Solution
So at 8pm the temperature is -2 degrees
At 10pm the temperature dropped 3 degrees = (-2 -3)degrees = -5 degrees
At 12am the temperature had dropped 5 degrees = (-2 -3 -5) degrees = -10 degrees
The temperature at 12am is -10 degrees
we want to factor the following expression: (x - 3)^2 - 64y^4 which pattern can we use to factor the expression? u and v are either constant integers or single variable expression.
The factored expression of (x - 3)^2 - 64y^4 is given as follows:
(x - 3)^2 - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
What is the subtraction of perfect squares?The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares as follows:
a² - b² = (a - b)(a + b).
In this problem, the expression is presented as follows:
(x - 3)^2 - 64y^4
This expression is a subtraction of perfect squares, as the terms are given as follows:
Term a: square root of (x - 3)² = x - 3.Term b: square root of 64y^4 = 8y².Then the expressions are given as follows:
a - b = x - 3 - 8y².a + b = x - 3 + 8y².Then the factored expression is presented as follows:
a² - b² = (a - b)(a + b).
(x - 3)² - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
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1. What is the rate of change(slope) of the following linear equation x-3y = 12?
Answer:
m= 1/3
Step-by-step explanation:
What is 2 plus 4 please help
Answer:
It is, 6
Step-by-step explanation:
Good luck! Have a good day!! <33
Act like you have 2 fingers up and then add 4 more.
If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation. Otherwise, use the values Σx = 2769 and Σx2 = 132,179 to compute the sample mean and sample standard deviation. (Round s to four decimal places.)
By using a statistical calculator, the actual sample mean and sample standard deviation are:
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
How to calculate the sample mean for the set of data?In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:
Mean = ∑x/(n - 1)
∑x represents the sum of all data values.(n - 1) represents the number of data contained in a sample.In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:
Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)
x represents the observed values of a sample.\(\bar{x}\) is the mean value of the observations.N represents the total number of of observations.By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
18 out of 25 students have a pet. What percent have a pet?
Answer:
72%
Step-by-step explanation:
18/25 x 4= 72/100
=72%
Answer:
72%
Step-by-step explanation:
To convert fractions into percentages we could change to decimal and then multiply by 100 but it would be easier to just make the fraction's denominator to 100 by finding an equivalent fraction:
18/25 = 18×4/25×4
72/100
So 72% of students have a pet
5) Is this dilation an enlargement or reduction
A) Englargement
B) Reduction
———————
6) What is the scale factor for this dilation? Hint: First identity if it’s an enlargement or reduction
A) 2
B) 1/2
C) 3
D) 1/3
A student ran a distance of 3 1/2miles each day for 5 days. Then the student ran a distance of 4 1/4 miles each day for the next 5 days. What was the total distance in miles the student ran during these 10 days?
Answer:
To find the total distance, we need to add up the distance the student ran in the first 5 days and the distance the student ran in the next 5 days.
Distance for the first 5 days = 3 1/2 miles/day × 5 days = 17.5 miles
Distance for the next 5 days = 4 1/4 miles/day × 5 days = 21.25 miles
Total distance = Distance for the first 5 days + Distance for the next 5 days
Total distance = 17.5 miles + 21.25 miles
Total distance = 38.75 miles
Therefore, the student ran a total of 38.75 miles during these 10 days.
PLEASE HELP ME WITH THIS MATH PROBLEM
m∠ A = 60°, m∠ A = 60°, m∠ A = 60° and the sum of the angles in the triangle is 180°
How to determine the angles
It is important to note that the sum of angles in a triangle equals 180°
The given structure is a triangle, thus, the angles sum up to 180°
m ∠ A + m ∠ B + m ∠ C = 180°
m∠ A = 60°
m ∠ B = 60°
m ∠ C = 60°
The sum of the angle in the triangle = 60° + 60° + 60° = 180°
Thus, m∠ A = 60°, m∠ A = 60°, m∠ A = 60° and the sum of the angles in the triangle is 180°
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What is
1 2/3-2 1/3
?
Answer:
I believe it's -2/3
\(1\frac{2}{3} - 2\frac{1}{3} = -\frac{2}{3}\)
Answer:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Exact Form: −2/3
Decimal: -0.6
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Xavier is buying fencing to surround his garden if his garden has a perimeter of 30 yards and fencing cost six dollars a yard how much money will he need for the fencing
Answer:
$180
Step-by-step explanation:
If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180
Which survey question could have been asked to produce this data display?
A How much does your dog weigh?
B How many times do you feed your dog each day?
C How many bags of dog food do you buy each month?
D How much does your bag of dog food weigh?
according to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570what was the number of number of female population
According to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570 the number of female population is 43,11,50,122.
To find the wide variety of girl population, we will subtract the quantity of male population from the full population.
Total population = 88,51,84,692
Number of male = 45,40,34,570
Number of female = Total population - Number of male
= 88,51,84,692 - 45,40,34,570
= 43,11,50,122
Therefore, the number of female population is 43,11,50,122.
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1. The proportion, p, of consumers who shop with coupons
is the ratio of the number, C, of consumers who use coupons
to the number, N, of consumers asked. Write an equation
for the proportion of consumers who shop with coupons.
The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.
What is equation?An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.
Here,
This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.
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Write out the differential equations, DO NOT solve, for the following word problems.
a. The acceleration, v'(t), of a coasting motorboat is proportional to the square of its velocity, v(t).
b. The population of Zootopia in year t, is P(t): Animals are born at a rate proportional to the population. The death rate is also proportional to the population. Animals move to Zootopia at a rate of 50,000 animals a year, and 40,000 animals move away in a year.
c. A function g(x) is described by the following property of its graph: At each point (x, y) on the graph y=g(x), the normal line to the graph passes through the point (0, -2). Use this information to find a differential equation of the form: dy/dx = f(x, y) Having the function g(x) as its solution.
Answer:
A differential equation of the form: \(dy/dx = f(x, y)\) is \(\frac{-x}{y+2}\)
Step-by-step explanation:
Step 1 of 3
a) Acceleration\($\rightarrow v^{\prime}(t)$\)
velocity \($\rightarrow v(t)$\)
Given that \($v^{\prime}(t) \propto v^{2}(t)$\)
\(\frac{d v}{d t}=k v^{2}\)
\(k\) is proportionality constant.
Step 2 of 3
b) The population of Zootopia in year \($t$\), is \($P(t)$\)
Let \($\beta$\) the 'birth rate of Animals and \($\delta$\) the death rate of the population.
Then the population model is
\(\frac{d p}{d t}=(\beta-\delta) P$$\)
Given that \($\beta=50000$\) and
\($\delta=40000$\)
So, \($\frac{d P}{d t}=10000 P$\)
Step 3 of 3
c) First we take the derivative of \($f(x)$\) i. e \($f^{\prime}(x)$\).
The evaluate it at \($m_{1}=f^{\prime}(2)\)
\(m_{2}=\frac{-1}{f^{\prime}(2)}$\)
The normal line with slope \($\frac{-1}{f^{\prime}(2)}$\)
\(y-(-2)=\frac{-1}{f^{\prime}(2)}(x-0) \\\)
\(y+2=\frac{-x}{f^{\prime}(2)}\)
\(f^{\prime}(2)=\frac{f x}{(y+2)} \\\)
\(&f^{\prime}(2)+\frac{x}{(y+2)}=0\)
\(\frac{d y}{d x}=\frac{-x}{y+2}\)
there are 538 jelly beans in a bowl hector and Michael decided to share the jelly beans how many jelly beans do Michael and hector get? Their mom tells them they can not eat all the jelly beans at once. They can each eat an equal amount of jelly beans for four days. How many jelly beans do hector and Michael eat each day for four days
Answer:
67.25
Step-by-step explanation:
Since they can each get 1/2 the jelly beans but need to eat it over 4 days they will be eating 1/2*1/4 jelly beans per day. This is equal to 1/8x where x is the total jelly beans. We know the total so we can plug 538 in for x and divide 538 by 8 to get 67.25
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Which pair of angles are Complementary Angles?
45 degrees and 95 degrees
or
38 degrees and 42 degrees
or
30 degrees and 51 degrees
or
63 degrees and 27 degrees
Answer:
63 degrees and 27 degrees
Step-by-step explanation:
Complementary angles are when two angles add to 90 degrees.
So, we can check if these pairs add up to 90 degrees.
45 + 95 = 140
38 + 42 = 80
30 + 51 = 81
63 + 27 = 90
The only pair of angles that are complementary is 63 degrees and 27 degrees.
3(4x+1)=15? X=
What is the solution?
Answer:
x=1
Step-by-step explanation:
3(4x+1)=15
12x+3=15
12x=15-3
12x=12
x=12/12
x=1
Pilar has 40 shells in her collection. She goes to the beach. She collects 6 more shells in the morning and 3 more shells in the afternoon. What is the percent change in Pilar's shell collection from the beginning of the day to the end? Show your work.
The percent change in Pilar's shell collection from the beginning of the day to the end is, 22.5%
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
Pilar has 40 shells in her collection.
She collects 6 more shells in the morning and 3 more shells in the afternoon.
The percent change in Pilar's shell collection from the beginning of the day to the end = ?
At the beginning of the day, Pilar has 40 shells.
In the morning, she collects 6 more shells, bringing her total to
= 40 + 6
= 46 shells.
Then, in the afternoon, she collects 3 more shells, bringing her total to
=46 + 3
= 49 shells.
To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:
percent change = (final value - initial value) / initial value * 100%
Plugging in the values we have:
percent change = (49 - 40) / 40 x 100%
percent change = 9 / 40 x 100%
percent change = 22.5%
Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.
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Daniel buys an ice cream sundae for $4.88 and is given $15.12 as change. Which equation represents the situation if x is the amount Daniel had before he bought the ice cream sundae?
Answer:
X = 4.88 + 15.12 or X - 4.88 = 15.12
So, Daniel had 20 dollars before he brought the ice cream sundae
The two boxes shown are cuboids.
20 cm
4 cm
30 cm
3 cm
50 cm
10 cm
Work out how many of the smaller boxes you would need
to completely fill the larger one.
Answer:
250.
The area of the larger box is 30,000 cm squared. Once you find the total area of the small box, divide that by the area of the larger box and you have your answer.
Answer:
205
Step-by-step explanation:
A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (-4, -5)(−4,−5). What is the vertex of the function defined as g(x)=-f(x)-2g(x)=−f(x)−2?
Answer:63M N 56
Step-by-step explanation:
Helpppppppp plsss ASAP math look at picture for details
At which values of x does the function Fx) have a vertical asymptote? Check
all that apply.
F(x) =
2/3x(x - 1)(x + 5)
I A. -1
B. 2
C. 1
D. -5
E. 0
F. 3
9514 1404 393
Answer:
C, D, E
Step-by-step explanation:
Vertical asymptotes are found where the denominator is zero. The denominator will be zero when any of its factors is zero. Then the vertical asymptotes are ...
x = 0 ⇒ x = 0 . . . . . . choice E
x -1 = 0 ⇒ x = 1 . . . . . choice C
x +5 = 0 ⇒ x = -5 . . . choice D
translate the sum of x and one half of x into a mathematical expression
Answer:
The above statement is written as
\(x + 1 \times \frac{1}{2} of \: x\)
of means multiplication
So the final answer is
\(x + \frac{3}{2} x\)
Hope this helps you.
Charges for advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is a percentage of the population of 110 million TV households. The CBS television show 60 Minutes recently had a rating of 7.8, indicating that 7.8% of the households were tuned to that show. An advertiser conducts an independent survey of 100 households and finds that at least b+1 were tuned to 60 Minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting at least 5+1 tuned to
60 Minutes.
The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.
How to calculate the probabilityP(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)
P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)
Using a calculator or software, we can find that:
P(X <= 4) = 0.000203
This means that the probability is 0.02%.
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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?
Solve 5x ≥ 25. Graph the solution.
Answer:
Step-by-step explanation:
Alright so we are going to solve
5x ≥ 25 Divide both sides by 5
x≥5
If your base pay is 10000 your commission rate is 40% you sell 15 cars and you earn 40000 how much does each car cost
Answer: $4,000
Step-by-step explanation:
If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.
Since the commission rate is 40%, we can set up the equation:
40% x Total Sales = Commission Earned
We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:
40% x Total Sales = Commission Earned
40% x (15 x Price per Car) = $30,000
6 x Price per Car = $30,000
Price per Car = $5,000
However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:
Commission per Car = 40% x Price per Car
Commission per Car = 40% x $5,000
Commission per Car = $2,000
Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:
Amount earned per Car = Total Earnings / Number of Cars Sold
Amount earned per Car = $40,000 / 15
Amount earned per Car = $4,000
Which one of the following examples represents a proper
fraction?
A. 15/22
B. 12/9
C. 3/2
O D. 8/8
A.15/22 is the correct answer.
The correct answer is:
A. 15/22, represents a proper fraction.
Here, we have,
A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).
Out of the given options, only option A,
15/22, represents a proper fraction because 15 is smaller than 22.
Therefore, the correct answer is:
A. 15/22, represents a proper fraction.
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Hue is arranging chairs. She can form 6 rows of a given length with 3 chairs left over, or
8 rows of that same length if she gets 11 more chairs. Write and solve an equation to
find how many chairs are in that row length.
Answer:
There are 7 chairs in each row length.
Step-by-step explanation:
Let number of chairs in 1 row be 'x'.
Let total number of chairs be 'y'.
Given:
Hue can form 6 rows of a given length with 3 chairs left over.
It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 6 plus number of chairs which is left which is 3.
Framing in equation form we get.
Also Given:
Hue can form 8 rows of that same length if she gets 11 more chairs.
It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 8 minus number of chairs which is required more which is 11.
Framing in equation form we get.
From equation 1 and equation 2 we can say that L.H.S is same.
So according to law of transitivity we get;
Combining like terms we get;
Using Subtraction and Addition property we get;
Now Using Division Property we will divide both side by 2.
6. Solve the problem. A carousel has a radius of 18 feet and takes 31
seconds to make one complete revolution. What is the linear speed of
the carousel at its outside edge? Express the answer in feet per second.
If necessary, round the answer to two decimal places.
Answer:
v = 3.64 ft/s
Step-by-step explanation:
Given that,
Radius of a carousel, r = 18 feet
It takes 31 seconds to complete revolution.
We need to find the linear speed of the carousel at its outside edge. Distance covered is equal to the circumference of the circle.
d = 2πr
d = 2π × 18 = 113.09 feet
Let v is the linear speed. It can be given by :
\(v=\dfrac{D}{t}\\\\v=\dfrac{113.09}{31}\\\\v=3.64\ ft/s\)
So, the linear speed of the carousel is 3.64 ft/s.