The rate at which the surface area of the sphere is increasing can be found using related rates in calculus. By differentiating the volume formula with respect to time, we relate the rates of change for the radius and surface area, and then plug in the given volume increase rate when the radius is 3m.
Explanation:The problem requires the application of related rates in calculus to find the rate at which the surface area of a sphere is increasing. To calculate this, we can use the formula for the volume of a sphere, which is V = \frac{4}{3}\pi r^3, and the formula for the surface area, which is S = 4\pi r^2. Given a rate of volume increase, \frac{dV}{dt} = 10 m^3/sec, we can differentiate the volume with respect to time to find the relationship between the rates of change of the radius and volume. Then we use the rate of change of the radius to find the rate of change of the surface area.
Step 1: Differentiate the volume with respect to time.
\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}
Step 2: Solve for \frac{dr}{dt} when the radius is 3m.
Step 3: Use the value of \frac{dr}{dt} to find \frac{dS}{dt} (the rate of surface area increase).
Step 4: \frac{dS}{dt} = 8\pi r \frac{dr}{dt}
1. Write the equation of the line with a slope of -5 and a y-intercept of (0,3). 2. Write the equation of the line with a slope of -1/3 and passing through the point (6, -4). 3. Write the equation of the line passing through the points (0, -4) and (-2, 2). 4. Write the equation of the line passing through the points (-6,1) and (-4,2). 5. Write the equation of the line with an undefined slope, passing through the point (2, 5). Hint: refer back to lesson 4.04 for help with this one.
Answer:
Step-by-step explanation:
1) The equation of a line is given by y = mx + c, where m = slope or gradient and c is intercept on y - axis. Given in this question, m = -5 and c = 3. Subtituting this in the equation y = mx + c, we have y = -5x + 3, therefore, the equation of the line is y = -5x + 3 or y + 5x = 3
2) The equation of a line is given as y-y1 = m(x-x1), where x1 = 6, y1 = -4 and m = -1/3. The equation of the line is y - -4 = -1/3(x - 6)
y+4 =-1/3(x-6)
3(y+4)= -1(x-6)
3y + 12 = -x+6
x+3y=6-12
x+3y= -6, therefore the equation of the line is x+3y = -6
3) The equation is y-y1=m(x-x1), where m=(y2-y1)/(x2-x1)=
(2- -4)/(-2-0)=6/-2=-3
y- -4= -3(x-0)= -3x
y+4= -3x
y+3x= -4
4) y-y1=m(x-x1)
m=(2-1) /(-4- -6)=1/2
y-1=1/2(x- -6)
y-1=1/2(x+6)
2(y-1) = x+6
2y-2=x+6
2y-x =6+2=8 2y-x=8
5) The equation is with undefined slope passing through (2, 5) is
x-2=0
x=2
If you invested $100 at an interest rate of 5% per year compounded quarterly, how much will the investment be worth at the end of two years? *
50 points
Answer: the investment would be
$110.45
Step-by-step explanation:
Initial amount deposited into the account is $100 This means that the principal is
P = 100
It was compounded quarterly. This means that it was compounded 4 times in a year. So
n = 4
The rate at which the principal was compounded is 5%. So
r = 5/100 = 0.05
It was compounded for 2 years. So
t = 2
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 100 (1+0.05/4)^4×2
A = 100 (1.0125)^8
A = $110.45
The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration of −5.65 m/s2 for 4.00 s, making straight skid marks 62.9 m long, all the way to the tree. With what speed (in m/s) does the car then strike the tree?
Answer: the speed with which the car strikes the tree is 27.025 m/s
Step-by-step explanation:
We would apply Newton's equation of motion. It is expressed as
S = ut + 1/2at²
Where
S represents the distance covered by the car
u represents the initial velocity of the car( the speed with which the car strikes the tree)
t represents the time taken to cover the distance
a represents the deceleration of the car.
From the information given,
S = 62.9 meters
a = - 5.65 m/s2
t = 4 seconds
Therefore
62.9 = u × 4 + 1/2 × - 5.65 × 4²
62.9 = 4u - 45.2
4u = 62.9 + 45.2
4u = 108.1
u = 108.1/4 = 27.025 m/s
Final answer:
The car's speed at the moment it strikes the tree, after decelerating with an acceleration of -5.65 m/s² for 4.00 seconds over a distance of 62.9 m, is calculated to be 22.6 m/s.
Explanation:
The question relates to the final speed of a car after it has been decelerating over a certain distance due to the driver applying the brakes. With an acceleration of −5.65 m/s² over a time period of 4.00 seconds, and the car making skid marks 62.9 m long, we are tasked with determining the speed at which the car eventually hits the tree.
To solve this problem, we first calculate the initial speed of the car before it started to decelerate. We use the kinematic equation: v = u + at, where 'v' is the final velocity (0 m/s, since the car eventually stops), 'u' is the initial velocity, 'a' is the acceleration, and 't' is the time. Rearranging this equation to solve for 'u', we get u = v - at. Substituting the given values, we find that the initial velocity 'u' was 22.6 m/s.
However, to find the speed at which the car hits the tree implies we need to know the speed at a specific point before it comes to a complete stop, specifically at the end of the 62.9 m distance. For this, considering the constant deceleration, the car's speed when it strikes the tree can be considered to be the same as its speed just before deceleration, which is calculated to be 22.6 m/s.
how can you write the statement "obtuse angles have greater measures than acute angles" so that it is a good definition
Since obtuse angles are greater than 90 degrees and acute angles are less than 90 degrees, then obtuse angles have greater measures than acute angles.
Happy to help
Answer:
Step-by-step explanation:
obtuse angles >90
acute angles <90
In his coin box , Brian has 12 fewer nickels than dimes. The value of his nickels and dimes is 2.40. Determine the exact number of nickels and dimes Brian has in his possession
Answer:
There are 8 nickels, and 20 dimes.
Brian has 20 dimes and 8 nickels in his coin box.
Explanation:Let's make a system of equations to solve this problem. Let's assume the number of dimes is 'x', then the number of nickels would be 'x - 12' since Brian has 12 fewer nickels than dimes.
The value of dimes in cents is 'x * 10', and the value of nickels in cents is '(x - 12) * 5'. We can write the equation: '10x + 5(x - 12) = 240' since the total value is $2.40 or 240 cents.
Simplifying the equation, we get '10x + 5x - 60 = 240'. Combining like terms, we have '15x - 60 = 240'. Adding 60 to both sides, we get '15x = 300'. Dividing both sides by 15, we get 'x = 20'.
Therefore, Brian has 20 dimes and 20 - 12 = 8 nickels.
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Joey spent $.75 on a bus ticket. Then he spent 1/2 of his money on the soccer ball. After that, he spent 1/4 of his money on lunch. With the last of his money, Joey spent $14.95 for soccer tickets. In the end, Joey had 5 cents left. How much money did he start out with?
Joey started his day with $63.
Step-by-step explanation:
Let,
x be the amount Joey started with.
Amount left = 5 cent = $0.05
Amount spent on bus ticket = $0.75
Amount spent on soccer ball = [tex]\frac{1}{2}x[/tex]
Amount spent on lunch = [tex]\frac{1}{4}x[/tex]
Amount spent on soccer tickets = $14.95
According to given statement;
Total amount - bus ticket - soccer ball - lunch - soccer tickets = Amount left
[tex]x-0.75-\frac{1}{2}x-\frac{1}{4}x-14.95=0.05\\\\x-\frac{1}{2}x-\frac{1}{4}x=0.05+0.75+14.95\\\\\frac{4x-2x-x}{4}=15.75\\\\\frac{x}{4}=15.75[/tex]
Multiplying both sides by 4
[tex]4*\frac{x}{4}=15.75*4\\x=63[/tex]
Joey started his day with $63.
Keywords: variable, addition
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A parachute rate during a free fall reaches 70 meters per second. What is the rate in feet per second? At this rate how many feet will the parachute fall during 20 seconds of free fall
Answer:
229.659 ft/s4,593.18 ftStep-by-step explanation:
1 foot is 0.3048 meters, so ...
70 m/s = (70 m/s)×(1 ft)/(0.3048 m) ≈ 229.659 ft/s
At that speed, the distance covered in 20 seconds is ...
(20 s)(229.659 ft/s) = 4,593.18 ft
The parachutist will fall 4593 feet during 20 seconds of free fall at 229.7 ft per second.
_____
Final answers are rounded. Intermediate values are not.
Im in desperate need of help!
Answer:
umm, my regards, how should I help lol
Write the expression in radical form. x 1/5
Answer:
[tex]x^{\frac{1}{5} } = \sqrt[5]{x}[/tex]
Step-by-step explanation:
A radical expression is an expression with a variable, number, or combination of both of them under a root symbol.
A radical expression has a general form of [tex]\sqrt[n]{x}[/tex]
For the given expression [tex]x^{\frac{1}{5} }[/tex]
So, [tex]x^{\frac{1}{5} } = \sqrt[5]{x}[/tex]
[tex]x^{1/5}[/tex] in radical form is √5x.
To write the expression [tex]x^{1/5}[/tex] in radical form, we use the property of exponents where a fractional exponent represents a root. Specifically, the exponent 1/5 indicates the fifth root of the base.
Here are the steps:
Identify the base and the fractional exponent: base = x, exponent = 1/5.Rewrite the expression using the radical symbol, where the denominator of the exponent (5) becomes the index of the root.So,[tex]x^{1/5}[/tex] is equivalent to √5x.Therefore, the radical form of [tex]x^{1/5}[/tex] is √5x.
A ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (7, 4). What is the vector joining the ship to the rock?
Answer:
SR = (6,4)
Step-by-step explanation:
The ship position is (1,0)
The rocks position is (7,4)
SR is the vector line joining ship and rock
Using triangle law of addition
OS + SR = OR
SR = OR - OS
= ( 7 - 1 , 4 - 0)
= (6,4)
The vector line joining Ship and rock is (6,4)
A categorical variable whose values are purely qualitative and unordered is called a _______ variable. Please type the correct answer in the following input field, and then select the submit answer button or press the enter key when finished. Your answer:
Answer: Nominal
Step-by-step explanation:
A categorical variable whose values are purely qualitative and unordered is called a Nominal variable. Nominal variables are qualitative variables that does not have a particular rank, order or value. An example of nominal variables are colour (red,blue etc), gender (male, female), skin and hair colour etc.
Complete the following statement. The number of iPhones sold today at an Apple store is an example of ________ data.
a. interval,
b. classified as discrete ratio,
c. classified as continuous interval,
d. classified as continuous ratio,
e. classified as discrete
Answer: Option 'e' is correct.
Step-by-step explanation:
Since we know that
Discrete data are those data which is countable and it is expressed in exact numerical form.
Continuous data are those data which is lie within the interval and it varies so it does not expressed in exact numerical form.
Here, the number of iphones sold today at an Apple store is countable and it can be expressed in exact numbers.
So, it is considered as discrete.
Hence, Option 'e' is correct.
Final answer:
The number of iPhones sold today at an Apple store represents an example of quantitative discrete data.
Explanation:
The number of iPhones sold today at an Apple store is an example of classified as discrete data. This is because the number of iPhones can only take on specific numerical values and cannot be a fraction or a decimal. In other words, you cannot sell half an iPhone, so the data is quantitative discrete.
* ANSWER ASAP PLEASE *
- can anyone answer this question?? you have to find x.
Answer:
The answer is the last one
Step-by-step explanation:
Answer:
Step-by-step explanation:
X= 11/tan17
Where tan17= 3.494
Therefore, X = 3.148
Ronald is calculating the time required to fill the swimming pool at school. He found that it takes 8 minutes to fill the swimming pool with 72 gallons of water. At what rate does the swimming pool fill, in gallons per minute?
Answer:
The rate the swimming pool is filled is 9 gallons of water per minute
Step-by-step explanation:
Let's review the information provided by Ronald to us to help him to find the answer to the question:
Time it takes to fill the swimming pool = 8 minutes
Amount of water the swimming pool can hold = 72 gallons
2. At what rate does the swimming pool fill, in gallons per minute?
Rate the swimming pool is filled = Amount of water the swimming pool can hold /Time it takes to fill the swimming pool
Replacing with the real values, we have:
Rate the swimming pool is filled = 72/8 = 9 gallons of water per minute
a. Show that the following statement forms are all logically equivalent. p → q ∨ r, p ∧ ∼q → r, and p ∧ ∼r → q b. Use the logical equivalences established in part (a) to rewrite the following sentence in two different ways. (Assume that n represents a fixed integer.) If n is prime, then n is odd or n is 2.
Final answer:
The statement forms p → q ∨ r, p ∧ ¬q → r, and p ∧ ¬r → q are shown to be logically equivalent using principles of logical equivalence and contraposition. The original statement 'If n is prime, then n is odd or n is 2' can thus be rephrased in different ways while retaining the same meaning.
Explanation:
Logical Equivalences
To show that the statement forms p → q ∨ r, p ∧ ¬q → r, and p ∧ ¬r → q are all logically equivalent, we need to understand that logical equivalence means that the statements have the same truth value in every possible scenario. The implication p → q is equivalent to p∨ q, as a truth table would confirm. Likewise, by using the principle of contraposition, which states that p → q is equivalent to ¬q → ¬p, we can transform the given implications accordingly.
Considering the sentence "If n is prime, then n is odd or n is 2" and denoting p as "n is prime", q as "n is odd", and r as "n is 2", the original statement can be represented as p → q ∨ r. Using logical equivalences established earlier, two different ways to rewrite this sentence could be:
The logical equivalences show that all these forms express the same condition from different perspectives but with the same meaning.
Jack decides to grow and sell bean plants. Let P represent the number of plants he will grow and sell. After considering his expenses, the expression -3p(p-10)-6p(p-10) represents his profit.
a. Rewrite and simplify the profit expression by factoring out the greatest common factor.
b. Rewrite the expression in simplest form with no parentheses.
Answer:
b. [tex]\displaystyle 90 - 9p^2[/tex]
a. [tex]\displaystyle -9[-10 + p^2][/tex]
Step-by-step explanation:
b. [tex]\displaystyle 90 - 9p^2 = -3p^2 + 30 - 6p^2 + 60 = -3p(p - 10) - 6p(p - 10)[/tex]
a. [tex]\displaystyle -9[-10 + p^2] = 90 - 9p^2[/tex]
I am joyous to assist you anytime.
Final answer:
The profit expression -3p(p-10)-6p(p-10) simplifies first by factoring out the greatest common factor to -9p(p-10), and then further simplifies to -9p² + 90p by distributing the -9p across the parentheses.
Explanation:
The student is tasked with simplifying the profit expression given by -3p(p-10)-6p(p-10), first by factoring out the greatest common factor, and then by writing the expression in the simplest form without parentheses.
To begin, we notice that both terms in the expression share a common factor of p(p-10), so we can factor this out:
-3p(p-10) - 6p(p-10) = -9p(p-10).
Upon factoring out the common factor, our expression simplifies to -9p(p-10). Next, we simplify this expression by removing the parentheses and multiplying through by the common factor:
-9p(p - 10) = -9p² + 90p.
Therefore, the simplified profit expression with no parentheses is -9p² + 90p.
The probability that an event will not happen is Upper P (Upper E prime) = 0.94. Find the probability that the event will happen.
Answer: P(Upper E' prime) = 0.06
Step-by-step explanation:
Not happen:P(Upper E prime) = 0.94
Happen: P(Upper E' prime) = ?
P(Upper E' prime) + P(Upper E' prime) = 1
Therefore
P(Upper E' prime) + 0.94= 1
P(Upper E' prime) =1- 0.94
P(Upper E' prime) = 0.06
Robert is Running in a race that is 3 miles long. A Distance marker is placed evenly every 1/2 mile from the beginning of the race until the end. What is the total number of distance markers on the trail?
Answer: the total number of distance markers on the trail is 6
Step-by-step explanation:
The total distance that Robert covers in the race is 3 miles.
If a distance marker is placed evenly every 1/2 mile from the beginning of the race until the end, then the total number of distance markers on the trail would be
3/0.5 = 6
The Masterfoods Company says that before the introduction of purple, yellow candies made up 20% of their plain candies, red another 20%, and orange, blue and green each made up 10%. The rest were brown. If you pick a THREE M&Ms in a row (assume with replacement), what is the probability that they are all Brown?
a. 0.09
b. 0.027
c. 0.3
d. 0.6
Answer:
b. 0.027
Step-by-step explanation:
We have been given that the Masterfoods Company says that before the introduction of purple, yellow candies made up 20% of their plain candies, red another 20%, and orange, blue and green each made up 10%.
Probability of a yellow candy would be 0.20 and probability of a red candy would be 0.20.
Probability of orange candy would be 0.10, probability of blue candy would be 0.10 and probability of green candy would be 0.10.
The probability of brown candy would be [tex]1-0.20-0.20-0.10-0.10-0.10=0.30[/tex]
To find the probability that three candies are all Brown, we will use multiplication rule of independent events as:
[tex]0.30\times 0.30\times 0.30=0.027[/tex]
Therefore, the probability that that three candies are Brown would be 0.027 and option 'b' is the correct choice.
The probability that they are all Brown is option b. 0.027.
The calculation is as follows;The probability of brown candy should be
= 1-0.20 -0.20 -0.10 - 0.10-0.10
= 0.30
Now
the probability should be
[tex]= 0.3^3[/tex]
= 0.027
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You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0.793. How confident can you be that your predicted value will be reasonably close to the actual value? A. I can’t be confident at all; this is about as close to a random guess as you can get. B. I can be a little confident; it might be close, or it might be way off. C. I can be very confident; it will be close, but it probably won’t be exact. D. I can be certain that my predicted value will match the actual value exactly.
Answer:
The correct option is c.
can be very confident; it will be close, but it probably won’t be exact.
Step-by-step explanation:
Correlation coefficient r lies between -1 and +1 , if r is close to +1 the variables compared are highly positively correlated. If r is close to -1 then the variables compared are highly negatively correlated. If r is close to zero then the correlation between the variables compared is low. If r=0 then the variables compared do not correlate at all.
The closer the correlation coefficient is to +1, the better the prediction.
Therefore since r=0.793 , the correlation coefficient is close to +1 , it means there is a highly positive correlation between variables. Therefore the correct option is c. If r is exactly +1 then we can say without any shadow of doubt that the prediction will be perfect.
A 28ft ladder leans against a wall so that the base of the ladder is 5ft away from the base of the wall. How far up the wall does the ladder reach?
Round to the nearest tenth.
Answer:
the top of the ladder is 27.5ft above the ground.
Step-by-step explanation:
The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.
The length of the ladder represents the hypotenuse of the right angle triangle.
The ground distance from the base of the wall to the foot of the ladder represents the adjacent side of the right angle triangle.
Therefore, to determine how high up is the top of the ladder on the wall, x, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
28² = x² + 5²
784 = x² + 25
x² = 784 - 25 = 759
x = √759 = 27.5ft
Using the Pythagorean theorem, the ladder reaches approximately 27.5 feet up the wall when the base is 5 feet from the wall.
Explanation:The question involves finding the height up a wall that a 28ft ladder reaches when its base is 5ft from the wall. To solve this, we will use the Pythagorean theorem which relates the sides of a right-angled triangle. The ladder, wall, and ground form a right-angled triangle with the ladder as the hypotenuse and the wall and ground as the other two sides.
Let h be the height the ladder reaches up the wall. Using the Pythagorean theorem, we have:
28² = h² + 5²
Solving for h:
28² - 5² = h²
784 - 25 = h²
759 = h²
h ≈ √759
h ≈ 27.5 (to the nearest tenth)
Therefore, the ladder reaches approximately 27.5 feet up the wall.
Consider triangle GHJ. Triangle G H J is shown. Angle G H J is a right angle. The length of the hypotenuse is 10 and the length of another side is 5. What is the length of line segment HJ? 5 units 5 StartRoot 3 EndRoot units 10 units 10 StartRoot 3 EndRoot units
Length of segment HJ is 5√3 units
Step-by-step explanation:
Here, apply the Pythagorean relationship where sum of squares of the sides equals the square of the hypotenuse.
Given that the hypotenuse, c= 10 units, and one of the side, a=5 units, then the other side can be calculated as;
a²+b²=c²
5²+b²=10²
b²=10²-5²
b²=100-25
b²=75
b=√75 = √3*25 = √3 *√25 = √3 *5 = 5√3
Length of segment HJ is 5√3 units
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Answer:
B
Step-by-step explanation:
Out of 200 people sampled, 110 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.
Answer:
From the sample of n= 200 people,
The proportion of people with kids is:
p'= 110/200= 0.55
The confidence interval for population proportion is given by:
[tex]p' - Z_{\alpha /2} \sqrt[]{\frac{p'(1-p')}{n} } } \leq P\leq p' + Z_{\alpha /2}\sqrt[]{\frac{p'(1-p')}{n} } }[/tex]
[tex]= p' - Z_{\alpha /2} \sqrt[]{\frac{0.55(0.45)}{200} } } \leq P \le p' + Z_{\alpha /2} \sqrt[]{\frac{0.55(0.45)}{200} } }[/tex]
[tex]= p' - Z_{\alpha /2} 0.0352} } } \leq P\le p' + Z_{\alpha /2} 0.0352} }[/tex]
Where P is the population proportion and Z is the critical value at a given level of significance α.
I got 13.7 is that correct
Answer:
The answer to your question is 10.5 in
Step-by-step explanation:
Data
First triangle
height = x
base = 7 in
Second triangle
height = 12 in
base = 8 in
Process
1.- Use proportions to solve this problem, relates the sides of a triangle with the same sides of the other triangle.
[tex]\frac{x}{7} = \frac{12}{8}[/tex]
2.- Multiply both sides by 7
[tex]7\frac{x}{7} = \frac{7(12)}{8}[/tex]
3.- Simplify
x = [tex]\frac{84}{8}[/tex]
4.- Result
x = 10.5 in
When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do Upper P(Upper A)P(A) and Upper P(Upper A overbar)PA represent?
Answer:
When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do P(A) and P([math] \overline A [/math]) represent?
Step-by-step explanation:
To make lemonade, use 1 cup of lemon juice for every 3 cups of water. If you use 12 cups of water, how many cups of lemon juice will you need? Use a double number lineto solve.
Answer:
4 cups of lemon juice is required for 12 cups of water to make lemonade.
Step-by-step explanation:
Given:
To make lemonade 1 cup of lemon juice is required with 3 cups of water.
To find how many cups of lemon juice is required with 12 cups of water.
Solution:
We will construct a double number line of which one represents the cups of lemon juice and the other represents the cups of water.
From the number lines we can see that with 1 cup of lemon juice there are 3 cups of water.
So, ratio of cups of lemon juice to cups of water = 1 : 3
If we require [tex]x[/tex] cups of lemon juice with 12 cups of water then ratio = x : 12
Since ratio will always be equivalent, so we can write it as:
[tex]\frac{x}{12}=\frac{1}{3}[/tex]
Multiplying both sides by 12.
[tex]12.\frac{x}{12}=12\times\frac{1}{3}[/tex]
∴ [tex]x=4[/tex]
Thus, 4 cups of lemon juice is required for 12 cups of water to make lemonade.
A number is picked randomly in the range [2,8]. If past selection indicates that the numbers picked are less than 5, what is the probability that a number picked will be (a) less than 4 (b) greater than 4. What is the probability that the number picked is 4.5
Answer:
a) P = 2/7
b) P = 4/7
c) P = 1/7
Step-by-step explanation:
In the range of [2,8], we have the following integers which are: 2, 3, 4, 5, 6, 7, 8. So this is a total of 7 integers.
a) We look for the probability that the numbers are less than 4, so we conclude that there are possible numbers 2 and 3 out of possible 7, so the required probability is equal to P = 2/7.
b) We look for the probability that the numbers are greater than 4, so we conclude that there are possible numbers 5, 6, 7, 8 out of possible 7, so the required probability is equal to P = 4/7.
c) Based on the previous two examples, we conclude that the required probability is P = 2/7· 1/2=1/7.
The point of a square pyramid is cut off, making each lateral face of the pyramid a trapezoid with the dimensions shown. What is the area of one trapezoidal face of the figure?
The area of one trapezoidal face of the figure is 2 square inches
How to determine the area?The dimensions of the trapezoid are given as:
Base = 3 inchesHeight = 1 inchTop side length = 1 inch.The area of one trapezoidal face of the figure is the calculated using:
Area = 0.5 * (base + top side) * height
So, we have:
Area = 0.5 * (3 + 1) * 1
Evaluate
Area = 2
Hence, the area of one trapezoidal face of the figure is 2 square inches
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Answer: 2
Step-by-step explanation:
Rick buys and sells antiques via the Internet. So far, he has profited $2,502. Based on his profits to date, he developed the following linear model where x represents time in months, and y represents his total profits, in dollars. Interpret the slope.y = 2,502 + 417x
a. An additional month of buying and selling is associated with an additional $2,919 in profits.
b. An additional month of buying and selling is associated with an additional $2,502 in profits.
c. An additional month of buying and selling is associated with an additional $2,085 in profits.
d. An additional month of buying and selling is associated with an additional $417 in profits.
Answer:
d. An additional month of buying and selling is associated with an additional $417 in profits.
Step-by-step explanation:
We have general form of intercept form of equation:
y = m*x + c ----- (A)
Given equation is : y = 2502 + 417*x
Rewrite equation: y = 417*x + 2502 ------(B)
comparing equation (B) with equation (A), we get
m = 417 (additional benefits per month) because multiplied factor x is the month.
Final answer:
The slope in Rick's linear model represents an additional profit of $417 for each additional month of buying and selling antiques, making option d correct.
Explanation:
Rick's linear model for his profits from buying and selling antiques is given by the equation y = 2,502 + 417x, where x represents time in months and y represents his total profits in dollars. The coefficient of x in this equation, which is 417, represents the slope of the line.
In this context, the slope indicates that for each additional month of buying and selling antiques, Rick's profits are expected to increase by $417. Therefore, the correct interpretation of the slope is that an additional month of buying and selling is associated with an additional $417 in profits, making option d the correct answer.
which of the following values for x and y satisfy the following system of the equations?
{ x + 4y = 10
{5x + 10y = 20
a. x = 3, y = 2
b. x = 2, y - 3
c. x = -2, y = 3
d. x = 3, y = -2
Answer:
The answer to your question is letter C
Step-by-step explanation:
Equations
x + 4y = 10
5x + 10y = 20
Process
1.- Substitute all the options in both equations and evaluate them
a) x = 3, y = 2 This option is incorrect
(3) + 4(2) = 10 3 + 8 = 10 11 ≠ 10
5(3) + 10(2) = 20 15 + 20 = 20 35 ≠ 20
b) x = 2, y = -3 This option is incorrect
(2) + 4(-3) = 10 2 -12 = 10 -10 ≠ 10
(2) + 10(-3) = 20 2 - 30 = 20 -28 ≠ 20
c) x = -2, y = 3 This is the right answer
(-2) + 4(3) = 10 -2 + 12 = 10 10 = 10
5(-2) + 10(3) = 20 -10 + 30 = 20 20 = 20
d) x = 3, y = -2 This option is incorrect
(3) + 4(-2) = 10 3 - 6 = 10 - 3 ≠ 10
5(3) + 10(-2) = 20 15 - 20 = 20 -10 ≠ 10