The population of California by the year 2020 is 41 million.
What is population growth?The term population has to do with the number of people that live in a place or a town. We have the following information from the question;
Initial population (Po) = 37 million
Population growth rate (r) = 1.0%
Time interval (t) = 10 years
P = The population of the city of California at the time t
Now using the formula;
P = Poe^rt
P = 37 * 10^6 e^0.01 * 10
P = 4.089 * 10^7 or 41 million
They would have a population of 41 million in ten years.
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The number of days worked is inversely proportional to the number of people. If it takes 15 people to collect and pile sand for the construction of a classroom in five days, how many days would it take 20 men to complete the task?
15/4 days take 20 men to complete the task.
Given,
In the question:
The number of days worked is inversely proportional to the number of people.
If it takes 15 people to collect and pile sand for the construction of a classroom in five days.
To find the how many days take it 20 men to complete the task?
Now, According to the question:
Based on the given condition:
Formulate:
5 x 15 ÷ 20
Calculate :
5x 15/ 20
Cross out the common factor:
=15/4
Hence, 15/4 days take 20 men to complete the task.
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Question 5 (1 point) O O The angles that are marked the same are congruent. One mark congruent to one mark; two marks congruent to two marks; three marks congruent to three marks For the image shown, which of these statements is true? O O TH a HA If vertical angles are congruent, then the lines are parallel. If alternate interior angles are congruent, then the lines are perpendicular. If corresponding angles are supplementary, then the lines are parallel. d If corresponding angles are congruent, then the lines are parallel. b
Answer:
d. If corresponding angles are congruent, then the lines are parallel
Step-by-step explanation:
This is an example of two lines intersected by a transversal. If corresponding angles on both lines are equal, then the lines must be parallel! Think about it! If both of the two-mark angles were 30 degrees, both lines would be pointing in the exact same direction - parallel!
If corresponding angles are congruent, then the lines are parallel thus option (d) is correct.
What are parallel lines?Two lines in the same plane that are equally spaced apart and never cross each other are said two lines in the same plane that are equally spaced apart and never cross each other to be parallel lines.
As per the given two parallel lines and one transversal.
The angle with a single mark is collectively known as the corresponding angle.
If the corresponding angle is the same insure that both lines which intersect at single lines will be parallel.
Hence "If corresponding angles are congruent, then the lines are parallel".
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JK has endpoints J(-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of
2:1.
What are the two possible locations of L?
(-9, 0.5)
(-2, -1)
(-7, 0.25)
(0, -1)
(-6, 0)
(1, -1.5)
(-4,-0.5)
The two possible locations of L are (-2,-1) and (14/3, -5/3).
According to the question,
We have the following information:
JK has endpoints J(-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1.
We know that the following formulas are used to find the coordinates of a point:
x = [tex]\frac{(mx2+nx1)}{(m+n)}[/tex] and x = [tex]\frac{(mx2-nx1)}{(m+n)}[/tex]
y = [tex]\frac{(my2+ny1)}{(m+n)}[/tex] and y = [tex]\frac{(my2-ny1)}{(m+n)}[/tex]
In this case, we have the following values:
x1 = -10 and y1 = 1
x2 = 2 and y2 = -1
m = 2 and n = 1
So, we have:
x = {2*2+1*(-10)}/(2+1)
x = (4-10)/3
x = -6/3
x = -2
For the negative sign:
x = {2*2-1*(-10)}/3
x = (4+10)/3
x = 14/3
x = 4.67
The values of y:
y = {2*(-2)+1*1}/3
y = (-4+1)/3
y = -3/3
y = -1
For the negative sign:
y = {2*(-2)-1*1}/3
y = (-4-1)/3
y = -5/3
y = -1.67
Hence, the two possible locations of L are (-2,-1) and (14/3, -5/3).
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The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 135 minutes with a standard deviation of 44 minutes. At
= 0.01 level, is the student academic group's claim correct?
1. What is the p-value
The p-value of this sample proportion is equal to 0.0360.
At the 0.01 (1%) significance level, there isn't enough evidence to conclude that freshmen students study less than 2.5 hours per day, on an average.
How to calculate value of the test statistic?For this statistical study, we would use a t-test statistic and the null and alternative hypotheses would be given by:
H₀: p ≥ 150 minutes
H₁: p < 150 minutes
Mathematically, the t-test statistic can be calculated by using this formula:
[tex]t=\frac{x\;-\;\mu}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x represents the sample mean.μ represents the mean.σ represents the standard deviation.n represent the number of students.Substituting the given parameters into the formula, we have;
t-test, t = (135 - 150)/(44/√30)
t-test, t = (-15)/8.0333
t-test, t = -1.8672
From the t distribution table, the p-value is given by:
p-value = P(t < -1.8672)
p-value = 0.0360
Since the p-value (0.0360) is greater than the significance level (0.01), we fail to reject the null hypothesis because there is insufficient evidence to claim that the mean time of the freshman students is less than 2.5 hours per day.
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can u help me with this
Answer:
Step-by-step explanation:
220.5-(12.8+20.25+18.2+25.5)
220.5-(76.25)
143.75 lbs of ice left
4. (03.04)
Describe how to determine the average rate of change between x = 1 and x = 3 for the function f(x) = 3x³ +1. Include the average rate of change in your answer. (10 points)
Answer:
39
Step-by-step explanation:
The given function to us is ,
[tex]\longrightarrow f(x) = 3x^3 + 1\\ [/tex]
We need to find the average rate of change between [tex] x=1 [/tex] and [tex] x=3[/tex] .
We can calculate the average rate of change as ,
[tex]\longrightarrow A(x) =\dfrac{f(b)-f(a)}{b-a} [/tex]
So that ,
[tex]\longrightarrow A(x) =\dfrac{f(3)-f(1)}{3-1}\\ [/tex]
[tex]\longrightarrow A(x) =\dfrac{ \{ 3(3)^3 +1 -(3(1)^3+1)\}}{2}\\ [/tex]
[tex]\longrightarrow A(x) = \dfrac{ 81 +1 - 3 -1 }{2}\\[/tex]
[tex]\longrightarrow A(x) = \dfrac{78}{2}\\ [/tex]
[tex]\longrightarrow\underline{\boxed{ A(x) = 39}} [/tex]
model the expression on the number line by drawing an arrow -3- 2 1/2
A model of the given expression on a number line is represented by a number line with open circle on point negative 11 over 2 (-11/2) and arrow shaded to the left.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
From the information provided, we have the following mathematical expression:
x = -3 - 2 1/2
x = -3 - 5/2
x = -11/2 or -5.5.
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. You are a contractor specializing in small commercial projects. You have been contracted to refinish the restrooms in an office building. In order to lay out a tile pattern for the floor, you need to know how many tiles you will use in each row. The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side. Assuming there is no spacing allotment needed, how many tiles will you use for each row across the room?
The number of tiles is 96
From the question, we have
The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side.
16 feet = 192 inches
Number of tiles = (192*8)/(4*4)
= 96 tiles
The number of tiles is 96.
Multiplication:
The product of two or more numbers is computed by mathematicians using multiplication. In everyday life, it is a basic mathematical operation that is frequently used. We employ multiplication when we must combine groups of like sizes. The operation of multiplication serves as a representation of the fundamental idea of adding the same number repeatedly. The product of two or more numbers is what is obtained when those numbers are multiplied, and the factors are the quantities that are multiplied. Multiplying the numbers simplifies the process of adding the same number repeated.
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Question 3
Hint: see problem #3 on 3-6
Rollie has a credit Card limit of $4,000. He made the following purchases: $425.36, $358.33,
$377.11, and $90.20.
What is the total amount of purchases?
$
What is Rollie's available credit?
$
LA
N
The total amount of purchases of Rollie is $1,251. Rollie's available credit card limit after spending $1,251 from $4,000 is $2,749.
We are given:
Rollie has a credit card limit of $4,000.
He made the following purchases: $425.36, $358.33, $377.11, and $90.20.
We need to find the total amount of purchases and Rollie's available credit card limit.
To find the total amount of purchases, we need to perform the addition that is add all the expenses:
The total amount of purchases
= addition of all purchases
= $425.36 + $358.33 + $377.11 + $90.20
= $1251
We need to subtract the total amount of purchases from the credit card limit to get Rollie's available credit card limit.
So,
Rollie's available credit card limit
= credit card limit - the total amount of purchases
= $4000 - $1251
= $2749
Thus, the total amount of purchases of Rollie is $1,251. Rollie's available credit card limit after spending $1,251 from $4,000 is $2,749.
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The technician at the store worked on the computer for 4.25 hours and charged him $141 for parts. The total was $332.25. Write and solve an equation which can be used to determine x the cost of the labor per hour.
The cost of the labor per hour is $ 45
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The total cost of the parts is = $ 141
The total number of hours worked by the technician = 4.25 hours
The total cost of repair = $ 332.25
Let the cost of the labor be = y
The total cost of labor =
Cost of the labor per hour x Number of hours worked by the technician
The total cost of labor = 4.25y
Now ,
The total cost of repairing the computer =
Total cost of labor + Total cost of the parts
The total cost of repairing the computer = 141 + 4.25y
332.25 = 141 + 4.25y
Subtracting 141 on both sides , we get
4.25 y = 191.25
Divide by 4.25 on both sides , we get
y = $ 45
Therefore cost of labor per hour y = $ 45
Hence , the total cost of labor per hour is $ 45
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Determine an nth degree polynomial that satisfies the aforementioned conditions.
The nth-degree polynomial that satisfies the aforementioned conditions is the polynomial p (x) = -3 (x + 9) (x - 1 - 6i) (x - 1 + 6i).
Given that:
p is of degree 3.
1 + 6i and -9 are zeros of p.
Since 1 + 6i is an imaginary number equal to zero so 1 - 6i must also be the one equal to zero.
So, p (x) = A (x + 9) (x - (1 + 6i)) (x- (1-6i))
p (x) = A (x + 9) (x - 1 - 6i) (x - 1 + 6i) ........ (Z)
Using formula:
(a-b) (a+b) = a² - b²
(a-b)² = a² - 2ab + b²
Assume, x - 1 = a, 6i = b
p (x) = A (x + 9) (x² - 2x + 1 + 36)
As i² = -1
p (x) = A (x + 9) (x² - 2x + 37)
Solving this equation we get,
p (x) = A (x³ - 2x² + 37x + 9x² - 18x + 333)
p (x) = A (x³ + 7x² + 19x + 333) ....... (1)
Given that:
p(2) = -1221
Putting the value of x = 2 and p(2) = -1221 in equation (1).
p(2) = A (2³ + 7(2²) + 19(2) + 333)
=> -1221 = A (8 + 28 + 38 + 333)
=> A = -1221/407
=> A = -3
Putting the value of A = -3 in equation (Z).
Hence, the polynomial p (x) = -3 (x + 9) (x - 1 - 6i) (x - 1 + 6i).
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NO LINKS!! Please help me with this symmetry part 3 Select all that apply
Answer:
[tex]y=-\dfrac{1}{8}x^3[/tex]
Step-by-step explanation:
If a function is symmetrical about the origin, when y is replaced with (-y) and x is replaced with (-x), the resulting function will be equal to the original function.
Original function:
[tex]y=-\dfrac{1}{8}x^3[/tex]
Replace y with (-y) and x with (-x):
[tex]\implies -y=-\dfrac{1}{8}(-x)^3[/tex]
[tex]\implies -y=-\dfrac{1}{8}\cdot -x^3[/tex]
[tex]\implies -y=\dfrac{1}{8}x^3[/tex]
Multiply both sides by -1:
[tex]\implies y=-\dfrac{1}{8}x^3[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the origin.
Which of these equations is linear
A. -3x+y=8
B. y=x²-3
C. 4y-2x³=0
D. 3=xy+9
Answer:
a) -3x + y = 8
Step-by-step explanation:
Now we have to,
→ find which of these equations is linear.
Format of linear equation,
→ Ax + By = C
Then the linear equation is,
→ Ax + By = C
→ -3x + y = 8
Hence, answer is -3x + y = 8.
Answer:
A. -3x + y = 8
Step-by-step explanation:
Definition of a Linear Equation:
A linear equation is an equation for a straight line.The highest power of its variables is always one.Each variable is multiplied by a constant only.A. -3x + y = 8This is a linear equation as the highest power of its variables is one, and each variable is multiplied by a constant only.
B. y = x² - 3This is not a linear equation as the highest power of the term in x is 2.
C. 4y - 2x³ = 0This is not a linear equation as the highest power of the term in x is 3.
D. 3 = xy + 9This is not a linear equation as the x and y variables are multiplied by each other rather than by a constant.
Given that x(a + bx)(a − bx) = 25x - 4x³, find the value of b-ª
Answer:
[tex] {2}^{ - 5} [/tex]
Step-by-step explanation:
Please see picture on how to do it
Determine the number of subsets contained in Q if Q={x∣∣x is an even, positive integer and x < 27}
The number of subsets contained in Q if Q={x∣∣x is an even, positive integer and x < 27] is 13.
What is a subset?A subset implies a part of the mathematical concept that's referred to as the set. The set is the collection of the elements that are grouped in the curly braces.
In this case, since x is an even number and less than 27, this will be:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, and 26.
Therefore, the numbers are 13.
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Hey can someone please help me out and explain the problem? Look below. Thank you! I’ll give brainly
A hoyel has 124 pillows.The hotel gets more pillows in 5 styles wiyh 8 pillows of each syyle.Write and solve an equation to find out how many pillows the hotel has in all
Answer:
164 pillows
Step-by-step explanation:
Equation: 124 + 5(8)
(11x=28)
(7x-8)
Solve for x
what is 4 divided by 3.48
pls help
The solution to 4 divided by 3.48 is 0.87
DivisionDivision in mathematics is the method of dividing large numbers into smaller numbers or par
Step 1: Rewrite the question in mathematical terms then
[tex]\frac{3.48}{4}[/tex]= 0.87
Therefore, answer to the division is 0.87
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5 (a) (b) Identify the nature of two stationary points for y=4x³ - 96x² +576x.
Answer: (0,0) (12,0)
Step-by-step explanation:
y=4x³-96x²+576x
Let y=0
Hence,
4x³-96x²+576x=0
Divide both parts of the equation by 4:
x³-24x²+144x=0
x(x²-24x+144x)=0
x=0
Thus, (0,0)
x²-24x+144=0
x²-2(x)(12)+12(12)=0
x²-2(x)(12)+12²=0
(x-12)²=0
x-12=0
x=12
Thus, (12,0)
What happens to a parabola when you change certain elements of the equation?
Supoose a<1 compared to the parent function then parabola is wider than the parent function.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Direction the parabola opens the value of p as positive, the parabola opens up.
The focus and vertex both have the same x position, so the distance would be in terms of the y-coordinates only.
Supoose a<1 compared to the parent function then parabola is wider than the parent function
If "a" is a fraction less than one, therefore the parabola becomes wider.
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A freight train and a passenger train leave Portland at the same time on parallel tracks heading for Springfield. The passenger train goes 30 mi/hr faster than the freight train, and in 6 hr the passenger train travels three times farther. What is the speed of each train?
The passenger train traveling at 30 mi/hr faster than the freight train and traveling 3 times the distance traveled by the freight train, through the kinematic equations, indicates that the speed of the freight train is 15 mi/hr and the speed of the passenger train is 45 mi/hr.
What is kinematics?Kinematics is the study of the motion of an object without reference to the force that causes the motion.
The speed of the passenger train = 30 + The speed of the freight train
Distance traveled by the passenger train in 6 hours = 3 × The distance traveled by the freight train
Let v represent the speed of the freight train and let d represent the distance traveled by the freight train in 6 hours
From kinematic equations, we get;
Speed of the passenger train = 30 + v
Distance traveled by the passenger train in 6 hours = 3 × d
(30 + v) × 6 = 3•d
6•v = d
Which gives; (30 + v) × 6 = 3 × 6•v
180 + 6•v = 18•v
12•v = 180
v = 180 ÷ 12 = 15
The speed of the freight train is v = 15 mi/hr
The speed of the passenger train = 30 + v
The speed of the passenger train is (30 + 15) mi/hr = 45 mi/hr
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A regular polygon has 18 sides. If one of its angles measures (4h − 25)°, what is the value of h?
Answer: h = 46.25
Step-by-step explanation:
You can use the formula below to calculate the value of its interior angle:
n = number of sides = 18[tex]\frac{(n-2)*180}{n} =\frac{(18-2)*180}{18} =\frac{16*180}{18} =160[/tex]
So, each one of its interior angles is equal to 160°. Set that equal to the given angle measure and solve:
[tex]160=4h-25\\\\4h=160+25=185\\\\h=46.25[/tex]
Please help I was sick and missed out on class.Thank you
Kyra is participating in
i fundraiser walk-a-thon. She walks| 2 miles in 30 minutes. If she continues to walk at the same rate, determine how
many minutes it will take her to walk 7 miles.
Kyra takes 105 minutes to cover a distance of 7 miles if she walks at a speed of 1/15 miles per minute.
Given,
Kyra is participating in a fundraiser walk-a-thon.
She walks 2 miles in 30 minutes
We have to find the time taken by Kyra to cover 7 miles if she continues the same rate of speed;
Here,
2 miles in 30 minutes
Then,
Speed = distance / time
Speed = 2 / 30
Speed = 1/15 miles per minute
Now,
The time taken to cover 7 miles;
Speed = distance / time
1/15 = 7 / t
t = 7 x 15
t = 105 minutes
That is,
Kyra takes 105 minutes to cover a distance of 7 miles if she walks at a speed of 1/15 miles per minute.
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4x+7=1+2(2x+3) linear equations
Solving the Question
[tex]4x+7=1+2(2x+3)[/tex]
⇒ Our goal is to solve for x. We can do this by moving everything else to the other side of the equation.
⇒ Open up the parentheses:
[tex]4x+7=1+4x+6[/tex]
⇒ Simplify:
[tex]4x+7=4x+7[/tex]
Because both sides are equal, we end up with x = x.
In this case, we can say that all values of x are true.
AnswerAll values of x are true.
A combination padlock in which a sequence of numbers is used as the "key" to open
the lock. Suppose a combination padlock has 10 digits to choose from for each of the
four sections of the lock.
Does the "key" for a combination padlock involve permutations or combinations?
A. Permutation
B. Combination
The "key" for a combination padlock involves a 210 combination.
What is a combination?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
Here, we have
A combination padlock has 10 digits to choose from for each of the
four sections of the lock.
so, we apply a combination
¹⁰C₄ = 10! / (6! × 4!)
= (10 × 9 × 8 × 7 × 6!) / (6! × 4!)
= (10 × 9 × 8 × 7)/ 4!
= (10 × 9 × 8 × 7)/ (4 × 3 × 2 × 1)
= 210
Hence, the "key" for a combination padlock involves a 210 combination.
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Determine f(5) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4.
11
29
41
125
The value of the function when the value of x is 5 is 29.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
[tex]f(x)= \left \{ {{x^3 \;\;\;\;\;\; x < -3} \atop {2x^2-9\;\;\;-3\leq x < 4}} \atop {5x+4\;\;\;x > 4}}\right.[/tex]
As the value of the function is to be found when the value of x is 5.
So, we can write the function as,
f(5) = 5x + 4
f(5) = 5(5) + 4
f(5) = 29
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What do i right please help due tomorrow
5. If you were told that a specific tire could roll 200 yards in 27.28 revolutions, what is the radius of the tire?
The number of revolutions = Total distance divided by its circumference
The radius of the tire is 1.167 yards.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of
2πr.
The area of a circle is given as πr².
We have,
The number of revolutions = Total distance divided by its circumference
Total distance = 200 yards
Revolutions = 27.28
A tire is in the form of a circle.
So,
The circumference of the tire.
= 2πr
Now,
27.28 = 200 yards / 2πr
2πr = 200 yards / 27.28
r = 200/(27.28 x 2 x 3.14)
r = 200 / 171.32
r = 1.167 yards.
The radius of the tire is 1.167 yards.
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