Jeremiah is starting with 17 inches of snow.
It's melting at a rate of 0.5 inches per hour.
After 3 hours, you'd have 17 - 0.5 - 0.5 - 0.5 = 15.5 inches.
For every hours that passes, you'll lose another 0.5 inches. So after 3 hours, you lost 3*0.5 inches. After 7 hours, you'd lose 7*0.5. After t hours, you'd lost t*0.5 inches.
After t hours, the formula will be 17 - 0.5*t inches are left.
The amount of snow on the lawn after t hours of melting is given by the equation 17 - 0.5t
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To find out how much snow Jeremiah would have on his lawn 3 hours after the snow began to melt
We need to subtract the amount of snow that would have melted from the initial amount of snow.
Amount of snow that would have melted = rate of melting x time = 0.5 inches/hour x 3 hours = 1.5 inches
Snow after 3 hours = Initial snow - Amount of snow that would have melted
= 17 inches - 1.5 inches
= 15.5 inches
Therefore, Jeremiah would have 15.5 inches of snow on his lawn 3 hours after the snow began to melt.
To find out how much snow Jeremiah would have on his lawn after t hours of snow melting, we can use the same formula:
Amount of snow that would have melted = rate of melting x time
= 0.5 inches/hour x t hours
= 0.5t inches
Snow after t hours = Initial snow - Amount of snow that would have melted = 17 inches - 0.5t inches
Hence, the amount of snow on the lawn after t hours of melting is given by the equation : Snow after t hours = 17 - 0.5t
To learn more on Equation:
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Kaitlin is on the swim team. each day she swims 950 m. how far does she swim in 5 days? in kilometers
Kaitlin swims 950 m each day .
Number of days = 5 days.
Distance covered in 5 days is calculated as,
[tex]undefined[/tex]Two figures similar when corresponding side lengths are ______ and corresponding angles are __________
ANSWER and EXPLANATION
We want to find the property of Similar Figures.
Similar figures are figures that have the same shape.
For two figures to be similar, then the ratio of their corresponding sides must be equal. Also, their corresponding angles must be congruent or equal.
Therefore, to fill the gap:
Two figures similar when corresponding side lengths are proportional and corresponding angles are congruent
That is the answer.
This table shows the cost per-unit of printing a given number of copies of a book.
We can perform a scatter plot of this data as:
It seems that there is an inverse relation between the cost per unit and the number of copies.
The cost per unit approaches an asymptote, so it may correspond to a total cost that is equal to a fixed cost plus a variable cost depending on the number of copies.
We can then calculate the total cost for each option by multiplying the unit cost by the number of copies and we will get:
Then, if we transform the data, we can see a positive correlation between the total cost and the number of copies.
This correlation can not be seen just by looking at the unit cost per copy.
Answer:
- If we consider the transformed data (total cost vs. number of copies), we can see a positive correlation.
- If we ony consider the original table (unit cost vs. number of copies), we can not see any correlation.
4.7 x 10^-2 in standard form.
To write in standard form, Since the exponent is negative 2, move the decimal point two units to the left.
[tex]0.047[/tex]The prices of 10 single-family, three-bedroomhomes for sale in Boston, Massachusetts, arelisted for a recent year. Find the mean, median,and mode (if one exists).$300,000, $2,495,000, $2,120,000, $220,000,$194,000, $391,000, $315,000, $330,000,$435,000, $250,000
The Solution.
The given data is
300000, 2495000, 2120000, 220000, 194000, 391000, 315000, 330000, 435000, 250000.
Re-arranging the above data in ascending order of magnitude, we have
194000, 220000, 250000, 300000, 315000, 330000, 391000, 435000, 2120000, 2495000.
Therefore, the mean is
[tex]\begin{gathered} Mean=\frac{\text{ sum}}{\text{ number }} \\ \\ \text{Mean}=\frac{(194+220+250+300+315+330+391+435+2120+2495)1000}{10} \\ \\ \text{Mean}=\frac{7050000}{10}=\text{ \$705,000} \end{gathered}[/tex]The Median is the sum of the two middle numbers divided by 2. That is,
[tex]\text{Median}=\frac{315000+330000}{2}=\frac{645000}{2}=\text{ \$322,500}[/tex]There is no mode since none of the numbers appeared more than once.
[tex]\text{Mode}=\text{ does not exist}[/tex]What is 4x10^-7 ? In write in standard form
Answer:
0.0000004
Step-by-step explanation:
To write in standard form:
For each power of 10 bigger than 0, we add a zero at the end of the number.
For each power of 10 less than 0, we add a zero before the number(the first one before the decimal point).
In this question:
4x10^(-7)
7 zeros before the number 4, with the first before the decimal point. So
0.0000004
How to count 100 dollar bills
There are different ways to count 100 dollars
One of them is count 100 individual 1$dollar
Other possible way is count 20 individual $5 dollar
Other possible way is count 10 individual 10$ dollar
other possible way is count 5 individual $20 dollar
And the other possibility is just have one $100 dollar
You could count the dollar bills individually or in sections for example:
1x100
5x20
10x10
20x5
Area involving rectangles and circlesEspañolVA training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 82 m long and 64 m wide.Find the area of the training field. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
8463.36 m^2
Explanation:
Given the length(l) of the rectangle as 82m and the width(w) as 64m, we can go ahead and determine the area of the rectangle as follows;
[tex]\begin{gathered} \text{Area of a rectangle }=l\times b \\ =82\times64 \\ =5248m^2 \end{gathered}[/tex]The two semi-circles are equivalent to one circle with a diameter of 64m, so the radius of the circle will be;
[tex]\text{Radius(r)}=\frac{Diameter(d)}{2}=\frac{64}{2}=32m[/tex]Let's go ahead and determine the area of the circle given pi as 3.14;
[tex]\begin{gathered} Area\text{ of a circle=}\pi\times r^2 \\ =3.14\times(32)^2 \\ =3.14\times1024 \\ =3215.36m^2 \end{gathered}[/tex]Therefore, the area of the training field can be determined by adding the area of the rectangle and that of the two semicircles;
[tex]\begin{gathered} \text{Area of the training field}=\text{Area of rectangle + Area of two semicircles} \\ =5248+3215.36 \\ =8463.36m^2 \end{gathered}[/tex]On a recent trip, a trucker traveled 150 miles at a constant rate. Because of road conditions, the trucker then reduce the speed by 35 mph. An additional 40 miles was traveled at the reduced rate. The entire trip took three hours. Find the rate of the tracker for the first 150 miles.
We will have the following:
We will have that the first part of the travel had a rate of "r".
The second part of the travel had a rate of "r - 35".
Now, we recall that:
[tex]v\ast t=d[/tex]So, the following is true:
[tex]\begin{gathered} (r+r-35)(3)=150+150+40\Rightarrow3(2r-35)=340 \\ \\ \Rightarrow2r-35=\frac{340}{3}\Rightarrow2r=\frac{445}{3} \\ \\ \Rightarrow r=\frac{445}{6} \end{gathered}[/tex]So, the rate at which the trucker traveled for the first 150 miles was 445/6 mi/h.
I need help with this question my answer was 80percent
The correct option is 80%
Explanation:Raul's goal = $5000
Raul's sale = $4000
This week, the percentage of his goal which he has achieved is:
[tex]\begin{gathered} \frac{4000}{5000}\times100 \\ \\ =\frac{4}{5}\times100=80 \end{gathered}[/tex]Applications Involving Rational Equations Create an equation that represents each scenario. Then use that equation to solve the given problem.
Miriam needs 8 consecutive throws to win
Here, we want to calculate the number of throws consecutively that Miriam must make into the cup to beat Ishak
Since Ishak made 48% already, Miriam must make 52%
Out of 30, she made 12;
This represents a percentage of;
[tex]\frac{12}{30}\text{ }\times\text{ 100\% = 40\%}[/tex]Let the number of throws needed be x;
So;
[tex]\begin{gathered} \frac{x+12}{30+x}\text{ }\times\text{ 100 = 52} \\ \\ 100(x+12)\text{ = 52(30+x)} \\ \\ 100x\text{ + 1200 = 1560+52x} \\ \\ 100x-52x\text{ = 1560-1200} \\ \\ 48x\text{ = 360} \\ \\ x\text{ = }\frac{360}{48} \\ \\ x\text{ = 7.5 which is approx 8} \end{gathered}[/tex]So what this mean is that, out of 38 throws, 20 would enter, with the last 8 being consecutive
MatnYou are dealt one card from a 52 card deck. Find the probability that you are dealt a ten or a black card.The probability is I (Type an integer or a fraction. Simplify your answer.)re
We have to find the probability that you are dealt a ten or a black card.
Out of the 52 card deck, there are 26 black cards.
There are also 4 cards that are tens, but there are 2 cards that are both black and tens.
Then, if we define B: the event of a black card and T: the event of a ten, we can calculate the probability of B or T as:
[tex]P(B\cup T)=P(B)+P(T)-P(B\cap T)[/tex]Replacing with the values of the probability (success events divided by the total possible events), we can solve this as:
[tex]\begin{gathered} P(B\cup T)=P(B)+P(T)-P(B\cap T) \\ P(B\cup T)=\frac{21}{52}+\frac{4}{52}-\frac{2}{52} \\ P(B\cup T)=\frac{21+4-2}{52} \\ P(B\cup T)=\frac{23}{52} \end{gathered}[/tex]Answer: the probability of getting a black or a ten is 23/52.
James invested $4,000 in his college fund. Several years later he had earned $2,240 in interest at a simple interest rate of 8%. How long was James money invested in the college fund.
Solve for x.y=5xy=30Simplify your answer as much as possible.x = 0308X Х$?
Using the vertical angle image from problem 1, let ∠2 = 4x-4 and ∠4 = x+50.
A. What is the value of x?
B. What is the measure of ∠2?
C. Find the measure of ∠3.
Answer:
A) x = 18, B) ∠2 = 68°, C) ∠3 = 112°Step-by-step explanation:
According to vertical angles theorem, when two lines intersect the opposite angles are equal and adjacent angles are supplementary.
Given∠2 = 4x-4 and ∠4 = x+50A) Find the value of x:
4x - 4 = x + 504x - x = 50 + 43x = 54x = 54/3x = 18B) Find the measure of angle 2:
∠2 = 4*18 - 4 = 72 - 4 = 68C) Angles 2 and 3 are supplementary so their sum is 180°.
∠2 + ∠3 = 18068 + ∠3 = 180∠3 = 180 - 68∠3 = 112°Answer:
A. x = 18
B. m∠2 = 68°
C. m∠2 = 112°
Step-by-step explanation:
Given:
[tex]\angle 2=4x-4[/tex][tex]\angle4=x+50[/tex]Part AVertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Therefore:
[tex]\implies \angle 2 = \angle 4[/tex]
[tex]\implies 4x-4= x+50[/tex]
[tex]\implies 4x-4-x= x+50-x[/tex]
[tex]\implies 3x-4= 50[/tex]
[tex]\implies 3x-4+4= 50+4[/tex]
[tex]\implies 3x=54[/tex]
[tex]\implies 3x\div 3=54 \div 3[/tex]
[tex]\implies x=18[/tex]
Part BTo find the measure of ∠2, substitute the found value of x into the given expression for ∠2:
[tex]\implies m\angle 2 =(4x-4)^{\circ}[/tex]
[tex]\implies m\angle 2 =[4(18)-4]^{\circ}[/tex]
[tex]\implies m\angle 2 =(72-4)^{\circ}[/tex]
[tex]\implies m\angle 2 =68^{\circ}[/tex]
Part CAngles on a straight line sum to 180°:
[tex]\implies m\angle 2 +m\angle 3=180^{\circ}[/tex]
[tex]\implies 68 ^{\circ}+m\angle 3=180^{\circ}[/tex]
[tex]\implies m\angle 3=180^{\circ}-68 ^{\circ}[/tex]
[tex]\implies m\angle 3=112 ^{\circ}[/tex]
The coordinates of quadrilateral WXYZ are W (-5.3), X(-5, -3), Y (8.–7), and Z (8,7). Which shape best describes quadrilateral WXYZ? O A kite O B. rectangle C. rhombus D. Trapezoid.
First we have to draw a simple figure with the coordinates.
As we can see it seems a trapezoid. option D
I'm not home and my phone is about to die please help
ANSWER
x = 9, y = 5
EXPLANATION
We have a system of two simultaneous equations:
-4x + 9y = 9 ______(1)
x - 3y = -6 ______(2)
From (2), we have that:
x = 3y - 6
Put that in (1):
-4(3y - 6) + 9y = 9
-12y + 24 + 9y = 9
Collect like terms:
-12y + 9y = 9 -24
-3y = -15
y = -15 / -3
y = 5
Recall that x = 3y - 6:
=> x = 3(5) - 6
x = 15 - 6
x = 9
So, x = 9, y = 5
Word problem involving a sine or cosine function: Problem type 1
Given:
a.) Amplitude = 9 cm
b.) Period = 0.5 seconds
c.) At time = 0, displacement from rest is -9 cm
The general equation for displacement as a function of time is:
[tex]\text{ d = -A }\cdot\text{ Cos}(\text{Bt - C) }+\text{ D}[/tex]The amplitude is given by A. Here, since amplitude is 9 cm, so we have:
A = 9
The period of the object is 0.5 seconds, so we have:
[tex]\text{ Period = 2}\frac{\text{ }\pi}{\text{ B}}[/tex][tex]\begin{gathered} 0.5\text{ }=\frac{1}{2}\text{= 2}\frac{\pi}{\text{ B}} \\ \text{ B = }(\text{ 2}\frac{\pi}{\text{ B}})(2) \\ \text{ B = 4}\pi \end{gathered}[/tex]Since the minimum displacement is at t = 0, so there is no phase shift.
Therefore, C = 0
Also since there is no vertical shift, so D = 0.
In Summary, we get: A = 9, B = 4π, C = 0 and D = 0
Thus the equation modeling the displacement d as a function of time t is given by:
[tex]\text{ d = -A }\cdot\text{ Cos}(\text{Bt - C) }+\text{ D}[/tex][tex]\text{ d = -9 }\cdot\text{ Cos}(4\pi\text{t - 0) }+0[/tex][tex]\text{ d = -9Cos}(4\pi\text{t)}[/tex]Therefore, the equation is:
[tex]\text{ d = -9Cos}(4\pi\text{t)}[/tex]B Order the sides of the triangle from shortest to longest. (HINT: Find the missing angle values first)
ANSWER
AB, AC, BC
EXPLANATION
We have the given triangle with an unknown angle.
Let us find the unknown angle first.
The angles in a triangle sum up to 180 degrees.
So:
65 + 40 + 5 + 7x = 180
110 + 7x = 180
=> 7x = 180 - 110 = 70
=> x = 70 / 7
x = 10
The unknown angle is therefore:
5 + 7(10) = 5 + 70
= 75 degrees
So, the angles of the triangle are 40, 65 and 75 degrees.
The sides of the triangle correspond to the angles opposite them. This means that the larger the angle, the longer the side opposite it.
The angles and their corresponding opposite sides area:
40 degrees => AB
65 degrees => AC
75 degrees => BC
This means that in the order of shortest to longest, the list is:
AB, AC, BC
In triangle ABC, if c = 46, b = 47....
1) In this question, the best way to tackle it is to sketch out that triangle:
2) Let's use The Law of Sines and then perform some algebraic manipulation:
[tex]\begin{gathered} \frac{b}{\sin(B)}=\frac{c}{\sin(C)} \\ \frac{47}{\sin(112)}=\frac{46}{\sin (C)} \end{gathered}[/tex]So let's cross multiply then:
[tex]\begin{gathered} \frac{47}{\sin(112)}=\frac{46}{\sin(C)} \\ 47\cdot\sin (C)=46\cdot\sin (112) \\ \frac{47\cdot\sin (C)}{47}=\frac{46\cdot\sin (112)}{47} \\ \sin (C)=\frac{46\cdot\sin(112)}{47} \end{gathered}[/tex]And that's the answer.
the graph shows the height, h, in itches of a plant after d days. What equation can you use to represent the situation?
From the given graph, we can note a linear behavior. In order to find the line equation, we need 2 points. One point is (0,0) and the other point is (6,4)
The line equation in slope-intercept form is
[tex]h=md+b[/tex]Since the slope formula for 2 point is
[tex]m=\frac{h_2-h_1}{d_2-d_1}[/tex]with
[tex]\begin{gathered} (d_1_{},h_1)=(0,0) \\ (d_2,h_2)=(6,4) \end{gathered}[/tex]we have that
[tex]\begin{gathered} m=\frac{4-0}{6-0} \\ \text{which gives } \\ m=\frac{4}{6}=\frac{2}{3} \end{gathered}[/tex]Then, our line equation has the form
[tex]h=\frac{2}{3}d+b[/tex]and we can find the y-intercept b by replacing one of the 2 points, The "easy" point in this case is (0,0), which gives
[tex]\begin{gathered} 0=\frac{2}{3}(0)+b \\ \text{then} \\ 0=0+b \\ or \\ b=0 \end{gathered}[/tex]Therefore, the answer is
[tex]h=\frac{2}{3}d[/tex]which corresponds to the last option from top to bottom
Lin is shopping for a couch with her dad and hears him ask the salesperson, "How much is your commission?" The salesperson says that her commission is 5% of the selling price, How much commission will the salesperson earn by selling a couch for $4957 Round your answer to the nearest hundredth
We have the following:
To calculate the value of the commission, we must multiply the value of the purchase by the percentage of the commission, in the following way:
[tex]4957\cdot\frac{5}{100}=247.85[/tex]Therefore, the answer is $247.85
Which equation shows 2.4 as the constant of proportionality? B. = C. a = 2-6 D.
Answer
Option B is correct.
(12/5) = 2.4
Explanation
If a varies directly as b, which can be written as
a ∝ b
Introducing the constant of variation, k, we have
a ∝ b
a = kb
Looking at the options, we can see that the last three options are the only ones in this form and of the three of them, only option B has the value before b equal to 2.4
Hope this Helps!!!
What is 3/4 of 1/2 of 64
Answer
24
Explanation
(3/4) of (1/2) of 64
Noting that 'of' stands for the multiplication sign, we have
[tex]\begin{gathered} \frac{3}{4}\times\frac{1}{2}\times64 \\ =\frac{3\times1\times64}{4\times2} \\ =3\times8 \\ =24 \end{gathered}[/tex]Hope this Helps!!!
5. BASEBALL Brandon ended the season with 30 hits out of 93 at bats. Mario ended the season with 20 hits in 62 at bats. Which player has a higher batting average, at bats ? hits
Answer:
Brandon and Mario have the same batting average.
Explanation:
We need to calculate the number of hits per bats for Brandon and for Mario.
So, the number of hits per bats for Brandon is:
[tex]\frac{30\text{ hits}}{93\text{ bats}}=0.323[/tex]At the same way, the number of hits per bats for Mario is:
[tex]\frac{20\text{ hits}}{62\text{ bats}}=0.323[/tex]Therefore, the number of hits per bats is equal for both players. It means that they have the same batting average.
_/4=12/16Find the answer for the blank space
We have to fill the blank to find an equivalent fraction:
[tex]\begin{gathered} \frac{x}{4}=\frac{12}{16} \\ x=\frac{12}{16}\cdot4 \\ x=12\cdot\frac{4}{16} \\ x=12\cdot\frac{1}{4} \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]Answer: fill the blank with 3.
What is the equation of the graphed line written in standard form? 1. 2x + 3y = -6 2. 2x + 3y = 6 3. y= -2/3 x -24. y= 2/3 x -2
Step 1
Write the point form slope equation of a line
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Wherefrom the graph
[tex]\begin{gathered} y_2=0 \\ x_2=-3 \\ x_1=0 \\ y_1=-2 \end{gathered}[/tex]Step 2
Substitute and get the equation
[tex]\begin{gathered} y\text{ -(-2)=}\frac{0-(-2)}{-3-0}(x-0) \\ y+2=\frac{2}{-3}x \\ y\text{ = -}\frac{2}{3}x-2 \end{gathered}[/tex]Hence the right answer is option C
Please Help!
{64,60,57,63,61,64,50,62,60,56,53,62,54,60,64,53,61,58,60,64,57,56,64,61,63}
According to Chebyshev's theorem, at least 88.9% of the data falls between approximately 47.62 and Blank
. (Round to the nearest hundredth.)
Answer: 100
Step-by-step explanation:
Because 88.9% of the data falls between approximately 47.62 and Blank.
Hello! I think I know the answer to this but I'm not 100% sure
Answer:
The system has no solutions.
Step-by-step explanation:
The intersection between the two lines is the only solution for the system. Since two parallel lines will never intersect.
There is NO solution for this system.
A T-shirt company has a goal to earn a monthly profit of more than $3,500.
20x -1500 > 3500
company charges $20 per shirt
$1500 = fixed cost
x Is the number of T-shirts. that needed to be sold for the company to meet its goal.
Since x is multiplied by 20 which is the charge per shirt, it is the number of t-shirts ( not profit )