It is true that the set consisting of all integers between -2 and -1 is empty.
Integers are numbers that are not fraction. They are simply the whole numbers on the number line.
There are positive and negative integers.
Positive Integers are: 1, 2, 3, 4, 5, and so on
Negative Integers are: -1, -2, -3, -4, -5, and so on.
Between -2 and -1, there are no integers. Therefore, the set consisting of all the integers between them is empty.
Daniel and his mother flew fromMiami, Florida to Maine to visit family.When they left Miami, the temperaturewas 84°. When they arrived in Maine itwas -7°. What was the temperaturechange Daniel and his mother?
the temperature change will be the difference or the subtraction between bout temperatures so it will be:
[tex]84-(-7)=91º[/tex]so there are 91º of temperature difference
chance the pilot of a boeing 727 flew e plane so it took off at an angle of elevation 21 degrees. after flying one kilometer, what is the altitude (height) of the plane that chance was flying rounded to the nearest meter? (1 km= 1000 meters)
To solve the exercise, it is convenient to first draw a picture of the situation posed by the statement:
As you can see, a right triangle is formed. So to find the height at which the plane was when the pilot had flown one kilometer, you can use the trigonometric ratio sin(θ):
[tex]\sin (\theta)=\frac{\text{Opposite side}}{\text{ Hypotenuse}}[/tex]Then, in this case, you have
[tex]\begin{gathered} \sin (21\text{\degree})=\frac{\text{ Altitude}}{1000m} \\ \text{ Multiply by 1000m on both sides of the equation} \\ \sin (21\text{\degree})\cdot1000m=\frac{\text{ Altitude}}{1000m}\cdot1000m \\ \sin (21\text{\degree})\cdot1000m=\text{ Altitude} \\ 358.37m=\text{ Altitude} \\ \text{ Rounding to the nearest meter} \\ 358m=\text{ Altitude} \end{gathered}[/tex]Therefore, the altitude or height of the plane after flying one kilometer is 358 meters.
Q4 O center (-1,3), radius = 1 What is the center and radius of the circle, 2 2 r + y + 2x - 6y +9=0 - 9 center (1,-3), radius = 1 center (-1,3), radius = 9 center (1,-3), radius = 3
Step 1: Write out the formula
The equation of a circle given by
[tex](x-a)^2+(y-b)^2=r^2[/tex][tex]\begin{gathered} \text{where} \\ (a,b)\text{ is the center of the circle} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]Step 2: Write out the given equation and rewrite it in the form shown above
[tex]x^2+y^2+2x-6y+9=0[/tex][tex]\begin{gathered} x^2+2x+y^2-6y+9=0 \\ \text{ By completing the square, we have} \\ (x+1)^2-(+1)^2+(y-3)^2-(-3)^2+9=0 \\ \end{gathered}[/tex][tex]\begin{gathered} (x+1)^2+(y-3)^2-1-9+9=0 \\ (x+1)^2+(y-3)^2=1=1^2 \end{gathered}[/tex]By comparing the equation with the formula above, we have
[tex]a=-1,b=3,r=1[/tex]Therefore,
center (-1,3), radius = 1
Liam wants to find the average of the following numbers. 53, 46, 57, 52, 49 He estimates the average as 50 and then finds the average. Which describes how close Liam is to his estimate?
You find the average by adding all of the numers and then divide by the ammount of numbers that were added:
[tex]A=\frac{53+46+57+52+49}{5}\Rightarrow A=51.4[/tex]So the average is 51.4 and therefore Liam was off by 1.4 units.
Describe how the graph of y = ln (-x) relates to the graph of its parent function y = ln x.
The graph of function f(-x) can be obtained from graph of pareant funcion f(x) by refecting the graph over y-axis.
We need to obtain the graph of ln (-x) from parent function ln x, which is nothing but replace of x by -x. So graph of ln (-x) is obtained by reflection of graph of function ln (x) over y-axis.
Answer: y-axis reflection
values for relation g are given in the table. which pair is in g inverse
Given
Values for relation g
Find
Which pair is in g inverse.
Explanation
In the inverse function , it satisfies when y = f(x)
[tex]x=f^{-1}(y)[/tex]so , in the inverse of g
since g(4) = 9 , so
[tex]4=g^{-1}(9)[/tex]g(5) = 13 , so
[tex]13=g^{-1}(5)[/tex]g(3) = 5 , so
[tex]5=g^{-1}(3)[/tex]g(2) = 2 , so
[tex]2=g^{-1}(2)[/tex]so , (13 , 5) would be found in the inverse of g
Final Answer
Hence , the correct option is (13 , 5)
The volume of a large tank is 350 ft. It is 65 ft wide and 4 ft high. What is the length of the tank?
The volume of a rectangular prism can be calculated by the formula
[tex]V=l\cdot w\cdot h[/tex]in which l, w and h represent the length, width, and heght respectively.
clear the equation for l
[tex]l=\frac{V}{w\cdot h}[/tex]replace with the data given
[tex]undefined[/tex]Do not round ant intermediate computations, and round your final answers to the nearest cent
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
PART ONE;
a) Find the interest that will be owed after 78 days:
[tex]Simple\text{ Interest = }\frac{Principal\text{ x Rate x Time}}{100}[/tex][tex]Simple\text{ Interest =}\frac{15,600\text{ x 3. 6 x }\frac{78}{365}}{100}=\text{ \$ 120.01}[/tex]PART TWO:
Assume that she doesn't make any payment, the amount owed after 78 days:
[tex]\begin{gathered} Amount\text{ = Principal + Simple Interest} \\ Amount\text{ = \$15600 + \$ 120.01} \\ Amount\text{ = \$ 15,720.01} \end{gathered}[/tex]K
There are 48 runners in a race. How many ways can the runners finish first, second, and third?
There are different ways that the runners can finish first through third.
(Type a whole number.)
The number of different ways that the runners can finish first through third. is 103776
There are 48 runners in a race
The number of options for the first place is 48, as only one can be in 1st postion and there are a total of 48 persons
The number of options for the second place is 47, as the person who became first cannot be in the second position
The number of options for the third place is 46, as the person who became first and second cannot be in the third position
There are different ways that the runners can finish first through third. is
48 x 47 x 46 = 103776
Therefore, the number of different ways that the runners can finish first through third. is 103776
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5. Input Output 4 3 3 1
It is not a function because a function should assign one element in the domain to one and only one in the range.
A researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. Her data is expressed in the scatter plot and line of best fit below. What is the meaning of the yy-value on the line when x=80x=80?
The line of best fit approximates the relationship between the independent and the dependent variables. Here, the x-values give us the number of chirps per minute while the y-values give us the temperature in degrees Fahrenheit.
When x = 80, the number of chirps per minute is 80. The corresponding y is approximately 62.5 degrees Fahrenheit, which is the predicted temperature when the x-value is 80.
So, the answer is the first option: The predicted temperature in degrees Fahrenheit if the cricket has chirped 80 times.
Solve each system of equations using linear combination.1.3x +5y = 82x - 5y = 22
x = 6, y = -2
Explanations:The given system of equations is:
3x + 5y = 8..................................(1)
2x - 5y = 22................................(2)
Add equations (1) and (2) together
(3x + 5y) + (2x - 5y) = 8 + 22
3x + 2x + 5y - 5y = 30
5x = 30
x = 30/5
x = 6
Substitute x = 6 into equation (1)
3x + 5y = 8
3(6) + 5y = 8
18 + 5y = 8
5y = 8 - 18
5y = -10
y = -10/5
y = -2
The solution to the system of equations is:
x = 6, y = -2
A rectangular paperboard measuring 33 in long and 21 in wide has a semicircle cut out of it as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.)
Explanation
The question wants us to obtain the perimeter of the paperboard that remains after the semicircle has been removed
To do so, we will follow the steps below:
Step1: Find the Perimeter of the rectangle
The perimeter of a rectangle is simply the sum of all its sides
So in our case, we will have to sum sides A as given below
[tex]Perimeter\text{ of rectangle= 21 +33+33= 87 inches}[/tex]Step 2: Find the perimeter of the semi-circle
The perimeter of a semi-circle is given by:
[tex]\begin{gathered} \frac{\pi D}{2} \\ where \\ \pi=3.14 \\ D=diameter\text{ of the semicircle =21 inches} \end{gathered}[/tex]Simplifying
[tex]Perimeter\text{ of semicircle=}\frac{3.14\times21}{2}=32.97\text{ inches}[/tex]Step 3: Find the sum of the perimeters of the rectangle and semicircle
Therefore, the perimeter of the paperboard that remains after the semicircle is removed will be
[tex]\begin{gathered} perimeter\text{ }of\text{ }the\text{ }rectangle+\text{ perimeters of the semicircle =87inches + 32.97 inches} \\ perimeter\text{ }of\text{ }the\text{ }rectangle-\text{ perimeters of the semicircle =119.97 inches} \end{gathered}[/tex]Hence, the perimeter of the paperboard that remains after the semicircle is removed will be 119.97 in
solve x 9/× = x/4 what is x
can you help me with my work
1. the initial value of A is 50 and B is 25 so a is bigger so A>B
2. A hits the grond on 6.53 and B on 10.477 so A is less , so A
3. A grows to 2.5 and B to 5 so A
4. the maximum of a is 2.5 and B is 5 so A
5. the maximum height of A is 81.25 and B 150 so A>B
what is .8 divided by 40
Problem
0.8 divided 40
Solution
We can do the following:
[tex]\frac{0.8}{40}=\frac{0.8\cdot10}{40\cdot10}=\frac{8}{400}[/tex]and if we simplify we got:
[tex]\frac{8}{400}=\frac{4}{200}=\frac{2}{100}=\frac{1}{50}=0.02[/tex]find the equation of the line with slope 6 and containing the point (3,1). Write the equation in function notation
ANSWER
f(x) = 6x - 17
EXPLANATION
The equation of a line with slope m and y-intercept b is:
[tex]f(x)=mx+b[/tex]We know the slope of this line, m = 6, so we have this equation:
[tex]f(x)=6x+b[/tex]To find the y-intercept we have to replace f and x with the given point: f(3) = 1:
[tex]\begin{gathered} 1=6\cdot3+b \\ 1=18+b \\ b=1-18 \\ b=-17 \end{gathered}[/tex]The equation is:
[tex]f(x)=6x-17[/tex]According to a report from a particular university, 46% of female undergraduates take on debt. Find the probability that none of the female undergraduates have taken on debt if 9female undergraduates were selected at randomWhat probability should be found?MA PO female undergraduates take on debt)OB P(9 female undergraduates take on debt)OC P(1 female undergraduate takes on debt)OD P(2 female undergraduates take on debt)The probability that none of the female undergraduates take on debt is I(Type an integer or decimal rounded to three decimal places as needed)1}0vo(0.MorexHelp Me Solve ThisView an ExampleGet More HelpClear AllCheck Answer
For this exercise we use the probability function of the binomial distribution, also called the Bernoulli distribution function, is expressed with the formula:
[tex]P(x)=\frac{n!}{(n-x)!\cdot x!}\cdot p^x\cdot q^{n-x}[/tex]Where:
• n, = the number of trials
,• x, = the number of successes desired
,• p,= probability of getting a success
,• q, = probability of getting failure
From the exercise we can identify:
[tex]\begin{gathered} n=9 \\ x=0 \\ p=0.46 \\ q=1-p \\ q=0.54 \end{gathered}[/tex]Replacing in the equation of the binomial distribution:
[tex]\begin{gathered} P(0)=\frac{9!}{(9-0)!\cdot0!}\cdot(0.46)^0\cdot(0.54)^{9-0} \\ P(0)=0.0039 \\ P(0)=0.004 \end{gathered}[/tex]The answer is P(0 female undergraduates tak on debt)
A bag contains 6 apples and 4 bananas. If two fruits are drawn one by one with replacement, find the probability that the first one is an apple and the second one is banana.
we have
probability first one is an apple:
[tex]\frac{6}{6+4}=\frac{6}{10}[/tex]probability the second one is banana:
[tex]\frac{4}{6+4}=\frac{4}{10}[/tex]therefore, the probability that the first one is an apple and the second one is banana:
[tex]\frac{6}{10}\times\frac{4}{10}=\frac{24}{100}=\frac{6}{25}[/tex]answer: 6/25
evaluate [tex]3 {x}^{2} - 4[/tex]when x=2.
3x^2 - 4 , at 2 is = 3•2^2 - 4
. = 12 - 4 = 8
build build a machine that can automatically clean a coffee mug Bill wants the machine to be able to do an amount of work represented by the inequality x + y greater than or equal to 2 while using battery power that remains at level represented by the inequalities for x + y greater than or equal to -1 where X and Y both represent the number of minutes spent on cleaning different parts of the tank at the machine Spence 5 in three minutes on X & Y respectively does he meet those requirements?
We have to meet these restrictions:
Amount of work:
[tex]x+y\ge2[/tex]Battery power:
[tex]x+y\ge-1[/tex]If the values of x and y are x=5 and y=3, then we have to evaluate each restriction:
[tex]\begin{gathered} x+y=5+3=8\ge2\longrightarrow\text{true} \\ x+y=5+3=8>-1\longrightarrow true \end{gathered}[/tex]Answer: Yes, they meet the requirements.
please i need your help i will appreciate it
The value of c is 5/2 that satisfy the conclusions of the mean value theorem.
Given Function:
f(x) = x^2-3x+3 on interval [1,4].
The Mean Value Theorem states that for a continuous and differentiable function f(x)=x^2-3x+3 on the interval [1,4] there exists such number c from the interval [1,4] that [tex]f'(c)=\frac{f(4)-f(1)}{4-1}[/tex].
f(4) = 4^2-3*4+3
= 16-12+3
= 4+3
= 7
f(1)=1^2-3*1+3
= 1-3+3
= 1
f'(c) = 2c -3
2c-3 = 7 - 1 / 4 - 1
2c - 3 = 6/3
2c -3 = 2
2c = 5
c = 5/2
Therefore the value of c = 5/2 that satisfy the conclusions of the mean value theorem.
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Math sequence 1,2,4,7,__
Maths sequence :
1+1 = 2
2+2 =4
4+3 =7
7+4 =11
11+5 = 16
16 +6 = 22
22+7 = 29......
rule : add the answer with the next number to .
sequence is that the pattern rule.
find the slope (-10,8) (5,-3)
The slope can be calculated with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, you have the following points:
[tex]undefined[/tex]Martha drove her car east for a total of 9 hours at a constant velocity. In one-third of that time, she drove 180 kilometers. What was her velocity?
time = one third of 9 hours = 1/3 x 9 = 3 hours
Distance = 180 km
Velocity = Distance / time
Replacing:
V = 180 km/3 h = 60 km per h
Given the definitions of f(x) and g(2) below, find the value of g(f(-3))f(x) = -3x – 12g(x) = 3x2 – 2x – 14
Given data:
Itis given that
[tex]\begin{gathered} f(x)=-3x-12 \\ g(x)=3x^2-2x-14 \end{gathered}[/tex]Now to calcualte g(f(-3)) first let us calculate f(-3)
[tex]\begin{gathered} f(-3)=-3(-3)-12 \\ =9-12 \\ =-3 \end{gathered}[/tex]Now, g(f(-3)) will be
[tex]\begin{gathered} g(f(-3))=g(-3) \\ =3(-3)^2-2(-3)-14 \\ =3(9)+6-14 \\ =27-8 \\ =19 \end{gathered}[/tex]So, value of g(f(-3)) is 19.
use the distributive property to write an equivalent expression for 88 plus 55
We are asked to use the distributive property to write an equivalent expression for 88 plus 55.
Let us first understand what is distributive property?
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]The above property means that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
But we have only two numbers 88 and 55 so how are we going to apply this property?
We need to break these numbers.
Let us find out the GCF (greatest common factor) of these two numbers.
11 is the greatest common factor of numbers 88 and 55
So, we can break the numbers as
[tex]\begin{gathered} 88=11\cdot8 \\ 55=11\cdot5 \end{gathered}[/tex]Now we have three numbers so let us apply the distributive property.
[tex]\begin{gathered} a\cdot(b+c)=a\cdot b+a\cdot c \\ 11\cdot(8+5)=11\cdot8+11\cdot5 \end{gathered}[/tex]Therefore, the equivalent expression for 88 plus 55 is
[tex]88+55=11\cdot(8+5)_{}[/tex]denominator of a fraction is 2 more than the numerator . if both numerator and denominator are increased by 10 , a simplified result is 9/10. Find the original fraction. Do not simplify
Let the numerator = x
The denominator of a fraction is 2 more than the numerator
So, the denominator = x + 2
if both numerator and denominator are increased by 10, a simplified result is 9/10.
So,
[tex]\frac{x+10}{(x+2)+10}=\frac{9}{10}[/tex]Solve for x:
[tex]\begin{gathered} \frac{x+10}{x+12}=\frac{9}{10} \\ \\ 10(x+10)=9(x+12) \\ 10x+100=9x+108 \\ 10x-9x=108-100 \\ x=8 \end{gathered}[/tex]so, the original fraction will be = 8/10
So, the answer will be = 8/10
Find the angle between the vectors (-9, -8) and (-9,5). Carry your intermediate computations to at least 4 decimalplaces. Round your final answer to the nearest degree.| 。x 6 ?
The vector for (-9,-8) is,
[tex]u=-9\hat{i}-8\hat{j}[/tex]The vector for (-9,5) is,
[tex]v=-9\hat{i}+5\hat{j}[/tex]The formula for the angle between vector u and vector v is,
[tex]\cos \theta=\frac{u\cdot v}{|u\mleft\Vert v\mright|}[/tex]Determine the angle between vectors.
[tex]\begin{gathered} \cos \theta=\frac{(-9\hat{i}-8\hat{j)}\cdot(-9\hat{i}+5\hat{j})}{\sqrt[]{(-9)^2+(-8)^2}\cdot\sqrt[]{(-9)^2+(5)^2}} \\ =\frac{81-40}{\sqrt[]{145}\cdot\sqrt[]{106}} \\ =\frac{41}{\sqrt[]{15370}} \\ \theta=\cos ^{-1}(0.3307) \\ =70.688 \\ \approx71 \end{gathered}[/tex]So angle between the vector is 71 degree.
Use a net to find the surface area of the prism.25 cm3.5 cm13 cmThe surface area of the prism is (Simplify your answer.)
A rectangle prism of sides 25, 3.5 and 13 cm can be drawn as:
It will have 6 faces (4 lateral, a base and a top face)
Each face has a surface area that is the product of two of the sides. We have two faces for each pair of sides.
So if we have sides a, b and c, the surface area can be written as:
[tex]S=2(a\cdot b+a\cdot c+b\cdot c)[/tex]With the sides of our prism we can calculate the surface area as:
[tex]\begin{gathered} S=2(25\cdot3.5+25\cdot13+3.5\cdot13) \\ S=2(87.5+325+45.5) \\ S=2\cdot458 \\ S=916\operatorname{cm}^2 \end{gathered}[/tex]Answer: The surface area of the prism is 916 cm^2