine the answer if it is not the word problem's solution.Solve word puzzles on a regular basis, teach students how to solve problems, Model or visualise the issue, Make that they specify the question at hand, Take the numbers off, Select the appropriate action for the circumstance.
Speed = Distance/ time
Distance / Speed = Time
= 350 mi / 70 mph
= 5.7142 hours
= 0.7142 hours
≈ 60(0.7142)
≈ 5 hours 43 minutes
Hence, The trip takes 5 hours and 43 minutes to reach their first stop.
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an international food festival charges for admission and for each sample of food admission and 4 samples cost $8.75 admission and 9 samples cost $13.75 write a linear function rule to model the cost t for any number of samples x
Answer:
t = x +4.75
Step-by-step explanation:
You want the linear function rule relating t to x, given (x, t) = (4, 8.75) and (9, 13.75).
SlopeThe slope of the function can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (13.75 -8.75)/(9 -4) = 5.00/5 = 1.00
InterceptThe y-intercept of the function can be found from ...
b = y -mx
b = 8.75 -(1.00)(4) = 4.75
Slope-intercept equationThe slope-intercept equation is of the form ...
y = mx +b
For m=1 and b=4.75, and using t instead of y, we have ...
t = x +4.75 . . . . linear function rule
in a valid syllogism, . group of answer choices the conclusion is true. all of the others. the conclusion follows from the premises. the premises are true.
In a valid syllogism, the conclusion follows logically from the two premises.
A syllogism contains information that is compatible with the facts, it is said to make truthful assertions. A syllogism can, however, be true without being valid or valid without being true. When a syllogism's conclusion flows naturally from its premises, it is considered legitimate or logical. When a syllogism contains information that is compatible with the facts, it is said to make truthful assertions.
Here is a good categorical syllogism illustration: The majority of mammals have warm-blooded systems. Minor: Black dogs are all animals. Consequently, all black dogs have heated blood.
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Paul has 400 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answer: i believe the dimension that maximizes the area is 100 yards by 100 yards, which is 10000 square yards
Step-by-step explanation:
Gabriella is deciding between two landscaping companies for her place of business. Company A charges $30 per hour and a $225 equipment fee. Company B charges $55 per hour and a $125 equipment fee. Let AA represent the amount Company A would charge for tt hours of landscaping, and let BB represent the amount Company B would charge for tt hours of landscaping. Write an equation for each situation, in terms of t,t, and determine the number hours, t,t, that would make the cost of each company the same.
The number of hours that the cost will be the same is 4 hours.
How to illustrate the equation?From the information illustrated, Gabriella is deciding between two landscaping companies for her place of business.
Company A charges $30 per hour and a $225 equipment fee. Thus will be:
225 + 40h
Company B charges $55 per hour and a $125 equipment fee. This will be:
125 + 55h.
h = number of hours
Collate the equations
225 + 30h = 125 + 55h
Collect like terms
55h - 30h = 225 - 125
25h = 100
Divide
h = 100 / 25
h = 4
The number of hours is 4 hours
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