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Related Questions
How many orders of magnitude is $1000 than a nickel?
Answers
Hope this helped :D good luck!!! have a nice day. :D
1000/.05=20,000=2*10^4
Since the since the exponent of the 10 power is 4, $1000 is 4 orders of magnitude greater than a nickel
find the solution of the system of equations.
-7x-6y=59
-8x-6y=58
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-7x - 6y = 59
-1( -8x - 6y = 58)
New equations...
-7x - 6y = 59
8x + 6y = 58 (Add equations)
---------------------
1x = 1
Divide
x = 1
Now find the y value.
-7(1) - 6y = 59
-7 - 6y = 59
Add 7 to both sides.
-6y = 66
Divide
y = -11
So your solution is ( 1, -11)
I hope this helps love! :)
six turns of a wire are wrapped around a pipe with a length of 24 inches in length and a circumference of 4 inches. What is the length of the wire?
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Length of wire = 4*6 = 24 inches
Suppose a parabola has a vertex (5,-3) and also passes through (6,1). Write the equation of the parabola in vertex form
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[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ \begin{cases} h=5\\ k=-3 \end{cases}\implies y=a(x-\stackrel{h}{5})^2\stackrel{k}{-3} \\\\\\ \textit{now, we also know that } \begin{cases} x=6\\ y=1 \end{cases}\implies 6=a(1-5)^2-3 \\\\\\ 9=a(-4)^2\implies 9=16a\implies \cfrac{9}{16}=a\qquad thus\quad \boxed{y=\cfrac{9}{16}(x-5)-3}[/tex]
The equation of the parabola with vertex (5, -3) and passing through (6, 1) in vertex form is y = [tex]4(x - 5)^2 - 3.[/tex]
To write the equation of a parabola in vertex form, we use the formula:
y = [tex]a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola. Given the vertex (5, -3) and a point (6, 1) the parabola passes through, we can plug these values into the equation to find a.
For the point (6, 1):
[tex]1 = a(6 - 5)^2 - 3[/tex]
[tex]1 = a(1)^2 - 3[/tex]
4 = a
So, the equation of the parabola in vertex form is:
y = [tex]4(x - 5)^2 - 3[/tex]
how to convert 8.6 into mixed numbers
Answers
8.6/1
Now, move the decimal one place to the right to make the numbers whole.
86/10
Divide and find the remainder.
86 / 10 = 8 remainder 6.
8 would be the big number, 6 the numerator, and 10 the denominator. That looks like this:
[tex]8 \frac{6}{10} [/tex]
We can simplify 6 and 10, though, by dividing both of them by 2.
6 / 2 = 3
10 / 2 = 5
Now, we have this:
[tex]8 \frac{3}{5} [/tex]
A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 30 thousand miles and a standard deviation of 10 thousand miles. complete parts (a) through (c) below.
a. nbsp what proportion of trucks can be expected to travel between 18 and 30 thousand miles in a year?
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To solve this problem, we have to make use of the z statistic. The formula for z score is:
z = (x – u) / s
where x is the sample value = 18,000 to 30,000, u is the sample mean = 30,000, and s is the standard deviation = 10,000
at x = 18,000
z = (18,000 – 30,000) / 10,000 = - 1.2
at x = 30,000
z = (30,000 – 30,000) / 10,000 = 0
So find for the P at values of z = -1,2 and z = 0.
P (z = - 1.2) = 0.1151
P (z = 0) = 0.5000
The proportion in between is the difference:
P (18,000 < x < 30,000) = 0.5000 – 0.1151 = 0.3849
So about 38.49% can be expected to travel 18,000 to 30,000 miles in a year
Using z-scores and the normal distribution, we can calculate that approximately 38.49% of trucks can be expected to travel between 18 and 30 thousand miles in a year.
Explanation:This problem involves the normal distribution in mathematics, particularly statistics. Given that the distance travelled per truck per year is normally distributed, we can calculate the proportion of trucks that may be expected to travel between 18 and 30 thousand miles in a year using z-scores.
The first step is to calculate the z-scores for the two distances we are concerned with. The z-score is a measure of how many standard deviations an element is from the mean. Given a mean of 30 thousand miles and a standard deviation of 10 thousand miles, the z-score for 18 thousand miles is (18 - 30) / 10 = -1.2, and the z-score for 30 thousand miles is (30 - 30) / 10 = 0.
You then need to find the area between these two scores on a standard normal distribution table, which gives you the proportion of trucks likely to travel this distance. Looking up -1.2 and 0 in a standard normal table gives us values of 0.1151 and 0.5000 respectively. The difference between these two areas (0.5000 - 0.1151) is 0.3849, or 38.49% when expressed as a percentage. Thus, we can expect approximately 38.49% of trucks to travel between 18 and 30 thousand miles in a year.
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How many different pairs of numbers with a difference of 12
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e.g
12-0
13-1
14-2
Three years ago, Marry was three times as old as his brother. Five years from now he will be twice as old as his brother. How is Marry now?
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m - 3 = 3(b - 3)
m - 3 = 3b - 9
m + 6 = 3b
m/3 + 2 = b
5 years from now:
m + 5 = 2(b + 5)
m + 5 = 2b + 10
m - 5 = 2b
m/2 - 5/2 = b
combine:
m/3 + 2 = m/2 - 5/2
1. multiply by 6
2m + 12 = 3m - 15
2. add 15 - 2m to both sides
27 = m
Marry is 27 years old.
Which of the following ordered pairs represents the solution to the system of equations below?
-3x+2y=2
7x-3y=7
A. (2, 4)
B. (4, 7)
C. (7, 14)
D. (8, 13)
Answers
7x - 3y = 7 eq (2)
Mutiply eq (1) by 3 and eq (2) by 2:
-9x + 6y = 6
14x - 6y = 14
Add th two new equations:
-9x + 14x = 6 + 14
=> 5x = 20
=> x = 20/5
=> x = 4
Now from eq (1)
-3(4) + 2y = 2
=> 2y = 2 + 12
=> 2y = 14
=> y = 14 / 2
=> y = 7
So the ordered pair is (4,7)
Answer: option B. (4,7)
A rectangular floor is 24 feet long and 9 feet wide. What is the area of the floor in square yards?
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24
x
9
_____
216
you have a credit card with a balance of $1256.34 and a 9.5% APR. A late payment fee of $29.00 is added to the principal if you pay after 5/28. You make a payment for $200.00 on 5/28. How much interest did you pay?
Answers
Answer:
The interest paid will be $9.946 ≈ $9.95.
Step-by-step explanation:
p = 1256.34
r = [tex]9.5/12/100=0.007917[/tex] (monthly)
Now, given is :
A late payment fee of $29.00 is added to the principal if you pay after 5/28. You make a payment for $200.00 on 5/28.
As the payment is made on the last date, so no extra charge will be paid. So, it is simple interest of [tex]1256.34\times0.007917=9.946[/tex]
Hence, the interest paid will be $9.946 ≈ $9.95.
x+29=−11
what does X equal
Answers
-29 -29
x = -40
29 - 29 = 0
0 - (-11) = -11
-29 + -11 = -40
-40 + 29 = -11
The average American consumes about 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will 50 Americans consume in one week? Round to the nearest hundredth.
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We are given that one American consumes around 20 gallons of ice cream in a year. This means that the consumption is 20 gallons in 52.1429 weeks.
Now, first we will calculate the amount consumed by 1 American in one week using cross multiplication as follows:
consumption per week = (1*20) / (52.1429) = 0.38356 gallons
Now, to know the consumption of 50 Americans in one week, we will simply multiply the consumption of one American by 50 as follows:
consumption of 50 Americans = 0.38356 * 50 = 19.18 gallons/week
An interior angle and an exterior angle are adjacent. The interior angle measures 84°. What is the measure of the exterior angle?
Answers
so the exterior angles = 180 - 84 = 96 segrees.
The measure of the exterior angle is
What is Exterior Angle?External angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.
We have,
The interior angle measures 84°.
We know that
Exterior angle + interior angle = 180
Exterior angle = 180 - Interior angle
Exterior angle = 180 - 84
Exterior angle = 96
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Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?
Answers
have a great day :)
Answer:
11.33%
Step-by-step explanation:
Amount of salt which Larry has to mix= 15 grams
In 210 gm of salt solution, content of salt= 5%
Amount of salt in salt solution= 5 % of 210 grams
Amount of salt in salt solution= [tex]\frac{5}{100}[/tex] of 210 grams
Amount of salt in salt solution= [tex]\frac{21}{2}[/tex]
Amount of salt in salt solution= 10.5 grams
Now the 15 grams of salt have to mix with 5% of salt solution
Total amount of salt= 15+ 10.5
Total amount of salt = 25.5 gram
Total amount of salt solution=15+ 210= 225 grams
Percentage of salt in new solution=[tex]\frac{amount of new salt}{ amount of new solution}[/tex] ×100
Percentage of salt in new solution=[tex]\frac{25.5}{ 225}[/tex] ×100
Percentage of salt in new solution= 0.13333×100
Percentage of salt in new solution= 11.33% (approx)
Hence, the correct answer is 11.33%
Two students, Jennifer and Jamal, factored the trinomial 6x2 − 3x − 9. Jamal factored it as 3(2x − 3)(x + 1) and Jennifer factored it as (2x − 3)(3x + 3). Indicate which student factored the trinomial completely and which student did not, and explain why. (10 points)
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Jennifer multiplied the 3 into the (x+1) factor.
One month,ruby worked 6 hours more than Isaac, and Svetlana worked 4 times as many hours as ruby. Together they worked 138 hours find the number of hours each person worked
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Isaac- 18
Svetlana - 96
Find the perimeter of a triangle with sides 11 inches, 5 inches, and 13 inches. Show your work.
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11 + 5 + 13 = 29
29 inches is the perimeter.
What is the product of 4.5 ⋅ 105 and 1.6 ⋅ 102?
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Mr. Smith wishes to retire in 16 years. When he retires he would like to have $500,000 in his bank account. Mr. Smith's bank pays 10% per year compounded annually. How much should he deposit now to attain his goal?
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Final answer:
Mr. Smith should deposit $119,631.97 now to have $500,000 in his bank account after 16 years, assuming a 10% annual compound interest rate.
Explanation:
To calculate how much Mr. Smith should deposit now to attain his retirement goal of $500,000 in 16 years with an annual compound interest rate of 10%, we use the formula for the present value of a future sum, which is:
PV = FV / (1 + r)^n
Where:
PV is the present value (the amount to deposit now)
FV is the future value (the desired amount in the account)
r is the annual interest rate (as a decimal)
n is the number of years
Plugging in Mr. Smith's values, we have:
PV = $500,000 / (1 + 0.10)^16
Calculating the denominator first:
(1 + 0.10)^16 = 1.10^16 = 4.1772
Now, divide the future value by this amount:
PV = $500,000 / 4.1772
= $119,631.97
Therefore, Mr. Smith should deposit $119,631.97 now to reach his goal of $500,000 in 16 years with a 10% annual compound interest rate.
the scale on a map is 2 cm=25 miles. Dave measured the distance to the next town at 5cm. Hoiw many miles away is the next town?
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Answer:
The next town is 62.5 miles away.
Step-by-step explanation:
Scale problems can be solved by a simple rule of three.
The scale on a map is 2 cm=25 miles
This means that for each 2cm we measure on the map, the real distance is 25 miles.
Dave measured the distance to the next town at 5cm. Hoiw many miles away is the next town?
How many miles are 5 cm. So
2cm - 25 miles
5cm - x miles
[tex]2x = 25*5[/tex]
[tex]x = 62.5[/tex]
The next town is 62.5 miles away.
How to find the derivative of functions: y=(5x+7)(x+5)^3
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We want dy/dx.
dy/dx = (5x+7)(x+5)^3
dy/dx = (5x+7)3(x+5)^2 + (x+5)^3 (5)
We now simplify as much as possible.
dy/dx = 3(5x+7)(x+5)^2 + 5(x+5)^3
a shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50 if you buy 5 bags and spend $17 how many of each size bag did you buy
Answers
3 one-pound bags;2 three-pound bags
Answer
Find out the how many of each size bag did you buy .
To proof
Let us assume that the one-pound bags = x
Let us assume that the three-pound bags = y
As given
if you buy 5 bags
than the equation becomes
x + y = 5
As given
a shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50
if you buy 5 bags and spend $17
than the equation becomes
2x + 5.50y = 17
2x + 5.50y = 17
than the two equation are
2x + 5.50y = 17 and x + y = 5
mulitply x + y = 5 by 2 and subtracted from 2x + 5.50y = 17
2x - 2x + 5.50 y - 2y = 17 - 10
3.5y = 7
[tex]y = \frac{7}{3.5}[/tex]
y = 2
put y = 2 in x + y = 5
x = 5 -2
x = 3
Therefore one-pound bags of peanuts bags are 3 and three-pound bags of peanuts bags are 2 .
Hence proved
A cafe only sells two types of sandwiches, turkey, and steak. The cafe charges $4 for turkey sandwiches and $6 for steak sandwiches. Last month, the cafe sold $4524 worth of sandwiches. The cafe sold a total of 925 sandwiches.
How many turkey sandwiches did they sell?
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4t + 6s = 4524
4t + 6(925 - t) = 4524
4t + 5550 - 6t = 4524
-2t = 4524 - 5550
-2t = -1026
t = 1026/2
t = 513 <== 513 turkey sandwiches
t + s = 925
513 + s = 925
s = 925 - 513
s = 412 <=== 412 steak sandwiches
Answer:
They sold 513 turkey sandwiches.
Step-by-step explanation:
Let t be the number of turkey sandwiches and s be the number of steak sandwiches.
With these variables, we can create equations for the totals they've given us:
Total sandwiches = [tex]t+s=925[/tex]
Total income = [tex]4t+6s=4524[/tex]
Now we can solve the system for the number of turkey sandwiches and steak sandwiches
Isolate t for [tex]t+s=925[/tex] => [tex]t=925-s[/tex]Substitute [tex]t=925-s[/tex] into [tex]4t+6s=4524[/tex][tex]4\left(925-s\right)+6s=4524[/tex]
Solve for s[tex]3700-4s+6s=4524\\3700+2s=4524\\3700+2s-3700=4524-3700\\2s=824\\\frac{2s}{2}=\frac{824}{2}\\s=412[/tex]
For [tex]t=925-s[/tex] substitute s = 412[tex]t=925-412\\t=513[/tex]
They sold 513 turkey sandwiches and 412 steak sandwiches.
Jerry lost his credit card and instead of reporting it right away, he decides to continue looking for it believing he could find it. Some time passes and after two weeks, he logs into the account activity page of his credit card and sees a recent $500 internet purchase that was made by someone else. At that moment, he calls to report his card stolen. How much of this $500 charge is Jerry at risk for having to pay?
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Jerry did not report his lost credit card right away believing that he could find it. Fraudulent transactions were made on his account and he is responsible to pay the maximum amount of $50 under the Fair Credit Billing Act (FCBA).
Given points K'(1, -2) and L'(1, -4), what are the coordinates of the point J' that produces a triangle J'K'L' congruent to JKL resulting from a rotation of 90 degrees clockwise around the point (1, -6)?
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F(x, y) = y3/x, p(1, 3), u = 1 3 2i + 5 j (a) find the gradient of f.
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The gradient of F is (partial derivative of F with respect to x) i + (partial with respect to y) j.
Thus, G(x,y) = the gradient in question = (-y^3/x^2) i + (0) j (answer)
PLZ HELP!!!!! D: D: IM FAILING PLZ HELP ;cccc
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or
-2 is greater than -5
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a loss of 5 points is greater in magnitude than a loss of 2 points
meaning that the person who lost 5 points had a bigger loss (even though -5 is smaller than -2)
Another way to think of it: -5 is further away from 0, compared to the distance from -2 to 0. I recommend drawing a number line if you're having trouble visualizing it.
How many cubic centimeters are there in 2.11 yards^3? express your answer in cubic centimeters to three significant figures?
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1 cubic inch=16.39 cubic cm. 1 yard=36 inches. 36 x 2.11=75.96 cubic inches.
75.96 cubic in x 16.39 = 1244.9844 = 1.24 x 10³ cubic cm.
I believe this is correct
Answer:
1,613,219.190 cm^3
Step-by-step explanation:
There is 1 inch per every 2.53 cm, we just need to do the multiplication to the square:
[tex](\frac{2,11yards^3}{x})(\frac{91,44 cm}{1 yard})(\frac{91,44 cm}{1 yard})(\frac{91,44 cm}{1 yard})=\frac{764,558,8579cm^3*2,11yd^3}{1yd^3}\\x=1,613,219.190 cm^3[/tex]
SO now we know that 2,11 yards^3 are equal to 1,613,219.190 cm^3
Brittany received 8 silver dollars on her eighth birthday. After her next birthday she had 15 and after the next she had 22. After her eleventh birthday she had 29 silver dollars. How many silver dollars will she have after her 16th birthday if her collection increases at the same rate every year?