5 is at the one-place value, and 0.5 is at the tenth-place value. 5 is ten times the value of 0.5.
What is described as the once and tenth place?There are one or more digit numbers in a number. 43 has the digits 4 and 3. The value of a numeral is determined by its position in the number.The number one in the number twelve is located in the tens place. The 2 in 12 is now in the one position. 95 has a 9 with in tens position and a 5 with in ones position.The number 0 is significant. The zero in twenty indicates there are no ones. That tells us that the 2 in 20 are in the tens. 20 is made up of two tens and zero ones.For the given question;
The speed of the world's biggest submarine is 25.5 miles per hour on the surface.
Thus, in the value of 25.5, the digit 5 lies on the once place.
The value 0.5 lies on the tenth place.
Now, it is clear that the 5 is the 10 times the value of 0.5, which is the required relation.
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8 A geometric sequence has all
positive terms. The sum of the
first two terms is 15 and the sum
to infinity is 27.
a
Find the value of the common
ratio.
b Hence, find the first term.
Let the terms be a, ar, ar², ...
The sum to infinity being 27 means that:
[tex]\frac{a}{1-r}=27 \implies a=27(1-r)[/tex]
The sum of the first two terms being 15 means:
[tex]a+ar=15 \\ \\ (27-27r)+r(27-27r)=15 \\ \\ 27-27r+27r-27r^2 =15 \\ \\ 27r^2 -12=0 \\ \\ 27r^2 =12 \\ \\ r^2=\frac{12}{27}[/tex]
Since all the terms are positive, r>0.
[tex]\boxed{r=\frac{2}{3}} \\ \\ \implies a=27\left(1-\frac{2}{3} \right)=\boxed{9}[/tex]
PLEASE HELP 4/z>3; z=2
answer and steps to get it in the picture
negative 19 plus the quantity negative 4 and five tenths plus 6 and 87 hundredths end quantity divided by 3 all times 5 squared minus 7 and 3 tenths
19.6
−18.4
31.45
−6.55
Answer:The answer is actually 19.6
Step-by-step explanation:
trust me I did the test
unlike others
4.
Juan was competing in a 1000 meter
race. He had to pull out of the race after
running 3/4 of it. How many meters did
he run?
Answer:14
Step-by-step explanation:
Step-by-step explanation:
B is the midpoint of AC, in other words it is the halfway point.
So A to B should be equal to B to C
Our expression is:
2x + 9 = 37
Subtract 9
2x = 28
Divide by 2
x = 14
Answer:
750
Step-by-step explanation:
3/4 is 75%
Juan did 75% of the 1000 meters meaning he did 750
To get the answer u just do (3/4)*1000 and you get 750
help please I don't quite understand the question much.
The profit in 2012 must be 4.5(in hundreds of dollars) to break even.
Profit for a company is defined as the difference between the revenue and cost of a product.
Let us take an example to learn more about profit.
A company sells a product at a price of 'S' dollars and the company spends 'C' dollars to manufacture the product. Here C includes the cost of raw materials, labor cost, transport etc.. Now the net profit for the company for selling one unit of this particular product is given by
Profit=S-C
When S>C the profit is positive.When S<C the profit is negative or loss .When S=C then the company breaks even.In the given chart it is shown the profit of the company is given as
2.5,1.75,-3.3 and -1.4 (in thousands of dollars) over 4 years.
Net profit over four years=[tex]2.5+1.75-3.3 -1.4=-0.45[/tex]
So over the past four years the company incurred a loss of
[tex]=0.45\times 1000\\[/tex]
[tex]=450[/tex] dollars
Now the company needs to break even in 2012.
So net profit must be zero over 5 years.
Therefore Profit in 2012=0-(-450)=450 dollars
Profit=4.5 (hundreds of dollars)
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Find the unique solution to this system of equations. Give your answer as a point
Answer:
(x, y, z) = (-4, -5, 2)
Step-by-step explanation:
You want the solution to the 3×3 system of equations ...
3x -y -4z = -15-4x -4y -z = 342x +3y +5z = -13ToolsThere are many tools available for solving a system of equations. A typical hand-held graphing calculator offers at least two methods. An online graphing calculator solution is shown in the attachment.
For the attached solution, we defined z in terms of x and y using the second equation. This effectively reduces the system to a 2×2 system, which is easily solved. The same "substitution" method can be used when solving the system by hand.
The graph shows the solution to be (x, y, z) = (-4, -5, 2).
Manual solutionUsing z = -4x -4y -34 from the second equation, the system reduces to ...
3x -y -4(-4x -4y -34) = -15
19x +15y = -151
and
2x +3y +5(-4x -4y -34) = -13
-18x -17y = 157
Writing these equations in general form, we have ...
19x +15y +151 = 018x +17y +157 = 0The "cross multiplication method" gives the solution for x and y as ...
D = (19)(17) -(18)(15) = 53
x = (15(157) -17(151))/D = -212/53 = -4
y = (151(18) -157(19))/D = -265/53 = -5
Then z is ...
z = -4(-4) -4(-5) -34 = 16 +20 -34 = 2
The solution is (x, y, z) = (-4, -5, 2).
__
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a multiplication problem that will have the answer of -48.
[tex]{\sf{12 \times ( - 4) = -48}}[/tex]
You’re assisting a craft vendor at a fair who sells 5 knit hats for $9.50 each. She then sells the sixth and seventh for $11.25 each, and the eighth and ninth for $8.75 each. At the end of the fair, she is charged 15% of her gross earnings for the booth space. How much money does she make after paying for the booth space?
She earned a total of:
[tex]5(9.50)+2(11.25)+2(8.75)=\$ 87.50[/tex]
If she pays 15% for the booth space, she keeps 85%.
[tex]87.50(0.85) \approx \boxed{\$ 74.38}[/tex]
through(–3, 8) and perpendicular to y=-1/4x-3
Answer:
it's is the way to do it
Step-by-step explanation:
the equation is X-4y-35
= How many gallons of a 60% antifreeze solution must be mixed with 60 gallons of 30% antifreeze to get a mixture that is 50% antifreeze?
Answer:
120
Step-by-step explanation:
60 gallons of 30% antifreeze means there are 18 gallons of antifreeze.
Let the number of gallons of 60% antifreeze be x. Then,
[tex]\frac{0.6x+18}{x+60}=\frac{1}{2} \\ \\ 1.2x+36=x+60 \\ \\ 0.2x=24 \\ \\ x=129[/tex]
If I add 9 by pi will it be irrational or rational?
Answer: irrational
Step-by-step explanation:
because it still cant be turned into a fraction after adding 9 to pi
differentiate xlnx from first principles
Answer:
formula for the derivative of x*lnx is equal to 1 + lnx.
Step-by-step explanation:
we need to find derivative of f(x) = x*lnx,
so we take the limiting value as x approaches x + h.
To simplify this, we set x = x + h,
and we want to take the limiting value as h approaches 0.
Now according to first derivative formula we have;
f'(x) = [tex]\lim_{h \to \zer0}[/tex]f(x+h) - f(x)]/[(x+h) - x]
[tex]\lim_{h \to \zer0}[/tex][ ln (1 + x) ] / x = 1
ln a - ln b = ln(a/b)
Using the above formulas, we have
d(xlnx)/dx = [tex]\lim_{h \to \zer0}[/tex][(x+h) ln(x+h) - xlnx]/[(x+h) - x]
= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) + h ln(x+h) - xlnx]/h
= [tex]\lim_{h \to \zer0}[/tex][x ln(x+h) - x lnx + h ln(x+h)]/h
= [tex]\lim_{h \to \zer0}\\[/tex][x(ln(x+h) - lnx) + h ln(x+h)]/h
=[tex]\lim_{h \to \zer0}[/tex][x ln [(x+h)/x] + h ln(x+h)]/h
=[tex]\lim_{h \to \zer0}[/tex][x ln (1+h/x) + h ln(x+h)]/h
=[tex]\lim_{h \to \zer0}[/tex] [x ln (1+h/x)]/h + limh→0 ln(x+h)
= [tex]\lim_{h \to \zer0}[/tex][ ln (1 + h/x) ] / (h/x) + limh→0 ln(x+h)
= 1 + lnx --- [Using limit formula [tex]\lim_{h \to \zer0}[/tex] [ ln (1 + x) ] / x = 1]
Hence, we have proved that the formula for the derivative of x*lnx is equal to 1 + lnx.
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Answer:
Step-by-step explanation:
In this section, we will determine the differentiate of xlnx using the first principle of derivatives, that is, the definition of limits. To derive the derivative of f(x) = xlnx, we take the limiting value as x approaches x + h. To simplify this, we set x = x + h, and we want to take the limiting value as h approaches 0. We will use the following formulas to prove the result:
f'(x) = limh→0[f(x+h) - f(x)]/[(x+h) - x]
limx→0 [ ln (1 + x) ] / x = 1
ln a - ln b = ln(a/b)
Using the above formulas, we have
d(xlnx)/dx = limh→0[(x+h) ln(x+h) - xlnx]/[(x+h) - x]
= limh→0[x ln(x+h) + h ln(x+h) - xlnx]/h
= limh→0[x ln(x+h) - x lnx + h ln(x+h)]/h
= limh→0[x(ln(x+h) - lnx) + h ln(x+h)]/h
= limh→0[x ln [(x+h)/x] + h ln(x+h)]/h
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Help, I don’t know how to solve this
Answer:
a=A/8
Step-by-step explanation:
This MIGHT be the answer, I am 99% sure!
What's the current temperature? 5 + (-12) = ?
Answer:
-7
Step-by-step explanation:
To add a positive number, 5, and a negative number, -12, take the absolute value of both numbers.
You get 5 and 12.
Subtract the smaller absolute value from the larger absolute value.
12 - 5 = 7
The sign of the answer is the same sign as the number that has the larger absolute value. The absolute of 5 is 5. The absolute value of -12 is 12. -12 has the larger absolute value, and -12 is negative, so the answer is negative.
5 + (-12) = -7
Find the values of x and y
(5x+4) (3x-24) (2y) 114
The values of x and y are 25° and 33° respectively.
How to determine the valuesIt is important to note the following;
Supplementary angles sum up to 180 degreesAngles on a straight line sum up to 180 degrees.From the information given, we have that
Angles 5x + 4 and 3x - 24 are supplementary.
This is represented as;
5x + 5 + 3x - 24 = 180
collect like terms
8x = 180 + 20
add lik terms
8x = 200
x = 200/8
x = 25°
Also,
2y and 114 are on a straight line
This is represented as;
2y + 114 = 180
collect like terms
2y = 180 - 114
2y = 66
Make 'y' the subject
y = 66/2
y = 33°
Thus, the values of x and y are 25° and 33° respectively.
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Megan's text messaging plan costs $15 for the first 500 messages and 5¢ for each additional text message. If she owes $21.55 for text messaging in the month of May, how many text messages did she send that month?
Answer:
631
Step-by-step explanation:
This problem can be expressed as:
0.05x + 15 = 21.55
0.05x + 15 - 15 = 21.55 - 15
0.05x = 6.55
0.05x/0.05 = 6.55/0.05
x = 131
We also know that:
0.05x + 15 = x + 500
If x = 131:
x + 500
131 + 500
631
Based on the two equivalent forms of the function h(t)=96t−16t2=t⋅(96−16t),At what time(s) is the ball 50 feet above the ground?
the height will be 50 ft after 0.575 seconds and after 5.424 seconds.
At what time(s) is the ball 50 feet above the ground?The equation that models the height is:
h(t) = 96*t - 16*t^2
Here we want to find the time such that the height is 50ft, then we need to solve the equation:
h(t) = 50 = 96*t - 16*t^2
Now we can solve that for t, we have the quadratic equation:
50 = 96*t - 16*t^2
0 = -16*t^2 + 96*t - 50
Then the solutions are:
t = (-96 ± √(96*96 - 4*(-50)*(-16))/(2*-16)
t = (-96 ± 77.6)/(-32)
The two solutions are:
t = (-96 + 77.6)/(-32) = 0.575t = (-96 - 77.6)/(-32) = 5.424This means that the height will be 50 ft after 0.575 seconds and after 5.424 seconds.
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Which expression is equivalent to 4−3(x+2)+2(3−2x)? −7x+16 −7x+4 −x+16 −x+4
The equivalent expression of 4 − 3(x + 2) + 2(3 − 2x) is -7x + 4
How to determine the equivalent expression?The expression is given as:
4 − 3(x + 2) + 2(3 − 2x)
Open the brackets
4 − 3(x + 2) + 2(3 − 2x) = 4 - 3x - 6 + 6 - 4x
Collect the like terms
4 − 3(x + 2) + 2(3 − 2x) = - 3x - 4x + 4 - 6 + 6
Evaluate the like terms
4 − 3(x + 2) + 2(3 − 2x) = -7x + 4
Hence, the equivalent expression of 4 − 3(x + 2) + 2(3 − 2x) is -7x + 4
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Solve the following equation. 4x/3 = 8Then place the correct number in the box provided.
Answer:
x = 6
Step-by-step explanation:
4x/3 = 8
Solve for x
Multiply each side by 3
4x/3 *3 = 8*3
4x = 24
Divide each side by 4
4x/4 = 24/4
x = 6
Answer:
[tex] \sf \large \: x=6[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
4x/3 =8
Step 1: Multiply both sides by 3.
4x/3=8
(4x/3)*(3)=(8)*(3)
4x=24
Step 2: Divide both sides by 4.
4x/4 = 24/4
x=6
Answer for i^372
And i^527 with explanation please
[tex]i {}^{372} = 1 \\ i {}^{527 } = - i[/tex]
Step-by-step explanation:
Greetings !
Note that:-
[tex]i {}^{2n} = 1.\: if \: n \: is \: even \\ \: \: \: \: \: \: \: = - 1. \: if \: n \: is \: odd[/tex]
And also
[tex]i {}^{2n + 1} = i. \: if \: n \: is \: even \\ \: \: \: \: \: \: \: \: \: \: = - i.\: if \: n \: is \: dd[/tex]
Thus, remembering these general formula plug in values in the place of n and solve.
Therefore,
[tex]i {}^{2(186)} = i {}^{372} = 1[/tex]
where n is even thus its 1 from the above explanation
[tex]i {}^{2(263) + 1} = i {}^{527} = - i[/tex]
following the same procedure the values exceeds to be -i.
Hope it helps !!!
WILL GIVE BRAINLIEST!!!
I have 200 hours to make as much Lemonade as possible, and I can make 1 pitcher every 10 minutes.
Write an inequality to represent my time constraint.
Answer:
33.33
Step-by-step explanation:
Well, we already know the amount of time it takes to make the lemonade, and we know the rate as well.
We need to find out how many pitchers you can make in an hour. If you can make one pitcher in 10 minutes, then you can make 6 pitchers in 60 minutes, AKA an hour.
So we make 6 pitchers per hour.
If we make 6 an hour, then we multiply 6 by 200 to get the number of pitchers we can make in 200 hours.
We can make 33.33 pitchers in 200 hours
I cannot do this help me to this
How many times smaller is 5×10-7 than 8.5×10-4
Answer:
Approximately 1.86 times smaller
Step-by-step explanation:
5×10-7 = (5×10=50) = 50-7 = 43
8.5×10-4 = (8.5×10=84) = 84- 4 = 80
80/43 = approximately 1.86
43×1.86 = approximately 80
80/1.86 = approximately 43
over a period of a week the 4 people in group C ran a total pf 27 miles while the 6 people in group D ran a total lf 39 miles. On avarage who ran more miles Group C or Group D.
Group C ran more miles than Group D
the central value of a set of data is expressed by the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. The average of 2, 3, and 4 is, for instance, (2+3+4)/3 = 9/3 = 3. The center value of 2, 3, and 4 in this instance is 3, thus. Finding the mean value of a bunch of numbers is the definition of average.
Average = Total Values / Total Values
Group C = 27/4 = 6.75
Group D = 39 /6 = 6.5
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Give the slope of a line that is perpendicular to the line −9x−y=−4 .
I'm stuck
Answer:
1/9
Step-by-step explanation:
[tex]y = - 9x - 4[/tex]
The slope of the perpendicular line is the interverse(opposite) of the slope of the original line.
Hope this helps!
Have any questions? Feel free to ask!
What is the sum of -1 + (-3)
Answer:
-4.
Step-by-step explanation:
When you add two negatives together it stays a negative. So the answer is -4.
You are in charge of drinks for a community barbecue. You need to supply at least 120 cups of
beverage to provide enough for the projected number of people that will attend. So far, you have
received the following donations:
o Enough mix to make 4 gallons of lemonade
o 7 bottles of fruit juice that each contain 64 fl. oz.
How many cups of beverage do you have?
Will you have enough for the barbecue?
O no
O yes
You have 120 cups. The cups of beverage will be enough.
Will the cups be enough?In order to determine the cups of beverage I have, the first step is to convert gallons and oz to cups.
1 gallon = 16 cups
16 x 4 = 64 cups
1 fluid ounce = 0.125 cups
64 x 0.125 x 7 = 56 cups
Total cups you have = 56 + 64 = 120 cups
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Find the slope(m) and y-intercept (b) of each representation below.
m= 15
b= 45
y= 15x +45
Concept:Overall equation
The equation of a line in slope-intercept form is given by y= mx +b, where m is the slope and b is the y-intercept.
Slope, m
The slope is the measure of how steep the line is. It also defines how the y-axis changes with respect to the x-axis. The formula for finding slope is as shown below.
[tex]\boxed{\text{Slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]
where [tex](x_1,y_1)[/tex] is the first coordinate and [tex](x_2,y_2)[/tex] is the second coordinate
y-intercept, b
This is the y-value in which the line cuts through the y-axis (vertical axis).
Working:Slope, m
Let's identify two pairs of coordinates on the line.
2 square units on the y-axis represent $30. Thus, 1 unit on the y-axis represents $15.
The 2 points are: (0, 45) and (5, 120)
Substitute the 2 points into the slope formula:
Slope
= [tex]\frac{120-45}{5-0}[/tex]
= [tex]\frac{75}{5}[/tex]
= 15
Thus, m= 15.
y-intercept, b
From the graph, the line cuts through the y-axis at y= 45.
Thus, b= 45.
Overall equation
Substitute m= 15 & b= 45 into y= mx +b:
∴ The equation of the line is y= 15x +45.
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angles are measured in _________
You are going down a road with a 5% grade.
You are going down 1 feet every 20 feet horizontally.
The slope of the road as a reduced fraction is??
The slope of the road as reduced fraction [tex]\frac{1}{20}[/tex] for grade which is 5%.
The slope of a road is defined as the ratio of the vertical height that a road rises to the horizontal distance covered to rise to that height.
While slope is expressed as a fraction grade is the percentage form of that fraction. The slope can also be defined as [tex]tan[/tex] [tex]\theta[/tex] where [tex]\theta[/tex] is the angle of elevation of the road. For example a slope of [tex]\frac{1}{4}[/tex] has a grade of 25%.
Here the given grade is 5%.
Per-cent refers to per one-hundred. So a 5% grade is 5 per one -hundred.
That means if the road is climbing then for every 100 units of horizontal distance covered, the altitude increases by 5 units.
Now slope of the road=vertical distance ÷ horizontal distance
[tex]=\frac{5}{100}\\=\frac{1}{20}[/tex]
Therefore we can say that the slope of the road is [tex]\frac{1}{20}[/tex]
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