Since the denominator of the expression (1 + 0.1t) cannot be zero, the domain of the model is between t = 0 and t = -10.
How Can I Determine an Equation's Domain and Range?In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).
(b) We must assess the model at t = 0 in order to determine the starting number of elk in the herd:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(0))/(1 + 0.1(0))
P = 10/1
P = 10
(c) We can easily enter the relevant values of t into the model to determine the populations of elk after 25, 59, and 113 years, then round the results to the nearest integer.
When t = 25:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(25))/(1 + 0.1(25))
P ≈ 47
When t = 59:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(59))/(1 + 0.1(59))
P ≈ 189
When t = 113:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(113))/(1 + 0.1(113))
P ≈ 458
(d) We can use the expression's limit as t approaches infinity to determine the expected population limit:
lim P as t → ∞ = lim (10 + 3.3t)/(1 + 0.1t) as t → ∞
Using L'Hopital's rule, we can find that the limit is equal to:
lim P as t → ∞ = lim 3.3/0.1 as t → ∞
lim P as t → ∞ = 33
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- TRAIN The table shows the number of riders on the train each day for
two weeks. Compare and contrast the measures of variation for
both weeks.
Number of Riders on the Train
Week 1
Day
Monday
Tuesday
Wednesday
Thursday
Friday
72
84
78
67
86
se 1 Chapter 11 Statistical Measures
Week 2
79
86
75
49
137
Answer:
8
Step-by-step explanation:
Number of Riders on the Train
Week 1
Day
Monday
Tuesday
Wednesday
Thursd
PLEASEEE HELP URGENT
The scale factor between the original and resulting points is equal to 4 / 3.
How to derive the scale factor
In this problem we find a representation of a quadrilateral and its image depicted in Cartesian plane. According to the statement, the coordinates of the original and resulting points are, respectively:
B(x, y) = (- 3, 6), B'(x, y) = (- 4, 8)
Then, the scale factor can be found by means of the following formula:
B'(x, y) = k · B(x, y)
(- 4, 8) = (- 3 · k, 6 · k)
k = 4 / 3
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place the four problem-solving steps in order
Since the sum of a triangle's internal angles is always 180 degrees, x has a value of 40 degrees.
what is triangle ?The polygonal shape of a triangle has three edges and three angles. It is one of the most fundamental and significant geometric shapes and is utilised in a wide range of mathematical, scientific, and engineering fields. The edges and angles of a triangle can be used to classify it in various ways. Triangles can be categorised in one way by their sides: Three equal sides make up an equilateral triangle. Two of the edges of an isosceles triangle are equal. Three of the edges of a scalene triangle are unequal.
given
The property of angles in a triangle, which says that the sum of a triangle's interior angles is always 180 degrees, can be used to determine the value of x in the given figure.
Triangle ABC consists of:
∠A + ∠B + ∠C = 180
Since we know that A = 50 degrees and B = 90 degrees, we can use these numbers as a substitute:
50 + 90 + ∠C = 180
When we simplify the solution, we obtain:
140 + ∠C = 180
140 from both sides is subtracted, giving us:
∠C = 40
Since the sum of a triangle's internal angles is always 180 degrees, x has a value of 40 degrees.
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89.600-47.131 How to regroup and show my work
By using all steps below we can regroup the 89.600 - 47.131 = 42.469.
What is the tenth place?The first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredth place. The remaining digits continue to fill in the place values until there are no digits left.
To regroup and show your work for the subtraction problem 89.600 - 47.131, you can line up the numbers vertically with the decimal points aligned, like this:
89.600 - 47.131 =
Start by subtracting the one's place (0 - 1). Since 0 is less than 1, you need to borrow 1 from the tens place, which becomes 8 - 1 = 7.
The one place becomes 10 + 0 - 1 = 9.
89.600 - 47.131 = 2.469
Next, subtract the tenth place (0 - 3). Since 0 is less than 3, you need to borrow 1 from the one place, which becomes 9 - 1 = 8.
The tenth place becomes 10 + 0 - 3 = 7.
89.600 - 47.131 = 42.469
Finally, subtract the hundredth place (9 - 1), which gives 8.
89.600 - 47.131 = 42.469
Therefore, By using all the above steps we can regroup the 89.600 - 47.131 = 42.469.
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Find the value of x. If necessary, round your answer to the nearest tenth
The value of x in the chord is 2.8 units
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The circle and the chords
Represent the radius of the circle with r
Next, we calculate the radius using each chord using the Pythagoras theorem
Using the above as a guide, we have the following:
r² = x² + (38/2)²
r² = 12² + (30/2)²
By substitution, we have
x² + (38/2)² = 12² + (30/2)²
So, we have
x² = -(38/2)² + 12² + (30/2)²
Evaluate
x² = 8
Take the square root of both sides
x = 2.8
Hence, the value of x is 2.8 units
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The record for the most amount of rain in the shortest period of time in the united states was 12 inches in 42 minutes. How much rain fell in 15 minutes?
SHOW YOUR WORK AND HOW YOU GOT THE ANSWER!!!!
We can say that approximately 4.29 inches of rain fell in 15 minutes.
We can apply a proportion to determine the amount of rain that fell in 15 minutes.
We can calculate the proportion because we know that 12 inches of rain fell in 42 minutes:
x inches in 15 minutes equals 12 inches in 42 minutes.
where x is how much rain fell in 15 minutes.
We can cross-multiply and simplify to find x's value:
42 minutes equals 12 inches times 15 minutes (x inches)
180 = 42x
x = 180 / 42
x = 4.2857...
We may estimate that 4.29 inches of rain, rounded to the nearest hundredth, fell in 15 minutes.
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Can you pls solve? Thanks
Answer:
[tex](r \;\circ\;q)(4) = \boxed{5}\\\\(q \;\circ\;r)(4) = \boxed{13}\\[/tex]
Step-by-step explanation:
We have the following functions
[tex]q(x) = x^2+4\\\\and\\\\r(x) = \sqrt{x+5}\\\\[/tex]
1. To find
[tex](r \;\circ \;q)(4) = r(\;q(4)\;)[/tex]
First find
[tex]q(4) = 4^2 + 4 = 16 + 4 = 20[/tex]
Substitute this value for x in r(x)
[tex]r(20) = \sqrt{20 + 5} = \sqrt{25} = 5[/tex]
So
[tex]\bold{(r \;\circ \;q)(4) = 5}[/tex]
2. To find
[tex](q \;\circ\;r)(4) = q(\;r(4)\;)[/tex]
First find
[tex]r(4) = \sqrt{4 + 5} = \sqrt{9} = 3\\\\[/tex]
Substitute this value for x in q(x)
[tex]q(3) = 3^2 + 4 = 9 + 4 = 13\\\\\bold{(q \;\circ\;r)(4) = 13}[/tex]
The compositions of functions are:
(r o q)(4) = 5(q o r)(4) = 13How to find the compositions of the functions?Here we have the two functions:
q(x) = x² + 4
r(x)= √(x + 5)
We want to find the two compositions:
(r o q)(4) = r(q(4))
First let's find:
q(4) = 4² + 4 = 16 + 4 = 20
Then:
r(q(4)) = r(20) = √(20 + 5) = 5
And the other composition is:
(q o r)(4) = q(r(4))
First, r(4) = √(4 + 5) = 3
Then:
q(r(4)) = q(3) = 3² + 4 = 9 + 4 = 13
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elsa made 20,000 in taxable income last year. Suppose the income tax rate is 10% for the first 9,000 plus 16% for the amount over 9,000
Answer:
Elsa's income tax for last year was 2,660 dollars.
Step-by-step explanation:
01
c. Is it possible to rearrange the locations of the
4 plates in the original figure so that (1) their
distance from the center of the table does not
change, (2) their centers remain somewhere on the
rectangle design, and (3) the resulting figure has a
rotational symmetry of order 4? If so, draw the
figure. If not, explain why.
Using the concept of rotational symmetry, the angle of rotation about the center that results in an image that matches the original figure is; Option A: 90
What is rotational symmetry?Rotational symmetry is defined as a process that requires the rotation of a given object about a reference point to produce its image which has the same characteristics. This tells us that its dimensions, measure of internal angles and size do not change except its orientation. The orientation depicts the way in which the object is positioned.
here, we have,
The sum of an angle formed at a point is 360 degrees.
Thus turning a given object about a point implies its rotation with respect to a measured angle.
Thus in the diagram given in the question, the pattern shown divides the angle at the centered point into four equal parts.
Thus;
Angle of rotation = 360/4 = 90 degrees
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Ayden filled up his car with gas before embarking on a road trip across the country. The car uses 2 gallons of gas for every hour driven, and after driving for 4 hours, there were 4 gallons of gas left in the tank. Write an equation for
�
,
G, in terms of
�
,
t, representing the number of gallons of gas remaining in Ayden's gas tank after
�
t hours of driving.
The solution is,
Total capacity: 12 gallons
Equation: G = 12 - R*t
What is mathematical expression?A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
here, we have,
Let R be rate of gas consumption by car = 2 gallons/hr
Let G be the gallons in the car left
let g be the gallons used by the car while driving
Driven time, t = 4 hrs
Remaining gas =4 gallons
according to the question,
consumption rate, R = g/t
After driving for 4 hours
2 = g/4
g = 2*4 = 8 gallons
remaining gas = 4 gallons
therefore, total capacity of the car = 8 + 4 = 12 gallons
equation in terms of gas left,
G = 12 - R*t
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In Mrs. stones class 18 out of 20 students turned in their homework on time. What percent of the class turned in their homework on time?
Answer: 90%
Step-by-step explanation:
18/2=9
20/2=10
9 out of 10 is 90%
Answer: 81.82%
Step-by-step explanation: A percentage is a number or ratio that can be expressed as a fraction of 100.
here, we have,
given that,
In Mrs. Stone's class, 18 out of 22 students turned in their homework on time.
now,
the percent of the class turned their homework in on time is,
18/22 * 100
=81.82%
find the angle x in each question below. give reasons for your answer
The measure of x from the angles of the parallel lines are solved
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the figure be represented as A
Now , let the missing angle be represented as x
a)
Let the figure be A
Now , the measure of m∠x = 125° ( corresponding angles )
So , the measure of angle x = 125°
b)
Let the figure be A
Now , the measure of m∠x = 57° ( alternate interior angles )
So , the measure of angle x = 57°
c)
Let the figure be A
Now , the measure of m∠x = 70° ( Vertically opposite angles are same )
So , the measure of angle x = 70°
d)
Let the figure be A
Now , the measure of m∠x = 180° - 105°( co interior angles add up to 180° )
So , the measure of angle x = 75°
e)
Let the figure be A
Now , the measure of m∠x = 180° - 53°( co interior angles add up to 180° )
So , the measure of angle x = 127°
f)
Let the figure be A
Now , the measure of m∠x = 180° - 133° ( corresponding angles )
So , the measure of angle x = 47°
Hence , the measures of angles are solved
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A road-building company plans to construct a bridge across a pond to connect Main Street and Second Street, as shown in the diagram below. How long will this bridge need to be? Show your work.
The bridge needs to be 1.6 miles long. The solution has been obtained by using Pythagoras theorem.
What is Pythagoras theorem?
According to the Pythagorean Theorem, the square of a right-angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides.
We are given a right angled triangle with base 3 miles and the hypotenuse 3.4 miles.
The perpendicular is given to be 'x'.
Using Pythagoras theorem, we know that
⇒Hypotenuse² = Perpendicular² + Base²
⇒(3.4)² = x² + 3²
⇒11.56 = x² + 9
⇒x² = 2.56
⇒x = 1.6 miles
Hence, the bridge needs to be 1.6 miles long.
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Evaluate the expression 4xy-(x+7) if x=-2 and y=5
Given:-
[tex] \tt \: x = -2[/tex][tex] \: [/tex]
[tex] \tt \: y = 5[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 4xy - ( x + 7 )[/tex]now , put the given values of x = -2 nd y = 5 in equation :
[tex] \: [/tex]
[tex] \tt \: 4( -2 ) ( 5 ) - ( -2 + 7 )[/tex][tex] \: [/tex]
[tex] \tt \: -8( 5 ) - 5[/tex][tex] \: [/tex]
[tex] \tt \: -40 - 5[/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \orange{ \:-45 \: }}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
Answer:-45
Step-by-step explanation:
first plug in the x and the y values
4(-2)(5)-(-2+7)
The start using pemdas to simplify
*or bodmas depends on what you learned
Then you should arrive to this
4(-2)(5)+ -(5)
-8(5)+ -5
-40-5= -45
Hope that helps
In a board game, Maliq gets x points for landing on a red space, 2x points for landing on a blue space, and 5x points for going all the way around the board.He lands on 21 red spaces,19 blue spaces, and goes around the board twice, for a total of 21x+19 x 2x + 2 x 5x points. Which expression also represents Maliq's total points?
Answer Choices
A. (21+19)2x + 10x
B. 42x
C. 69x
D. (21+ 19 +2)(x+ 2x+5x)
Therefore , the solution of the given problem of expressions comes out to be option C. 69x is the right response.
What is an expression?
Calculations like multiplying, dividing, joining, and presently removing are required. If they were put together, it would say: An equation, some statistics, and a mathematical formula A statement of truth is composed of values, components, and mathematical processes like additions, subtractions, errors, subdivisions, and arithmetic formulas. Words and phrases can be evaluated and analysed.
Here,
The formula 21x + 19(2x) + 2(5x) can be made simpler as follows:
=> 21x + 38x + 10x = 69x
Maliq's total scores can therefore be written as 69x.
To determine which decision is equivalent to 69x, we can also look through the answer options.
A.
=> (21+19)2x + 10x = 40(2x) + 10x = 80x + 10x = 90x,
which is not equivalent to 69x..
B. 42x and 69x are not equal.
C. 69x is the same as 69x.
D. The sum of
=> (21+19+2)(x+2x+5x) = 42(8x) = 336x does not equal 69x.
Therefore, C. 69x is the right response.
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3.
Troy planned to make enough ice cream for 15 servings but only made 13
servings. What is the percent error in this situation?
Answer:
Approximately 13%
Step-by-step explanation:
Troy meant to make 15, but only made 13, meaning that he was off by 2. To find the percent error here, we will divide how off Troy was by the amount Troy meant to make:
2/15=0.133333333, or approximately 13% (multiply the decimal by 100 to find the percent, then round to the nearest integer.)
What percentage is equivalent to
12
/
30
Answer:
The answer you're looking for is 40%
Step-by-step explanation:
If you divide 12(numerator) by 30(denominator), you get 0.4.
After that, if you want to convert the decimal to a percent you always have to multiply by 100.
[tex]\frac{12}{30} =0.4=0.4 x 100=40%[/tex]
I hope this was helpful!
11.6%=x*17.8%+ (1-X)* 8.4%
To solve for x in the equation:
11.6% = x × 17.8% + (1 - x) × 8.4%
We can first convert the percentages to decimal form:
11.6% = 0.116
17.8% = 0.178
8.4% = 0.084
Substituting these values into the equation, we get:
0.116 = x 0.178 + (1 - x) × 0.084
Next, we can simplify the equation by distributing the (1 - x) term:
0.116 = x × 0.178 + 0.084 - x × 0.084
Simplifying further by combining like terms, we get:
0.116 = 0.178x + 0.084 - 0.084x
0.116 = 0.094x + 0.084
Subtracting 0.084 from both sides of the equation, we get:
0.032 = 0.094x
Finally, dividing both sides of the equation by 0.094, we get:
x = 0.3404 or approximately 0.34
Therefore, x is approximately 0.34
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=. Xavier wants to buy a new TV. Before he goes to the store, he measures his TV and notes that it is 56 inches long and 33 inches wide. When Xavier gets to the store, he realizes that TVs are measured by their diagonal length! What is the diagonal length of his current TV?
The diagonal length of his current TV is 65 inches.
What is Pythagoras Theorem?Pythagoras theorem states that for a right-angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude. It can be used to find the diagonal of a rectangle if we know the length and the width.
As per the given data:
Length of the TV (l) = 56 inches
Width of the TV (b) = 33 inches
To find the diagonal length (d) of the TV:
From Pythagoras theorem:
[tex]d = \sqrt{l^2 +b^2}\\d = \sqrt{(56)^2 +(33)^2}\\d = \sqrt{3136 +1089}\\d = \sqrt{4225}\\d = 65 inches[/tex]
Hence, the diagonal length of his current TV is 65 inches.
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In a certain study, the chances of encountering a car crash on the road are stated as "5 in 17." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer:
Step-by-step explanation:
To convert a degree of likelihood to a probability value, we use the formula:
probability = number of favorable outcomes / total number of possible outcomes
In this case, the chances of encountering a car crash on the road are stated as "5 in 17", which means there are 5 favorable outcomes (encountering a car crash) out of 17 possible outcomes (driving on the road).
So, the probability of encountering a car crash can be calculated as:
probability = 5/17
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. Therefore, the probability of encountering a car crash on the road is:
probability = 5/17 ≈ 0.2941
Since the probability value is between 0 and 1 inclusive, we can express the indicated degree of likelihood as a probability value of approximately 0.2941.
there are a group of 80 students 90% of them are right handed. how many students are right handed?
Answer:
72 of the students are right handed.
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
90 x 80
100
= 72
What is the area of this rhombus?
Enter your answer in the box.
m²
Answer:
area = 16
Step by step
The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t.
P=$8000, r=7.0%, t=3 months
In response to the aforementioned query, we may say that The future interest value of the loan, or the total amount due after three months, is $8140.
what is interest ?By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.
The following formula can be used to determine a loan's future value A:
[tex]A = P + Prt[/tex]
When P is the principal borrowed, r denotes the interest rate in decimal form, and t denotes the length of time in years.
P equals $8,000, r equals 0.07 (because the interest rate is specified as 7%), and t equals 3/12 to 0.25 years in this example (since the time period is given in months and we need to convert it to years).
With these values entered into the formula, we obtain:
[tex]A = $8000 + $80000.070.25\\A = $8000 + $140 \sA = $8140[/tex]
The future value of the loan, or the total amount due after three months, is $8140.
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- Calculate how many pupils there are in the class if there are 21 girls.
There are 37 pupils in the class.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, the ratio of girls to boys is 4:3, this means that for every 4 girls, there are 3 boys.
We can use this ratio to find the number of boys in the class. Let's set up a proportion:
4 girls : 3 boys = 21 girls : x boys
where x is the number of boys in the class.
To solve for x, we can cross-multiply:
4 girls * x boys = 3 boys * 21 girls
4x = 63
x = 15.75
We can't have a fractional number of students, so we need to round up to the nearest whole number. This means there are 16 boys in the class.
Total number of pupils = 21 girls + 16 boys = 37 pupils
Therefore, there are 37 pupils in the class.
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Complete question:
the ratio of girls to boys is 4:3. Calculate how many pupils there are in the class if there are 21 girls.
Mr. Clark suspended 2 out of every 5 students in the 9th grade. If there are 200 total 9th grade students, how many were suspended?
In the given equation, b is a positive constant.
The sum of the solutions of the equation is 5.
What is the value of b?
x²(x+3)(x - b) = 0
Answer:
0
Step-by-step explanation:
X^2(x+3)(x-b)=0x2 = 0x =√0x= 0
(hope this helps you <:)
what is the area of the triangle
The triangle has a surface area of 12 square centimetres.
We can apply the following formula to determine the triangle's area:
Area = base x height x half
The triangle's height in this instance is 4 cm, while its base is 6 cm. We can therefore determine the area by substituting these values into the formula as follows:
Area: 0.5 by 6.4 by 4.4 cm
Amount = 12 cm2
Hence, the triangle has a surface area of 12 square centimetres.
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x
2
+7x=
�
x
Solving Quadratics by Factoring
The solutions to the quadratic equation [tex]X^2 + 7X = 0[/tex] are X = 0 and X = -7.
What is quadratic equation?
A quadratic equation is a polynomial equation of the second degree, which means it contains one or more terms that are raised to the power of two. The standard form of a quadratic equation is:
[tex]ax^2 + bx + c = 0[/tex]
where a, b, and c are constants, and x is the variable. The value of x that satisfies the equation is called the root or solution of the quadratic equation.
Quadratic equations can have one, two, or no real solutions, depending on the value of the discriminant [tex]b^2 - 4ac[/tex]. If the discriminant is positive, the equation has two real solutions; if it is zero, the equation has one real solution; and if it is negative, the equation has no real solutions but two complex solutions.
To solve the quadratic equation [tex]X^2 + 7X = 0[/tex] by factoring, we first write it in the standard form:
[tex]X^2 + 7X = 0[/tex]
Next, we factor out the common factor X:
X(X + 7) = 0
Now, we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. In this case, we have:
X = 0 or X + 7 = 0
Solving for X in each equation, we get:
X = 0 or X = -7
Therefore, the solutions to the quadratic equation X^2 + 7X = 0 are X = 0 and X = -7.
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Question:
[tex]X^2 + 7X = 0[/tex]
Solving Quadratics by Factoring
Lauren has $900 in a savings account that earns 10% interest per year.The interest is not compounded. How much will she have in total in 1 year?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$900\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ A = 900[1+(0.10)(1)] \implies A = 990[/tex]
7/25 equivalent in percents