let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{6\frac{1}{2}}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}}~\hfill \stackrel{mixed}{1\frac{5}{8}\implies \cfrac{1\cdot 8+5}{8}}\implies \stackrel{improper}{\cfrac{13}{8}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{total salad}}{\cfrac{13}{2}}\div \stackrel{\stackrel{\textit{conainer's}}{\textit{capacity}}}{\cfrac{13}{8}}\implies \cfrac{\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{\underset{1}{\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\cdot \cfrac{\stackrel{4}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies 4[/tex]
Jamie went to the his 6 friends. For each friend, he spent $4.75 for a sandwich, $1.25 for a cold beverage, and $.56 for a piece of fruit. How many did he spend in total to buy lunch for his friends?
Answer:
Jamie spent $39.36 in total.
Step-by-step explanation:
First, add the money spent for the sandwich, beverage, and fruit together.
4.75 + 1.25 + .56 = 6.56
Then, multiply the amount spent for one friend by six to find the total.
6.56 x 6 =39.36
I hope this helped you!
What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve. tions of the equation 9
Answer:
Step-by-step explanation:
Let [tex]u^2=x^4\\u = x^2[/tex]
Subbing in:
[tex]9u^2-2u-7=0[/tex]
a = 9, b = -2, c = -7
The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:
[tex]9u^2-9u+7u-7=0[/tex]
Group together in groups of 2:
[tex](9u^2-9u)+(7u-7)=0[/tex]
Now factor out what's common within each set of parenthesis:
[tex]9u(u-1)+7(u-1)=0[/tex]
We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:
[tex](u-1)(9u+7)=0[/tex]
Remember that [tex]u=x^2[/tex]
so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.
[tex](x^2-1)(9x^2+7)=0[/tex]
The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring [tex](x^2-1)[/tex] gives us that x = 1 and -1. The other set is a bit more tricky. If
[tex]9x^2+7=0[/tex] then
[tex]9x^2=-7[/tex] and
[tex]x^2=-\frac{7}{9}[/tex]
You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:
[tex]x=[/tex]±[tex]\sqrt{-\frac{7}{9} }[/tex]
which will simplify down to
[tex]x=[/tex]±[tex]\frac{\sqrt{7} }{3}i[/tex]
Those are the 4 solutions to the quartic equation.
The area of a bulletin board is 52 square feet the length is three feet less than four times the width find the length and width of the bulletin board
Answer:
Length: 13 feet,
Width: 4 feet.
Step-by-step explanation:
Let w represent width of bulletin board.
We have been given that the length is 3 feet less than 4 times the width. So the length of the bulletin board would be [tex]4w-3[/tex].
We have been given the area of a bulletin board is 52 square feet. We know that a bulletin board is in form of rectangle, so its area would be length times width.
We can represent this information in an equation as:
[tex]w(4w-3)=52[/tex]
Let us solve for w.
[tex]w(4w-3)=52[/tex]
[tex]4w^2-3w=52[/tex]
Use quadratic formula:
[tex]w=\frac{-(-3)\pm\sqrt{(-3)^3-4\cdot 4\cdot (-52)}}{2\cdot 4}[/tex]
[tex]w=\frac{3\pm\sqrt{9+832}}{8}[/tex]
[tex]w=\frac{3\pm\sqrt{841}}{8}[/tex]
[tex]w=\frac{3\pm29}{8}[/tex]
[tex]w=\frac{3-29}{8}\text{ (or) }w=\frac{3+29}{8}[/tex]
[tex]w=\frac{-26}{8}\text{ (or) }w=\frac{32}{8}[/tex]
[tex]w=\frac{-13}{4}\text{ (or) }w=4[/tex]
Since width cannot be negative, therefore, width of the bulletin board is 4 feet.
Substitute [tex]w=4[/tex] in expression [tex]4w-3[/tex] to find length of bulletin board.
[tex]4w-3\Rightarrow 4(4)-3=16-3=13[/tex]
Therefore, length of the bulletin board is 13 feet.
Harriet used the work below to determine the percent equivalent to 1/8.
Step 1: 1/8=?/100
Step 2: 8 divided by 100 = 0.08
Step 3: 0.08 multiplied by 1 = 0.08
Step 4: 0.08
What was Harriet’s error?
-In Step 1, she set up the proportions incorrectly.
- In Step 2, she divided 8 by 100 instead of 100 by 8, so she cannot multiply the numerator by the factor.
-In Step 3, she multiplied the numerator instead of the denominator by the factor. -In Step 4, she forgot to move the decimal.
Answer:
Its B ''In Step 2, she divided 8 by 100 instead of 100 by 8, so she cannot multiply the numerator by the factor.''
Hence, in step [tex]2[/tex] she did the mistake.
What is the multiplication?
Multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here given that,
Step 1: [tex]\frac{1}{8}=\frac{?}{100}[/tex]
Step 2: [tex]8[/tex] divided by [tex]100 = 0.08[/tex]
Step 3: [tex]0.08[/tex] multiplied by [tex]1 = 0.08[/tex]
Step 4: [tex]0.08[/tex]
She did the mistake in step [tex]2[/tex] it would be,
[tex]\frac{100}{8}=12.5[/tex]
Hence, in step [tex]2[/tex] she did the mistake.
To know more about the multiplication
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Find the area of this kite
For this case we have that the area of the kite is given by the area of two triangles, the triangles share the same base of 2 + 2 = 4. One of the triangles has height of 6 and the other has height of 7.
So, the total area is given by:
[tex]A = \frac {1} {2} * 4 * 6 + \frac {1} {2} * 4 * 7\\A = \frac {1} {2} 24+ \frac {1} {2} 28\\A = 12 + 14\\A = 26[/tex]
So, the kite area is 26
ANswer:
Option D
Solve for a.
a = 0
a = -1
a = 1
none
Answer:
None.
Step-by-step explanation:
5/a - 2 / (1 - a) = 2 (a - 1)
Multiply each term by a(1 - a)(a - 1):
5 (1 - a)(a - 1) - 2a(a - 1) = 2a(1 - a)
5( a - 1 - a^2 + a) - 2a^2 + 2a = 2a - 2a^2
5(-a^2 + 2a - 1) - 2a^2 + 2a = 2a - 2a^2
-5a^2 + 10a - 5 - 2a^2 + 2a - 2a + 2a^2 = 0
-5a^2 + 10a - 5 = 0
-5(a^2 - 2a + 1) = 0
= -5(a - 1)^2 = 0
So a = 1.
But a = 1 cannot be a root because 2/ 1 - a would be 2/0 which is undefined.
Also 2 / (a - 1) is undefined.
The number of users of a cell tower in a small, developing town increased by a factor of 1.5 every year from 2010 to 2019. The function below shows the number of cell tower users, f(x), after x years from the year 2010:
f(x) = 5,000(1.5)x
Which of the following is a reasonable domain for the function?
A.2,010 ≤ x ≤ 2,019
B.0 ≤ x ≤ 5,000
C.0 ≤ x ≤ 9
D.All positive integers
Answer:
Option C) [tex]0 \leq x \leq 9[/tex]
Step-by-step explanation:
We are given the following information in the question:
The number of users of a cell tower increased by a factor of 1.5 every year from 2010 to 2019.
[tex]f(x) = 5000(1.5)^x[/tex]
where f(x) is the number of cell tower users and x is the years from the year 2010.
We have to find the domain for the given function.
Domain of a function is defined as the possible values of x the function can take, so that the function is defined.
Since this function gives the number of cell users from 2010 to 2019, thus, it is applicable from year 2010 to 2019.
x takes the value of years after 2010.
Thus for year 2010, x = 0 and for year 2019, x = 9
Thus, the domain of the given function is given by:
[tex]0 \leq x \leq 9[/tex]
PLZ HELP MARKIN BRAINEST!!!!
Answer:
it's definitely a positive nonlinear graph
Step-by-step explanation:
A basket contains 13 pieces of fruit five apples five oranges and three bananas Jonas takes piece of fruit at random from the basket in Bethex if you summon what is the probability that Jonas will get orange and Beth will get an apple
Answer:1 out of 13
Step-by-step explanation:
because you take both of them and add them together and if one gets a banana and the other one gets an orange that will be one out of thirteen
a taxi company charges $1.50 per mile for the first 3 miles of a trip and $1.20 for each additional mile. how much would a trip of 5.25 miles cost.
Answer:
5.25 miles - 3 miles = 2.25 miles
2.25 miles is the extra miles.
2.25 miles x $1.20 = $2.7
Total:
$2.7 + ($1.5 x 3 miles)
=$2.7 + $4.5
=$7.2
5.5 miles will cost $2.7.
What is the volume of the cone with radius 6 in. and height 10 in.? Express the answer in terms of π.
Answer:
120*pi in^3
Step-by-step explanation:
We are given
Radius of cone=r=6 in
Height of cone=h=10 in
We know that the formula for finding the volume of cone is:
[tex]V=\frac{1}{3}\pi *(r)^{2}*h[/tex]
Putting the values of radius and height:
[tex]V=\frac{1}{3}\pi *(6)^{2}*10\\=\frac{1}{3}\pi *36*10\\=\frac{360}{3}\pi\\=120\pi[/tex]
So, the volume of cone in terms of pi is 120pi cubic in^3 ..
Answer:
The volume of cone = 120π cubic inches
Step-by-step explanation:
Points to remember
Volume of cone = (πr²h)/3
Where r - Radius of cone and
h - Height of cone
To find the volume of cone
Here r = 6 in and h = 10 in
Volume = (πr²h)/3
= (π * 6² * 10)/3
= (π * 36 * 10)/3
= 360π/3
= 120π cubic inches
Therefore volume of cone = 120π cubic inches
please help asap will mark brainliest
Answer:
29; 30
Step-by-step explanation:
1. To the nearest whole number.
Whole numbers are numbers like 27, 28, 29, and 30.
A is between 28 and 29, but it is closer to 29.
To the nearest whole number, A = 29.
2. To the nearest 10
The tens are numbers like 10, 20, 30, and 40.
A is between 20 and 30, but it is closer to 30.
To the nearest ten, A = 30.
Solve the following equation: -4x - 6 = 10
4
-4
1
-1
If 2x-3y=14 and 5x+3y=21 then what is the value of x?
A) -1
B) 0
C) 7/3
D) 5
Answer:
D
Step-by-step explanation:
Given the 2 equations
2x - 3y = 14 → (1)
5x + 3y = 21 → (2)
Adding the 2 equations term by term will eliminate the y - term
(5x + 2x) + (- 3y + 3y) = (14 + 21)
7x = 35 ( divide both sides by 7 )
x = 5 → D
I coach a soccer team with 15 members. i want to choose a starting lineup consisting of 11 players, two of whom will represent the team in the captains meeting at the beginning of the game. in how many ways can i choose my starting lineup, including designating the two captains?
[tex]{_{15}C_{11}}\cdot {_{11}C_2}=\dfrac{15!}{11!4!}\cdot\dfrac{11!}{2!9!}=\dfrac{12\cdot13\cdot14\cdot15}{2\cdot3\cdot4}\cdot\dfrac{10\cdot11}{2}=75,075[/tex]
Answer: There are 715 ways to choose his starting lineup which includes designating the two captions.
Step-by-step explanation:
Since we have given that
Number of members = 15
Number of players = 11
Number of captions must be included = 2
So, Number of remaining members = 15-2 = 13
Number of remaining players = 11 - 2 = 9
So, Number of ways to choose starting line up is given by
[tex]^{13}C_9\\\\=715[/tex]
Hence, there are 715 ways to choose his starting lineup which includes designating the two captions.
which of the following is NOT equal to 50 millimeters?a. 5,000,000 nanometersb. 0.05 metersc. 5 centimetersd. 50,000 micrometers
Answer:its a. 5,000,000
Step-by-step explanation:
Final answer:
Option a, 5,000,000 nanometers, is the correct choice as it does not equate to 50 millimeters; it equates to 5 millimeters instead, making it not equal to the other options listed.
Explanation:
The question asks which of the provided options is not equal to 50 millimeters. We can convert each option to see which one does not equal 50 mm:
a. 5,000,000 nanometers (nm) - This equates to 5,000,000 nm × 1 m / 1,000,000,000 nm = 0.005 m or 5 mm, which is not equal to 50 mm.
b. 0.05 meters (m) - This is equal to 0.05 m × 1000 mm / 1 m = 50 mm, which is equal to 50 mm.
c. 5 centimeters (cm) - This is equal to 5 cm × 10 mm / 1 cm = 50 mm, which is equal to 50 mm.
d. 50,000 micrometers (µm) - As 1 µm is 1/1000 mm, this is equal to 50,000 µm × 1 mm / 1000 µm = 50 mm, which is equal to 50 mm.
Therefore, the correct answer is a. 5,000,000 nanometers, as it is the only option that does not equate to 50 mm.
PARKS Anika is hiking on a rectangular trail at the national park. There are four resting spots along the corners of the trail. On the map, they are marked with coordinates of (-2, 2), (1, 2), (1, -2), and (-2, -2). If each unit represents 1 mile, find the perimeter of the trail in miles, using the coordinates.
Answer:
[tex]14\ miles[/tex]
Step-by-step explanation:
Let
[tex]A(-2, 2), B(1, 2), C(1, -2),D(-2, -2)[/tex]
Plot the coordinates
see the attached figure
we know that
The perimeter is equal to
[tex]P=2(AB+AD)[/tex]
we have
[tex]AB=(1-(-2))=3\ units[/tex]
[tex]AD=(2-(-2))=4\ units[/tex]
substitute
[tex]P=2(3+4)=14\ units[/tex]
Convert to miles
If each unit represents 1 mile
then
[tex]14\ units=14\ miles[/tex]
Answer:
15 units sq
Step-by-step explanation:
Good job
The position of an object at time t is given by s(t) = -8 - 9t. Find the instantaneous velocity at t = 1 by finding the derivative.
Need help ASAP, Thank You!
Answer:
At t = 1s, The instantaneous velocity will be -9
Step-by-step explanation:
The position is given by
s(t) = -8 - 9t
If we find the derivative, we get the expression for the velocity
d(s(t))/dt = v(t) = -9
The velocity of the object is constant.
At t = 1s, it will be -9
Given cos =4/3 sqrt 3 and tan-sqrt 11/4,find sin
I will mark brainliest to the best answer!! Please please help!!
Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution:
2x-y=4
X+2y=2
A) no solution
B) one solution
C) infinitely many solutions
Answer:
B) one solution
Step-by-step explanation:
The ratio of x-coefficient to y-coefficient is different in the two equations, so the lines have different slopes. Two lines with different slopes will always have exactly one point of intersection. You don't need to graph the equations to know there is ...
one solution
__
A graph is attached. As it happens, the two lines are perpendicular. The solution is (2, 0).
Over 6 days jim jogged 6.5 miles 5 miles 3 miles 2 miles 2 miles 3.5 miles and 4 miles. What is the mean distance that jum jogged
Mean means average.
To find the average, add the data then divide it by the amount of individual data you have.
(6.5 + 5 + 3 + 2 + 2 + 3.5 + 5)/2 = mean
27/2 = mean
13.5 = mean
13.5 miles is the mean distance that Jim jogged.
Step 1: Collect and organize your data.
a) Using the Super Survey Simulator, survey 10 students of your choice and gather data. Create an organized representation of your data below.
3.6
2.7
3.0
3.3
1.7
1.5
2.7
3.0, 3.0,3.8
b) What do you think the purpose of this survey is? Explain.
Answer:
To better understand the data you're working with
Step-by-step explanation:
Note that, the sample is a subset of your whole population (population here is a general definition, it could be a population of cars for example), which means that if you want to understand your population your best "bet" would be using a sample to try to estimate some unknown characteristics of your population. Let's suppose you want to estimate the true mean of your population, then you would need a sample, and if this sample is big enough you could approximate the estimative to the true mean.
It's hard to say exactly what this survey could mean, but the general idea is to understand your data a little more, see if there is any pattern, if a certain value occurs more than others, to calculate the sample mean, median and standard deviation, and so on...
Hope it helped!
Answer:
For b, the answer is that your trying to find out what the type of funtion may be. It could be either exponential, linear, or quadratic.
Step-by-step explanation:
That's what the lesson in edg is all about.
Which three-dimensional figure is formed by the rotation given?
The three-dimensional figure that is formed by the rotation is (a) an hemisphere
How to determine the figure?From the figure, we can see that the line is rotated along the y-axis.
And the length of rotation reduces as the rotation moves downward
This rotation would create an hemisphere
The option (a) represents an hemisphere
Hence, the three-dimensional figure that is formed by the rotation is (a) an hemisphere
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Need help with a math question
Answer:
[tex]d =\sqrt{(b-0)^2 +(c-a)^2}[/tex]
Step-by-step explanation:
We know that the distance between two points is calculated using the following formula
[tex]d =\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
In this case we look for the RS distance
Then
The starting point is: (0, a)
The final point is (b, c)
So
[tex]x_2 = b\\x_1 = 0\\y_2 = c\\y_1=a[/tex]
The distance is:
[tex]d =\sqrt{(b-0)^2 +(c-a)^2}[/tex]
Evaluate................
Answer:
h(8q²-2q) = 56q² -10q
k(2q²+3q) = 16q² +31q
Step-by-step explanation:
1. Replace x in the function definition with the function's argument, then simplify.
h(x) = 7x +4q
h(8q² -2q) = 7(8q² -2q) +4q = 56q² -14q +4q = 56q² -10q
__
2. Same as the first problem.
k(x) = 8x +7q
k(2q² +3q) = 8(2q² +3q) +7q = 16q² +24q +7q = 16q² +31q
_____
Comment on the problem
In each case, the function definition says the function is not a function of q; it is only a function of x. It is h(x), not h(x, q). Thus the "q" in the function definition should be considered to be a literal not to be affected by any value x may have. It could be considered another way to write z, for example. In that case, the function would evaluate to ...
h(8q² -2q) = 56q² -14q +4z
and replacing q with some value (say, 2) would give 196+4z, a value that still has z as a separate entity.
In short, I believe the offered answers are misleading with respect to how you would treat function definitions in the real world.
In a survey in 2010, the population of two plant species were found to be growing exponentially. Their growth is given by these equations: species A, and species B, , where t = 0 in the year 2010. 4. After how many years will the population of species A be equal to the population of species B in the forest?
If we want to find when the population of species A will be equal to the population of species B, we need to see when the two equations for the population of each species are equal, ie. equate them and solve for t. Thus:
2000e^(0.05t) = 5000e^(0.02t)
(2/5)e^(0.05t) = e^(0.02t) (Divide each side by 5000)
2/5 = e^(0.02t) / e^(0.05t) (Divide each side by e^(0.05t))
2/5 = e^(-0.03t) (use: e^a / e^b = e^(a - b))
ln(2/5) = -0.03t (use: if b = a^c, then loga(b) = c )
t = ln(2/5) / -0.03 (Divide each side by -0.03)
= 30.54 (to two decimal places)
Therefor, the population of species A will be equal to the population of species B after 30.54 years.
I wasn't entirely sure about the rounding requirements so I've left it rounded to two decimal places.
Use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary.
Answer:
3/4
Step-by-step explanation:
a1 = (-1/3)^0 = 1
r = -1/3
Hence S = 1/(1+1/3) = 1/(4/3) = 3/4
Answer:
0.75.
Step-by-step explanation:
The common ratio = -1/3 and the first term = (-1/3)^0 = 1.
Sum to infinity = 1 / (1 - (-1/3))
= 1 / 4/3
= 3/4
= 0.75.
okay so what is a independent variable
Hello There!
In an experiment, The independent variable is the variable that the person doing the experiment changes on purpose so they can see if it affects another variable in the experiment. Independent variables are also called "The Manipulated Variables"
I Hope This Helped You!
Have Great Day!
Be Safe,
TheBlueFox
If a denotes some event, what does upper a overbar denote? if p(a)equals0.995, what is the value of p(upper a overbar)? if p(a)equals0.995, is upper a overbar unlikely?
[tex]P(A)=0.995\\P(A')=0.005[/tex]
So [tex]P(A')[/tex] is pretty much unlikely.
The function p(x) = –2(x – 9)2 + 100 is used to determine the profit on T-shirts sold for x dollars. What would the profit from sales be if the price of the T-shirts were $15 apiece?
Answer:
$28
Step-by-step explanation:
Put the given value into the formula and do the arithmetic.
p(15) = -2(15 -9)^2 +100
= -2(6^2) +100
= -72 +100
= 28
The profit on T-shirts selling for $15 would be $28.
Answer:
B -$28
Step-by-step explanation: