Explanation:
If he mowed the lawn exactly once, then 55 ≤ t ≤ 75 describes all the possible values of t. Basically t is between 55 and 75 inclusive of both endpoints.
Multiply each value by 3
55*3 = 165
75*3 = 225
That's how we end up with 165 ≤ t ≤ 225 to represent the possible span of time values where he mowed the grass three times. His fastest possible time is 165 minutes (2 hr, 45 min) and his slowest possible time is 225 minutes (3 hr, 45 min).
I am studying for the big test tomorrow and just need someone to go through this sheet I made with me.Sorry
SOLUTION
Let us solve the simultaneous equation
[tex]\begin{gathered} -2x-y=0 \\ x-y=3 \end{gathered}[/tex]using elimination
To eliminate, we must decide which of the variables, x or y is easier to eliminate. The variable you must eliminate must be the same and have different sign. Looking above, it is easier to eliminate y because we have 1y above and 1y below. But to eliminate the y's, one must be +y and the other -y. So that +y -y becomes zero.
So to make the y's different, I will multiply the second equation by a -1. This becomes
[tex]\begin{gathered} -2x-y=0 \\ (-1)x-y=3 \\ -2x-y=0 \\ -x+y=-3 \end{gathered}[/tex]So, now we can eliminate y, doing this we have
[tex]\begin{gathered} -2x-x=-3x \\ -y+y=0 \\ 0-3=-3 \\ \text{This becomes } \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]Now, to get y, we put x = 1 into any of the equations, Using equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2-y=0 \\ \text{moving -y to the other side } \\ y=-2 \end{gathered}[/tex]So, x = 1 and y = -2
Using substitution, we make y or x the subject in any of the equations. Looking at this, It is easier to do this using equation 2. From equation 2,
[tex]\begin{gathered} x-y=3 \\ \text{making y the subject we have } \\ y=x-3 \end{gathered}[/tex]Now, we will put y = x - 3 into the other equation, which is equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2x-(x-3)=0 \\ -2x-x+3=0 \\ -2x-1x+3=0 \\ -3x+3=0 \\ -3x=-3 \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]So, substituting x for 1 into equation 1, we have
[tex]\begin{gathered} -2x-y=0 \\ -2(1)-y=0 \\ -2\times1-y=0 \\ -2-y=0 \\ y=-2 \end{gathered}[/tex]Substituting x for 1 into equation 2, we have
[tex]\begin{gathered} x-y=3 \\ 1-y=3 \\ y=1-3 \\ y=-2 \end{gathered}[/tex]Now, for graphing,
d1 = 16 m; d2 = 14 m what's the rhombus?
Step 1 : To determine the area of the rhombus
[tex]\begin{gathered} d_1=16m,d_2\text{ = 14m } \\ Area\text{ = }\frac{1}{2}\text{ }\times d_1\text{ }\times d_2 \\ Area\text{ = }\frac{1}{2}\text{ }\times\text{ 16 }\times\text{ 14} \\ Area\text{ = }\frac{224}{2} \\ Area=112m^2 \end{gathered}[/tex]Therefore the area of the rhombus = 112m²
In 2002, the population of Isosceles City was 200,000. If expected growth is 10% per year, what will the expected population be in 2010?
The expected population in [tex]2010[/tex] will be [tex]428,717.762[/tex].
In [tex]2002[/tex] the population of Icosceles city was [tex]200,000[/tex].
The expected growth per year [tex]=10%[/tex]%
We have to find the expected population in [tex]2010[/tex].
From [tex]2002[/tex] to [tex]2010[/tex] the total years are [tex]8[/tex].
Since the population is increased every year so the population of previous year added. So we can see that the population is increased compound. We can find the total population by multiplying the population in 2002 with the rate assembled by one. So we can use the formula
Total population in [tex]2010=[/tex]Population in [tex]2002(1+\frac{rate}{100})^{year}[/tex]
Total population in [tex]2010=[/tex] [tex]2010=200,000(1+\frac{10}{100})^{8}[/tex]
Total population in [tex]2010=200,000(1+\frac{1}{10})^{8}[/tex]
Total population in [tex]2010=200,000(\frac{11}{10})^{8}\\[/tex]
Total population in [tex]2010=200,000(\frac{214,358,881}{100000000} )[/tex]
Total population in [tex]2010=200,000(2.14,358,881)[/tex]
Total population in [tex]2010=428717.762[/tex]
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I need help please and thank you and you have to graph it
From the graph provided we can determine two points which are;
[tex]\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(2,0) \end{gathered}[/tex]For the equation of the line given in slope-intercept form which is;
[tex]y=mx+b[/tex]We would begin by calculating the slope which is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We can now substitute the values shown above and we'll have;
[tex]\begin{gathered} m=\frac{(0-\lbrack-3\rbrack)}{2-0} \\ m=\frac{0+3}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]Now we have the slope of the line as 3/2, we can substitute this into the equation and we'll have;
[tex]\begin{gathered} y=mx+b \\ \text{Where;} \\ x=0,y=-3,m=\frac{3}{2} \end{gathered}[/tex]We now have the equation as;
[tex]\begin{gathered} -3=\frac{3}{2}(0)+b \\ -3=0+b \\ b=-3 \end{gathered}[/tex]We now have the y-intercept as -3. The equation now is;
[tex]\begin{gathered} \text{Substitute m and b into the equation,} \\ y=mx+b \\ y=\frac{3}{2}x-3 \end{gathered}[/tex]The graph of this is now shown below;
We shall now draw lines to indicate the 'rise' and 'run' of this graph.
ANSWER
Observe carefully that the "Rise" is the movement along the y-axis (3 units), while the "Run" is the movement along the x-axis (2 units).
This clearly defines the slope of the equation that is;
[tex]\frac{\Delta y}{\Delta x}=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{3}{2}[/tex]Solve the following simultaneous equation with elimination or substitution method
So, to solve the system:
To solve it, we could substitute the first equation in the second one and then solve for x:
We could solve the previous quadratic by factoring:
To find the values of y, just replace each vaue of x:
Therefore, the solutions of the system are
(x,y) = (-3,-1)
(x,y)=(1,3)
Henry had a batting average of 0.341 last season (out of 1000 at-bats, he had 341 hits). Given that thisbatting average will stay the same this year, answer the following questions. What is the probability that his first hit will not occur until his 5th at-bat? Answers. 0.64. 0.083. 0.129. 0.166
The probability of success (a hit) is given by:
p = 0.341
The complement (a failure) of this probability is:
q = 1 - 0.341 = 0.659
Then, we can construct a probability distribution for the first hit until his nth at-bat:
[tex]P(x=n)=p\cdot q^{n-1}[/tex]For his 5th at-bat, we have n = 5, then:
[tex]\begin{gathered} P(x=5)=0.341\cdot(0.659)^{5-1}=0.341\cdot0.659^4 \\ \\ \therefore P(x=5)=0.064 \end{gathered}[/tex]Which expression is undefined? (9-9) A 2 -3) )B. O C. )D. 0
Answer:
Option B
Step-by-step explanation:
Undefined expression:
An undefined expression is a division by 0, or a fraction in which the denominator is 0.
In this question, the undefined expression is given by option B.
Jacob is constructing a pentagonal tent for his school carnival. The tent has a side length of 5.13 meters. What is the area of the tent? What is the perimeter of the tent? What is the sum of three of the interior angles in the tent once Jacob obtains the value of its area and perimeter?
The tent is pentagonal , this means it has 5 sides. The tent have a side length of 5.13 meters.
The area of the pentagon can be calculated below
[tex]\begin{gathered} \text{area of the tent=}\frac{perimeter\times apothem}{2} \\ \tan \text{ 36=}\frac{2.565}{a} \\ a=\frac{2.565}{\tan \text{ 36}} \\ a=\frac{2.565}{0.726542528} \\ a=3.53041962601 \\ \text{perimeter}=\text{ 5.13}\times5=25.65\text{ meters} \\ \text{area =}\frac{25.65\times3.53041962601}{2} \\ \text{area}=\frac{90.5445}{2} \\ \text{area}=45.27225 \\ \text{area}\approx45.27meter^2 \end{gathered}[/tex]Each interior angle of a pentagon is
[tex]\begin{gathered} \text{ interior angle=}\frac{180\times3}{5}=\frac{540}{5}=108^{\circ} \\ \text{ Sum of thr}ee\text{ interior angles = 108}\times3=\text{ }324\text{ degre}e \end{gathered}[/tex]A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. Lin’s teacher uses the box to store her set of cubes with an edge length of 1/2 inch.If the box is completely full how many cubes are in the set?
To answer this question, we have to find the volume of one of the cubes from Lin's set. To do it use the formula to find the volume of a cube, which is the edgelength raised to 3:
[tex]\begin{gathered} V=ed^{3^{}} \\ V=(\frac{1}{2})^3 \\ V=\frac{1}{8} \end{gathered}[/tex]In this case, each cube has a volume of 1/8 cubic inches. To find the number of cubes in the set, perform the division of the volume of the box by the volume of one cube:
[tex]n=\frac{V_{box}}{V_{cube}}=\frac{56}{\frac{1}{8}}=8\cdot56=448[/tex]The set has 448 cubes.
100 points!!!!
PLS WRITE IN SLOPE INTERCEPT FORM
–18y + 8 = 12x
SOLVE FOR Y
Answer: y = (-2/3)x + (4/9)
Step-by-step explanation:
y = mx + b is the form expected
-18y + 8 = 12x
subtract 8 from both sides
-18y = 12x - 8
divide both sides by -18
y = (12x/-18) - (8/-18)
Simplify the negatives and pull x out of the parenthesis (this only works if x is in the numerator).
y = (-12/18)x + 8/18
Simplify the fractions
y = (-2/3)x + 4/9
Answer:
The required value of y is,
y = -(2/3)x + (4/9)Step-by-step explanation:
Given equation,
→ -18y + 8 = 12x
The slope-intercept form is,
→ y = mx + b
Let's rewrite the equation,
→ y = mx + b
→ -18y + 8 = 12x
→ -18y = 12x - 8
→ -y = (12x - 8)/18
→ -y = (2/3)x - (4/9)
→ y = -(2/3)x + (4/9)
Hence, this is the answer.
Jake and Joshua go to different theme parks during the day. Jake must pay a fee of $30 for a ticket and additional 4$ for every food/beverage. Joshua has to pay 50$ for a ticket and additional 6$ for the food and drinks. How many beverages and food would it take for Joshua to have the same amount of pay as Jake? Graph the item.Write a system of equations, graph them, and type the solution.
To answer this question, we will set a system of equations, and we will solve the system by the graphical method.
Let x be the number of times Jake buys drinks and food, then the total amount he will pay is determined by the following equation:
[tex]T=30+4x\text{.}[/tex]Its graph is:
Now, let x be the number of times Joshua buys drinks and food, then the total amount he will pay is determined by the following equation:
[tex]T=50+6x\text{.}[/tex]Graphing both equations we get:
The intersection of the graphs is the point,
a) rewrite each equation using function notation f(x) b) find f(3)
Hello there. To solve this question, we'll simply have to isolate y and plug in the value for x.
Given the equation:
4x - 3y = 8
To rewrite it using the notation y = f(x), subtract 4x on both sides and divide the equation by -3
-3y = 8 - 4x
y = - 8/3 + 4x/3
Now, plug in x = 3 in order to find f(3)
f(3) = -8/3 + 4 * 3/3 = -8/3 + 12/3 = 4/3
Question 1 of 10 - What is the value of the expression below when d= 5 and m = -2? d? + | dm|
Note the absolute value of any negative value is positive.
A pianist plans to play 4 pieces at a recital from her repertoire of 25 pieces, and is carefully consideringwhich song to play first, second, etc. to create a good flow. How many different recital programs arepossible?
Given 25 pieces of repertoire, if a pianist plans to play 4 pieces at a recital and is considering playing which song to play first, second, etc, the possible ways is,
[tex]^{25}P_4=\frac{25!}{(25-4)!}=\frac{25!}{21!}=303600\text{ possible recital programs}[/tex]Hence, the different recital programs possible is 303600
help meeeee pleaseeeee!!!
thank you
The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.
According to the question,
We have the following function:
f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]
Now, in order to find the value of f(0), we will put 0 in place of x.
f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]
f(0) = 0+7*0-0+12
(More to know: when a number is multiplied with 0 then the result is always 0 even the number being multiplied with zero is in lakhs.)
f(0) = 0+0-0+12
f(0) = 12
Now, in order to find the value of f(2), we will put 1 in place of x:
f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]
f(2) = -8+7*4-4+12
f(2) = -8+28-4+12
f(2) = 40 -12
f(2) = 28
Now, in order to find the value of f(2), we will put -2 in place of x:
f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]
f(-2) = -(-8) + 7*4+4+12
f(-2) = 8+28+4+12
f(-2) = 52
Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.
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Find the surface area of the cone. Use 3.14 for pi.The surface area is about __in.2.(I need just the answer, I don't need explanation)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
s = 50in
d = 20in
surface area of a cone = ?
Step 02:
surface area of a cone
SA = πr² + πrs
r = d/2 = 20in / 2 = 10in
SA = 3.14*(10in)² + 3.14*50in*10in
SA = 314in² + 1570in²
SA = 1884in²
The answer is:
SA = 1884in²
The table shows the linear relationship between the average height in feet of trees on a tree farm andthe number of years since the trees were planted,Average Tree HeightNumber of Years Sincethe Trees were planted1361115Average Height (ft)10244580108m
Rate of change = change in y / change in x
From the table, number of years since the tree are planted are the x
They are; 1, 3, 6, 11 , 15
Average height are y, and they are;
10, 24, 45, 80, 105
Now, to calculate the rate of change, we will find the difference between two values of y then divide it by the difference between 2 values of x
If we are going to pick the first and second value of y, we must also pick the first and second value of x
If we are to pick the second and 3rd value of y, we must then pick the 2nd and 3rd value of x
That is;
rate of change = 24 -10 / 3-2
= 14/2
= 7 ft/yr
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
-45 is an integer
√100 = 10 is a whole number
√89 is an irrational number-root
4.919191... is a rational decimal
-2/5 is a rational number-ratio
.12112111211112... is an irrational decimal
Finnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn
Kirsten is driving to a city that is 400 miles away. When Kirsten left home, she had 15 gallons of gas in her car. Assume that her car gets 25 miles per gallon of gas. Define a function f so that f(x) is the amount of gas left in her car after she has driven x miles from home. What are intercepts for that function. What do they represent.
The equation that gives us the amount of gas left in her car, given the driven miles, is
[tex]f(x)=15-\frac{x}{25}[/tex]Notice that when x=25, there will remain 14 gallons of gas in the tank.
The x-intercept is
[tex]\begin{gathered} f(x)=0 \\ \Rightarrow0=15-\frac{x}{25} \\ \Rightarrow x=15\cdot25=375 \end{gathered}[/tex](375,0). This is the maximum distance one can drive when the amount of gas in the tank reaches zero gallons.
On the other hand, the y-intercept is
[tex]\begin{gathered} x=0 \\ \Rightarrow f(x)=15 \end{gathered}[/tex](0,15). This is the number of gallons in the tank when we have driven 0 miles.
The number line below shows the values of x that make the inequality x > 1 true. Select all the values of x from this list that make the inequality x> 1 true. a. 3 b. -3c. 1 d. 700 e. 1.052. Name two more values of x that are solutions to the inequality.
Answer:
(a)3, 1, 700 and 1.05
(b)6 and 9
Explanation:
(a)The values of x from the list that make the inequality x> 1 true are:
3, 1, 700 and 1.05
(b)Two more values of x that are solutions to the inequality x>1 are:
6 and 9.
what is 9.77 with 8% tax
it will be 9.77+0.08(9.77)=10.5516
A deep-dish pizza is cut into twelve equal slices. If you eat four slices, how manydegrees of pizza do you eat?240°120°45°90°
The shape of the pizza is circular. This means that the total angle possible is 360 degrees.
Since the pizza have 12 equal slices
Then each slice will represent
[tex]\frac{360}{12}=30^0[/tex]Therefore, If you decide to eat 4 four slices, then
you will eat
[tex]4\times30^0=120^0[/tex]Answer = 120 degrees
Question
Refer to section 1.3.2, Credit scores, beginning on page 22 of the report.
Arrange the five tiers of credit scores in order, starting with the lowest tier of credit scores.
The five credit score tiers are listed in ascending order, starting with the lowest tier:
Deep Subprime < Subprime < near prime < prime < super prime
A consumer's credit score may have a big impact on their ability to receive credit. These interactive infographics show how lending practices have changed for borrowers with various credit score profiles.
We focus on the five credit score levels that are commercially available.
The range of subprime credit scores is 580 to 619.
The range of Prime's credit score is from 660 to 719.
Deep subprime credit scores fall below 580.
Near prime credit scores range from 620 to 659.
Super prime credit is defined as having a score of 720 or higher.
The following are the five credit scores, listed from lowest to highest:
Deep Subprime < Subprime < near prime < prime < super prime
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The owner of a movie theater was countingthe money from 1 day's ticket sales. He knewthat a total of 150 tickets were sold. Adulttickets cost $7.50 each and children's ticketscost $4.75 each. If the total receipts for theday were $891.25, how many of each kind ofticket were sold?
65 adult's ticket and 85 children's ticket was sold
Explanation:Let the number of tickets for children = x
Let the number of adults ticket = y
Total tickets = 150
x + y = 150 ....equation 1
The cost of tickets per child = $4.75
The cost of tickets per adult = $7.50
Total revenue from tickets = $891.25
Total revenue from tickets = The cost of tickets per child × number of children ticket +
The cost of tickets per adult * number of adults ticket
891.75 = 4.75(x) + 7.5(y)
891.75 = 4.75x + 7.5y ...equation 2
x + y = 150 ....equation 1
891.75 = 4.75x + 7.5y ...equation 2
Using substitution method by making x the subject of formula in equation 1:
x = 150 - y
Substitute for x in equation 2:
891.25 = 4.75(150 - y) + 7.5y
891.25 = 712.5 - 4.75y + 7.5y
891.25 = 712.5 + 2.75y
891.25 - 712.5 = 2.75y
178.75 = 2.75y
y = 178.75/2.75
y = 65
Substitute for x in equation 1:
x + 65 = 150
x = 150 - 65
x = 85
Hence, 65 adult's ticket and 85 children's ticket was sold
Rewrite the fallowing as an exponential expression in simplest form.
SOLUTION
[tex]\begin{gathered} 5x\sqrt[]{x} \\ 5x\times\sqrt[]{x} \\ 5x^1\times x^{\frac{1}{2}} \\ 5x^{1+\frac{1}{2}} \\ 5x^{\frac{3}{2}} \\ \end{gathered}[/tex]a sample size 115 will be drawn from a population with mean 48 and standard deviation 12. find the probability that x will be greater than 45. round the final answer to at least four decimal places
B) find the 90th percentile of x. round to at least two decimal places.
The probability that x will be greater than 45 is 0.1974.
The 90th percentile of x is 63.3786
Given,
The sample size drawn from a population = 115
The mean of the sample size = 48
Standard deviation of the sample size = 12
a) We have to find the probability that x will be greater than 45.
Here,
Subtract 1 from p value of the z score when x = 45
Then,
z = (x - μ) / σ
z = (45 - 48) / 12 = -3/12 = -0.25
The p value of z score -0.25 is 0.8026
1 - 0.8026 = 0.1974
That is,
The probability that x will be greater than 45 is 0.1974.
b) We have to find the 90th percentile of x.
Here,
p value is 0.90
Then, z score will be equal to 1.28155
Now find x.
z = (x - μ) / σ
1.28155 = (x - 48) / 12
15.3786 = x - 48
x = 15.3786 + 48
x = 63.3786
That is,
The 90th percentile of x is 63.3786
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May I please help with this. I have tried to find the correct answers but still couldn’t get them right
Solution
[tex]1cm\text{ to 7in}[/tex]We can use ratio to solve the problem
Part A
5cm to x in
[tex]\begin{gathered} 1cm\colon7in \\ 5cm\colon x\text{ in} \end{gathered}[/tex]Now
[tex]\begin{gathered} 1\colon7 \\ 5\colon x \\ \therefore\frac{1}{7}=\frac{5}{x} \\ \\ \text{cross multiply} \\ 1\times x=5\times7 \\ x=35 \end{gathered}[/tex]The final answer
[tex]5cm\text{ to 35inches}[/tex]Part B
Similar step as part a
[tex]\begin{gathered} 1\colon7 \\ y\colon63 \\ \frac{1}{7}=\frac{y}{63} \\ \\ \text{cross multiply} \\ 7y=63 \\ \text{divide both sides by 7} \\ \frac{7y}{7}=\frac{63}{7} \\ y=9 \end{gathered}[/tex]The final answer
[tex]9cm\text{ to 63inches}[/tex]Summary
please try to answer quickly because my brainly app keeps crashing before i get the answer.
Answer:
Explanations:
The formula for calculating the surface area of a sphere is given as:
[tex]SA=4\pi r^2[/tex]Determine the radius of the sphere given the Circumference 4cm. Recall that;
[tex]\begin{gathered} C=4cm \\ 2\pi r=4 \\ r=\frac{4}{2\pi} \\ \end{gathered}[/tex]Substitute the resulting radius into the sphere's surface area
[tex]\begin{gathered} SA=4\pi\cdot(\frac{4}{2\pi})^2 \\ SA=4\pi\cdot\frac{16}{4\pi^2} \\ SA=\frac{16}{\pi} \\ SA=\frac{16}{3.14} \\ SA=5.096\approx5cm^2 \end{gathered}[/tex]Hence the surface area of the spherical object is 5 squar
A popcorn stand offers buttered or unbuttered popcorn in three sizes: small, medium, and large. What is the P(buttered)
The popcorn we can order is either buttered or unbuttered.
Therefore, the probability of choosing buttered popcorn is 1/2
There is a raffle with 250 tickets. One ticket will win a $320 prize, one ticket will win a $240 prize, one ticket will win a $180 prize, one ticket will win a $100 prize, and the remaining tickets will win nothing. If you have a ticket, what is the expected payoff
Given that: There is a raffle with 250 tickets. One ticket will win a $320 prize, one ticket will win a $240 prize, one ticket will win a $180 prize, one ticket will win a $100 prize, and the remaining tickets will win nothing.
The expected payoff will be:
[tex]\begin{gathered} EV=\frac{1}{250}(320)+\frac{1}{250}(240)+\frac{1}{250}(180)+\frac{1}{250}(100)+\frac{246}{250}(0) \\ EV=\frac{320+240+180+100}{250} \\ EV=\frac{840}{250} \\ EV=3.36 \end{gathered}[/tex]So the expected payoff will be $3.36.
