32 miles ---------> 1 gallon
30 miles--------------> xgallons
Solving for x:
32/30 = 1/x
x = 30/32 = 0.9375 gallons
1 gallon ------>$2.55
0.9375 gallons----->$y
1/0.9375 = 2.55/y
Solving for y:
y = 2.55*0.9375 = $2.390625
It will cost $2.390625
Sophie is going to drive from her house to City A without stopping. Let D represent Sophie's distance from City A t hours after leaving her house. The table below has select values showing the linear relationship between t and D. Determine the average speed that Sophie travels, in miles per hour.
Answer:
55 miles per hour.
Explanation:
To determine the average speed traveled by Sophie, we find the slope of the function given from the linear table.
[tex]\begin{gathered} \text{Slope}=\frac{82.5-165}{2.5-1} \\ =-\frac{82.5}{1.5} \\ =-55 \end{gathered}[/tex]What this means is that Sophie's distance from City A is reducing at a rate of 55 miles per hour.
Thus, the average speed that Sophie travels, is 55 miles per hour.
could someone help me with this math problem? thanks a lot if you do (:
We will have the following:
First, we determine the slope of the linear relationship:
[tex]m=\frac{320-380}{2.75-2.5}\Rightarrow m=-240[/tex]a) Now, using this information and one point (2.50, 380) we will replace in the general equation for a linear function, that is:
[tex]\begin{gathered} N(p)-y_1=m(p-x_1)\Rightarrow N(p)-380=-240(p-2.5) \\ \\ \Rightarrow N(p)-380=-240p+600 \\ \\ \Rightarrow N(p)=-240p+980 \end{gathered}[/tex]So, the equation is:
[tex]N(p)=-240p+980[/tex]b) We determine the revenue function as follows:
[tex]\begin{gathered} R(p)=pN(p)\Rightarrow R(p)=p(-240p+980) \\ \\ \Rightarrow R(p)=-240p^2+980p \end{gathered}[/tex]So, the equation of revenue is:
[tex]R(p)=-240p^2+980p[/tex]c) We determine the critical points of the revenue:
[tex]\begin{gathered} R^{\prime}(p)=-480p+980=0\Rightarrow480p=980 \\ \\ \Rightarrow p=\frac{49}{24}\Rightarrow p\approx2.04 \end{gathered}[/tex]So, the price that maximizes revenue is approximately $2.04.
The maximum revenue will be:
[tex]\begin{gathered} R(2.04)=-240(2.04)^2+980(2.04)\Rightarrow R(2.04)=1000.416... \\ \\ \Rightarrow R(2.04)\approx1000.42 \end{gathered}[/tex]So, the maximum revenue is approximately $1000.42.
Can you help me with problem #1 I think I remember how to do it but just want to make sure
1)
[tex]3x-2y=-16[/tex]To convert this equation into slope-intercept form we have to isolate y. Subtracting 3x at both sides of the equation:
[tex]\begin{gathered} 3x-2y-3x=-16-3x \\ -2y=-3x-16 \end{gathered}[/tex]Dividing by -2 at both sides of the equation:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{-3x-16}{-2} \\ y=\frac{-3x}{-2}+\frac{-16}{-2} \\ y=\frac{3}{2}x+8 \end{gathered}[/tex]What is the distance between points (-8,5) and (7,-3)? (Hint. Use the distance formula)
SOLUTION:
We are to find the distance between points (-8,5) and (7,-3).
[tex]\begin{gathered} \sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \text{where x}_1=-8,x_2=7,y_1=5andy_2=-3_{} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{(7-(-8))^2+(-3-5)^2} \\ \\ \sqrt[]{(7+8)^2+(-8)^2} \\ \\ \sqrt[]{15^2_{}+(-8)^2} \\ \\ \sqrt[]{225+64} \\ \\ \sqrt[]{289} \\ 17\text{ units} \end{gathered}[/tex]CONCLUSION:
The distance between points (-8,5) and (7,-3) is 17 units.
What is the slope of (17, 11) (5, 0)
Solution
- The formula for the slope is given below:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where,} \\ (x_1,y_2)\text{ and (}x_2,y_2)\text{ are the coordinates of the points given} \end{gathered}[/tex]- We have been given the points (17, 11) and (5, 0).
- Thus, we can proceed to find the slope as follows:
[tex]\begin{gathered} x_1=17,y_1=11 \\ x_2=5,y_2=0 \\ \\ \therefore m=\frac{0-11}{5-17}=-\frac{11}{-12} \\ \\ \therefore m=\frac{11}{12} \end{gathered}[/tex]Final Answer
The value for the slope is
[tex]\therefore m=\frac{11}{12}[/tex]im on a bit of a time crunch so please go fast
Solution
[tex]undefined[/tex][tex]Slope=\frac{24-12}{4-2}=\frac{12}{2}=6[/tex]The final answer
[tex]6\text{ feets}[/tex]the Venn diagram below models the possibility of three events a b and c the probabilities for each event or given by the ratio of the area of the event to the total area of 72 for example event C is read-only so for the probability that event C,you haveP(C)=area Red/total area =18/12×6=18/72=1/4=0.25are A&B dependent or independent events use conditional probability to support your conclusion
The events A and B are dependent events. This is because unlike the red area, event A means green given that blue has already occured. Event A includes blue and green and then event B includes green and yellow. Therefore event B cannot take place unless event A (which includes green area) has already taken place. Same goes for event A, it cannot take place unless event B has occured because the green area occurs in event B. Both events are dependent events. The result of one will influence the result of the other on.
**Event C is the only independent event**
x^2+3x-6 Find the Discriminat and state how many solutions and type of zero
Solution
Discriminant
- The formula for the discriminant of a quadratic equation is:
[tex]\begin{gathered} \text{ Given,} \\ ax^2+bx+c \\ \\ \text{ The Discriminant is:} \\ D=b^2-4ac \end{gathered}[/tex]- Applying the formula, we have:
[tex]\begin{gathered} a=1,b=3,c=-6 \\ \\ \therefore D=3^2-4(1)(-6) \\ D=9+24 \\ D=33 \end{gathered}[/tex]- Discriminant is 33
How many solutions
- If the discriminant is > 0, then, the Quadratic equation has 2 solution.
- If the discriminant is = 0, then, the Quadratic equation has 1 solution
- If the discriminant is < 0, then, the Quadratic equation has no real solutions.
- The discriminant is 33 > 0, thus, the Quadratic equation has 2 solutions
Type of zero
- Since there are 2 solutions, then, it has real solutions
Final Answer
OPTION B
Where are you most likely to build up enough static charge to receive a shock? O A. In a rain forest B. On a concrete sidewalk on a dry day O c. On a nylon carpet in a dry area O d. On a nylon carpet in a hotel by the beach
Where are you most likely to build up enough static charge to receive a shock?
The correct answer is option C on a nylon carpet in a dry area
Explanation:
As nylon is a good conductor of electricity, the static electricity accumulatedin the body does ntot flow to the ground. Also, when we touch a metal object directly connected to the ground, a difference in electric charges creates a static electric discharge.iAs a reult ,we receive a shock.
To find the missing length below, would you use Law of Sines or Law of Cosines?Find the missing length. There are 2 answers, Law of _____ and missing side length.
A flagpole 3m tall casts a shadow5m long at the same time a nearby hill casts a shadow62m long. How Tall is the hill.
Explanation:
We are given information about the height of a flagpole and its shadow, and we also have information about the shadow of a hill.
This information is represented in the following diagram:
Where the symbol '?' represents what we are trying to find:
How tall is the hill
We will call this h for reference:
Since these shadows are happening at the same time, the ratio between these values must be the same, this is to say that
3/5 must be equal to h/62:
[tex]\frac{3}{5}=\frac{h}{62}[/tex]From this equation, we solve to find h:
[tex]\begin{gathered} \frac{3}{5}\times62=h \\ \end{gathered}[/tex]Solving the operations the result is:
[tex]\begin{gathered} 0.6\times62=h \\ \downarrow \\ 37.2=h \end{gathered}[/tex]The hill is 37.2 m tall.
Answer:
37.2 m
pls help for brainliest
Answer:
9 nickels, 8 dimes
Step-by-step explanation:
Let n = number of nickels, and let
d = number of dimes.
n + d = 17--------->.05n + .05d = .85
.05n + .10d = 1.25---->.05n + .10d = 1.25
------------------------
.05d = .40
d = 8, n = 9
Noah finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of the cutout squares used to make it. This is the graph Noah gets if he allows x to take on any value between -1 and 5.What is the approximate maximum volume for his box?
the real world domain would be 0 to 2.5, the maximum would be 15
3,400 mL. 34 L I need help which one is bigger
Answer: 34L is bigger than 3400mL
Given data
3, 400 mL and 34L
Firstly, we need to convert mL to L for unit consistency
1000mL = 1L
3, 400Ml = xL
Cross multiply
1000 * x = 1 x 3400
1000x = 3400
Divide both sides by 1000
1000x / 1000 = 3400/ 1000
x = 3.4 L
Therefore, 3400mL = 3.4L
34L is bigger than 3400mL
Given that sino =V48and cotê is negative, determine 0 and coté. Enter the angle O in degrees from the interval [0°, 360). Write the exact answer. Do not round.
In this problem
we have that
sin(theta) is positive and cos(theta) is negative
That means
the angle theta lies on the II quadrant
Remember that
[tex]\cot (\theta)=\frac{\cos(\theta)}{\sin(\theta)}[/tex]Find out the value of cos(theta)
[tex]\sin ^2(\theta)+\cos ^2(\theta)=1[/tex]substitute the given value
[tex](\frac{\sqrt[]{48}}{8})^2+\cos ^2(\theta)=1[/tex][tex]\cos ^2(\theta)=1-\frac{48}{64}[/tex][tex]\begin{gathered} \cos ^2(\theta)=\frac{16}{64} \\ \cos ^{}(\theta)=-\frac{4}{8} \end{gathered}[/tex]Find out the value of cot(theta)
substitute given values
[tex]\cot (\theta)=-\frac{4}{\sqrt[\square]{48}}[/tex]simplify
[tex]\cot (\theta)=-\frac{4}{\sqrt[\square]{48}}\cdot\frac{\sqrt[]{48}}{\sqrt[]{48}}=-\frac{4\sqrt[]{48}}{48}=-\frac{\sqrt[]{48}}{12}=-\frac{4\sqrt[]{3}}{12}=-\frac{\sqrt[]{3}}{3}[/tex]Find out the angle theta
using a calculator
angle in II quadrant
theta=120 degreesConvert to radians ---->The figure below shows a circular lawn. It’s diameter is 72 ft.a.Use 3.14 for n in your calculations,and do not round your answer.Make sure to include the correct units.B.Which measure would be used in finding the amount of fertilizer needed? C.Which measure would be used in finding the amount of tape needed?
Answers:
a) Area = 4069.44 ft²
Circumference = 226.08 ft
b) Area
c) Circumference
Explanation:
The area of the circular lawn can be calculated as:
[tex]\text{Area}=\pi\cdot r^2[/tex]Where π is 3.14 and r is the radius of the circular lawn.
The radius is half the diameter, so the radius is equal to:
[tex]r=\frac{\text{Diameter}}{2}=\frac{72\text{ ft}}{2}=36\text{ ft}[/tex]Then, the area of the lawn is equal to:
[tex]\begin{gathered} \text{Area = 3.14}\cdot(36ft)^2 \\ \text{Area}=3.14(1296ft^2) \\ \text{Area}=4069.44ft^2 \end{gathered}[/tex]On the other hand, the circumference of the lawn can be calculated as:
[tex]\text{Circumference = 2}\cdot\pi\cdot r[/tex]So, the circumference is equal to:
[tex]\begin{gathered} \text{Circumference = 2}\cdot\text{(3.14)}\cdot(36\text{ ft)} \\ \text{Circumference = }226.08\text{ ft} \end{gathered}[/tex]Finally, the fertilizer is applied to the region, so the measure that you would use to find the amount of fertilizer is the area.
In the same way, to surround the lawn, the measure that would be used to find the amount of tape is the circumference.
So, the answers are:
a) Area = 4069.44 ft²
Circumference = 226.08 ft
b) Area
c) Circumference
Me. Gray is going to save money until she can afford to buy a new television that cost $4,189 including tax. If she saves $60 each month
Given:
Ms. Gray wants to buy a new television that costs $4189.
She saves $60 each month.
To find the numbers of months will be required for her to save enough money to buy the television,
[tex]\frac{4189}{60}=69.8167\approx70[/tex]Verify,
[tex]\begin{gathered} \text{ \$ 60 for 70 months} \\ 60\times70=4200\text{ this is enough money to buy the television that costs \$4189} \end{gathered}[/tex]Answer: option J
|||RATIOS, PROPORTIONS, AND PERCENTSFinding the original amount given the result of a percentage...Va o- httpemployeesA company has been forced to reduce its number of employees. Today the company has 28% fewer employees than it did a year ago. If there are currently306 employees, how many employees did the company have a year ago?I need help with this math problem
The amount of employees on the previous year represents 100%. If today the company has 28% fewer employees, then the current amount of employees represents:
[tex]100\%-28\%=72\%[/tex]72% of the amount of employees of the previous year. Rewritting this percentage as a decimal, we have:
[tex]72\%=\frac{72}{100}=0.72[/tex]If we divide the current amount of employees by 0.72, we're going to find the original amount.
[tex]\frac{306}{0.72}=425[/tex]The company had 425 employees on the previous year.
Suppose 18 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 85% a month. If the yard can only sustain 100 plants, use a logistic growth model to estimate the number of plants after 3 months.
Answer
The estimated number of plants after 3 months using the logistic model = 70 blackberry plants
Explanation
If a population is growing in a constrained environment with carrying capacity K, and absent constraint would grow exponentially with growth rate r, then the population behavior can be described by the logistic growth model:
[tex]P_n=P_{n-1}+r(1-\frac{P_{n-1}}{K})P_{n-1}[/tex]From the question,
[tex]\begin{gathered} P_0=18,r=85\%=0.85,K=100 \\ \\ So, \\ \\ P_n=P_{n-1}=+0.85(1-\frac{P_{n-1}}{100})P_{n-1} \end{gathered}[/tex]After the first month,
[tex]\begin{gathered} P_{n-1}=P_0=18 \\ \\ \therefore P_1=P_0+0.85(1-\frac{P_0}{100})P_0 \\ \\ P_1=18+0.85(1-\frac{18}{100})18 \\ \\ P_1=18+0.85(1-0.18)18=18+0.85\times0.82\times18 \\ \\ P_1=18+12.546 \\ \\ P_1=30.546\text{ }plants \end{gathered}[/tex]After the second month,
[tex]\begin{gathered} P_1=30.546 \\ \\ \therefore P_2=P_1+0.85(1-\frac{P_1}{100})P_1 \\ \\ P_2=30.546+0.85(1-\frac{30.546}{100})30.546 \\ \\ P_2=30.546+0.85(1-0.30546)30.546=30.546+0.85\times0.69454\times30.546 \\ \\ P_2=30.546+18.033 \\ \\ P_2=48.579\text{ }plants \end{gathered}[/tex]So after 3 months,
[tex]\begin{gathered} P_2=48.579 \\ \\ \therefore P_3=P_2+0.85(1-\frac{P_2}{100})P_2 \\ \\ P_3=48.579+0.85(1-\frac{48.579}{100})48.579 \\ \\ P_3=48.579+0.85(1-0.48579)48.579=48.5796+0.85\times0.5142\times48.579 \\ \\ P_3=48.579+21.232 \\ \\ P_3=69.811\text{ }plants \\ \\ P_3\approx70\text{ }blackberry\text{ }plants \end{gathered}[/tex]The estimated number of plants after 3 months using the logistic model = 70 blackberry plants.
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.Passing through (5,3) with x-intercept 6Write an equation for the line in point-slope form.
In general, the equations of a line in point-slope form and slope-intercept form are:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y=mx+b \end{gathered}[/tex]respectively. Where m is the slope of the line, b is a constant, and (x_1, y_1) is a point on the line.
Thus, the point-slope form of the line described by the problem is:
[tex]y-3=m(x-5)[/tex]We simply need to calculate the slope of the line. For that, we simply require 2 points, we already have (5, 3) and, since the x-intercept is 6, we can deduce that the line goes through (0,6).
Therefore, the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-3}{0-5}=-\frac{3}{5}[/tex]Then, the solution is:
[tex]y-3=-\frac{3}{5}(x-5)[/tex]is √4 a perfect square root
A perfect square is a value that has a whole number square root. So, if the square root of anumber gives a whole number then the square root is called a perfect square root. The square root of 4, √4 is 2 . 2 is a whole number. So,Its square root is a whole number. Thus, √4 is a perfect square root.
y=2/3x-2y=-x+3solve for x and y
EXPLANATION
Given the system of equations:
(1) y = 2x/3 - 2
(2) y = -x +3
Substitute y= -x+3
-x + 3 = 2x/3 - 2
Isolate x for -x+3 = 2x/3 - 2
Subtract 3 from both sides:
-x + 3 - 3 = 2x/3 -2 - 3
Simplify:
-x = 2x/3 -5
Subtract 2x/3 from both sides:
-x - 2x/3 = 2x/3 - 5 -2x/3
Simplify:
-5x/3 = -5
Multiply both sides by 3:
3(-5x/3) = 3(-5)
Simplify:
-5x = -15
Divide both sides by -5
-5x/-5 = -15/-5
Simplify:
x = 3
Then, for y = -x + 3
Substitute x = 3
y = -3 + 3
Simplify:
y = 0
The solutions to the system of equations are:
y = 0 , x = 3
A circle has a diameter of 12 m. What is its circumference? Use 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer. Explanation Check 12 m 4
To find the circumference of a circle , we use the formula
[tex]C=\pi d[/tex]C = Circumference
d= diameter
[tex]\begin{gathered} C=3.14\times12 \\ C=37.68m^2 \end{gathered}[/tex]If angle A is a complement to angle B and the m
If Angle A is a complement to Angle B, then mIf we know the value of m[tex]\begin{gathered} m\measuredangle a+m\measuredangle b=90 \\ 31+m\measuredangle b=90 \\ m\measuredangle b=90-31 \\ m\measuredangle b=59 \end{gathered}[/tex]The measure of Angle B is 59°,
Write an equation in slope-intercept form of a line passingthrough the given point and parallel to the given line.3. (-3, -1);2y- 3x= 8
It's required to find the equation of a line that passes through (-3, -1) and is parallel to the line 2y - 3x = 8.
Solving for y:
[tex]y=\frac{3}{2}x+4[/tex]The slope of this line is 3/2 and the required line must have the same slope because they are parallel.
The point-slope form of a line passing through the point (h, k) and slope m is:
y = m(x - h) + k
Substituting:
[tex]\begin{gathered} y=\frac{3}{2}(x+3)-1 \\ Operate. \\ y=\frac{3}{2}x+\frac{9}{2}-1 \end{gathered}[/tex]Simplifying, the required line is:
[tex]y=\frac{3}{2}x+\frac{7}{2}[/tex]Can you help me solve the one with mrs Jones I want to know if I’m right
We know that
• 11 students own a cat.
,• 12 students own a dog.
,• 6 students own both a cat and a dog.
,• 3 students own neither.
First, let's draw a Venn diagram to visualize the problem.
First, we have to fund the total number of students inside the sets Cat and Dog. We need to subtract the number 6 once, otherwise, we'll count it twice.
[tex]11+12-6=17[/tex]Then, we include the students that own neither.
[tex]17+3=20_{}[/tex]Therefore, the total number of students is 20.-7(x - 2) = 38 - 3x
We need to solve the following expression:
[tex]-7(x-2)=38-3x[/tex]The first step to solve this problem is to apply the distributive property on the left side of the equation. This is given by the sum of the products. We have:
[tex]\begin{gathered} -7x-2\cdot(-7)=38-3x \\ -7x+14=38-3x \end{gathered}[/tex]We need to change the terms that have "x" from the right to the left. To do that we need to add "3x" on both sides.
[tex]\begin{gathered} -7x+14+3x=38-3x+3x \\ -7x+3x+14=38 \\ -4x+14=38 \end{gathered}[/tex]Then we need to subtract "14" on both sides to isolate the term with x on the left. We have:
[tex]\begin{gathered} -4x+14-14=38-14 \\ -4x=24 \end{gathered}[/tex]Then we need to divide both sides by "-4".
[tex]\begin{gathered} \frac{-4x}{-4}=\frac{24}{-4} \\ x=-6 \end{gathered}[/tex]The value of "x" that solves this equation is -6.
I need help with this I was absent in school and the teacher won’t help me
Step-by-step explanation:
Given the equation
-45n + 45 = 90
Step 1: Isolate n
We can isolate n by subtracting 45 from both sides
-45n + 45 - 45 = 90 - 45
-45n + 0 = 45
-45n = 45
Divide through by -45
-45n/-45 = 45/-45
n = -1
Hence, the value of n is -1
Which list includes the most important factors to consider when opening a savings account? O The fees, the interest rates, and the minimum deposit to open the account O The fees, the interest rates, and the bank's brand recognition O The fees, which bank your friend uses, and the minimum deposit to open the account O The fees, which bank your friend uses, and the bank's brand recognition
Answer:
The fees, the interest rates, and the minimum deposit to open the account
Answer: Based on the sales made by Micro Sales on bank credit cards, the journal entries would be:
Date Account Title Debit Credit
March 4 Cash $13,095
Card Service expense $ 405
Sales Revenue $13,500
How is the transaction by Micro Sales recorded?
The cash account will be debited with:
= 13,500 x (1 - 3%)
= $13,095
The Card service expense is:
= 13,500 x 3%
= $405
Sales revenue will be credited by the amount of sales which is $13,500.
Step-by-step explanation:
John has three parts that he mows each Park measures 2 and 1/2 miles by 2 3/4 miles how many square miles does he know in all
We will determine the number of square miles he mows as follows:
[tex]A=(2\frac{1}{2})(2\frac{3}{4})\Rightarrow A=(\frac{4}{2}+\frac{1}{2})(\frac{8}{4}+\frac{3}{4})[/tex][tex]\Rightarrow A=(\frac{5}{2})(\frac{11}{4})\Rightarrow A=\frac{55}{8}\Rightarrow A=6\frac{7}{8}\Rightarrow A=6.875[/tex]So, he mows 55/8 square miles for each park.