ANSWER
s < 10
EXPLANATION
With the 'less than' or 'greater than' symbol we can see that it's like an equal sign that has been shrinked on one end. In the smallest end we have to write the smallest expression or number and in the largest end we have to write the greatest expression or number.
For example: 5 < 10 is the same as 10 > 5, because the smallest number (5) is in the smallest end of the sign and the greatest number (10) is in the largest end of the sign in both expressions.
If 's' is the number of stamps, the expression says that there are 'less than' 10 stamps at the post office, so 's' has to be in the smallest end of the sign.
John wants to fence a rectangular garden, which is 30 feet. What would be the dimensions of the fence enclosing the greatest area?Options a) 7.7 x 7.5 b) 8 x 7 c) 20 x 10d) 15 x 15
The dimension of the rectangle that has the maximum area is 7.5 by 7.5 feet.
Let the length of the rectangular field be x and the width be y
Now the perimeter is 30
Therefore 2(x + y)=30
or, x + y = 15
or, y = 15 - x
Area of the rectangle = xy
Now we substitute the value of y
area = x ( 15 - x ) = 15x - x²
Now for the maximum area we have to differentiate the area function.
f(x) = 15x - x²
f'(x) = 15-2x
Now the differentiated function is equated to 0 to get the value of x for which the area is maximum.
15-2x = 0
or, x =7.5
therefore y -= 15 - x = 1 5 - 7.5 = 7.5 feet.
Hence for the area to be maximum the dimension of the field should be 7.5feet by 7.5 feet .
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Kaitlin is a software saleswoman. Her base salary is $2300, and she makes an additional $90 for every copy of English is Fun she sells.
Let P represent her total pay (in dollars), and let N represent the number of copies of English is Fun she sells. Write an equation relating P to N. Then use this
equation to find her total pay if she sells 22 copies of English is Fun.
The equation which represents total pay P and the number of copies sold N is P = 2300 + 90N and the total pay for 22 copies sells will be $4280.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Total pay = base salary + additional
Total pay = base salary + number of copies × per copy price
P = 2300 + N × 90
P = 2300 + 90N
Now for 22 copies
P = 2300 + 90(22) = $4280
Hence, the equation which represents total pay P and the number of copies sold N is P = 2300 + 90N and the total pay for 22 copies sells will be $4280.
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9. When Mei stopped 80% of the shots on
goal in the last game, she stopped 16 shots.
How many goals were scored?
Answer:
4 shots were scored
Clare said, "in the first five years, between 1977 and 1982, the cost fell by about $12 per year. but in the second five years, between 1983 and 1988, the cost fell only by about $2 a year." show that clare is correct.
Let p be the function that gives the cost , in dollars, of producing 1 watt of solar energy years after 1977. Here is a table showing the values of from 1977 to 1987.
t p(t) p(10)-p(0)
0 80 p(10)
1 60 p(10)- p(0)/10-0
2 45 p(10-0)
3 33.75
4 25.31
5 18.98
6 14.24
7 10.68
8 8.01
9 6.01
10 4.51
Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?
Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?
Which equation best captures the yearly average increase rate of solar prices between 1977 and 1987?
This discussion aims to help students remember what average rate of change for a function means and how it is computed. Select students to explain what each expression's value in this context means. For instance, the cost difference for a solar cell between 1977 and 1987 is represented by the formula p(10)- p(0), whereas the percent change between 1977 and 1987 may be calculated as p(10)/p(0). The fact that the real phrase for the average rate of change, p(10)-p(0)/10-0=-7.55, reveals that the price declined by -$7.55 on average per year since the expression considers the whole difference in price between the 1977 and 1987 divided by the total number of years that passed.
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identify the term in experimentation -2X
The given expression is
[tex]-2x^8+3x^2-x+11[/tex]Terms are the expressions separated by negative or positive signs. In this case, there are 4 terms.
Coefficients are the number multiplying the variable. IN this case, the coefficients are -2, 3, and -1.
The variable is just x because it's the only letter present in the expression.
The powers are x'8 and x'2.
The tables represent the functions f(x) and g(x).A table showing g(x) equals 2 x plus 15 with 2 columns and 7 rows. The first column, x, has the entries, negative 15, negative 12, negative 9, negative 6, negative 3, 0. The second column, g(x), has the entries, negative 15, blank, blank, blank, blank, 15.Which input value produces the same output value for the two functions?
x=-6
Explanation
to solve this, let´s complete the tables and then compare
Step 1
complete the table:
to do that we need to input the x value and evaluate to obtain f(x)
so
a) for
[tex]f(x)=\frac{2}{3}x+7[/tex]i)when x=-12
[tex]\begin{gathered} f(-12)=\frac{2}{3}(-12)+7 \\ f(-12)=-8+7=-1 \\ f(-12)=-1 \\ so \\ (-12,-1) \end{gathered}[/tex]ii) when x= -9
[tex]\begin{gathered} f(-9)=\frac{2}{3}(-9)+7 \\ f(-9)=-6+7=1 \\ f(-9)=1 \\ so \\ (-9,1) \end{gathered}[/tex]iii) when x=-6
[tex]\begin{gathered} f(-6)=\frac{2}{3}(-6)+7 \\ f(-6)=-4+7=3 \\ f(-6)=3 \\ so \\ (-6,3) \end{gathered}[/tex]iv) when x= -3
[tex]\begin{gathered} f(-3)=\frac{2}{3}(-3)+7 \\ f(-3)=-2+7=5 \\ f(-3)=5 \\ so \\ (-3,5) \end{gathered}[/tex]hence
Step 2
Now , for equation(2) g(x)
[tex]g(x)=2x+15[/tex]a) when x=-12
[tex]\begin{gathered} g(x)=2x+15 \\ g(-12)=2(-12)+15=-24+15=-9 \\ g(-12)=-9 \end{gathered}[/tex]b) when x=-9
[tex]\begin{gathered} g(x)=2x+15 \\ g(-9)=2(-9)+15=-18+15=-3 \\ g(-9)=9 \end{gathered}[/tex]c) when x=-6
[tex]\begin{gathered} g(x)=2x+15 \\ g(-6)=2(-6)+15=-12+15=3 \\ g(-6)=3 \end{gathered}[/tex]d)when x=-3
[tex]\begin{gathered} g(x)=2x+15 \\ g(-3)=2(-3)+15=-6+15=9 \\ g(-3)=9 \end{gathered}[/tex]so
Step 3
finally, compare and check wich input value produces the same out put
therefore, the answer is
x=-6
I hope this helps you
Answer:
x=-6
Step-by-step explanation:
exam
43 is 32% of what number
PLS HURRY!!!!!!!!
Answer:
134.375
Step-by-step explanation:
43 is 32% of what number
32% = 0.32
43/0.32 = 134.375
What is the product?
-1/5[-2 1/4]
Answer: 9/20 or 0.45 as a decimal :)
An initial amount of radioactive substance Y0is given, along with information about
the amount remaining after a given time t in appropriate units. For an equation of
the form y=yoekt that models the situation, give the exact value of k.
Y0=10 mg, the half-life is 100 days
The value of k in this exponential decaying situation of radioactive material is - 0.0069.
What is an exponential function?One of the key mathematical operations is the exponential function we allow the exponent to be the independent variable to create an exponential function.
Given, An equation of the form y = y₀e^(kt) models a situation of decaying radioactive material.
y₀ = 10mg, half-life = 100 days.
So, in 100 days the left-out radioactive material will be 5mg.
∴ 5 = 10.e^(100k).
e^(100k) = 1/2.
lne^(100k) = ln(1/2).
100k = - 0.69
k = - 0.69/100.
k = - 0.0069.
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Function g is represented by the table.Which statement correctly compares the two functions?
functionWe have:
The functions f and g have the same y-intercept, this is (0,4).
And the behavior as x approaches infinity is:
In the function f, value of the function approaches - 1.
In the function g, value of the function approaches - 1, too.
Therefore, they have the same behavior.
Answer: they have the same y-intercept and the same behavior as x approaches infinity.
Find an equation for the line below.A(-6, -3) B(2,-5)
Using Two point formula in getting the equation of the line.
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]x1 = -6
y1 = -3
x2 = 2
y2 = -5
Substitute to the formula :
[tex]\begin{gathered} y-(-3)=\frac{-5-(-3)}{2-(-6)}\lbrack x-(-6)\rbrack \\ y+3=\frac{-2}{8}(x+6) \\ y+3=-\frac{1}{4}(x+6) \\ y+3=-\frac{1}{4}x-\frac{3}{2} \\ y=-\frac{1}{4}x-\frac{3}{2}-3 \\ y=-\frac{1}{4}x-\frac{9}{2} \end{gathered}[/tex]The answer is :
y = -1/4 x - 9/2
How much must be doposited today into the following account in order to have $45,000 in 6 years for a down payment on a house? Assume no additional deposits are made.An account with annual compounding and an APR of 7%
Solution
[tex]F=p(1+\frac{r}{n})^{nt}[/tex]where:
F=future value = 45000
P=present value
r=rate (as a decimal) = 7%=0.07
n=number of compounding periods per year = 1
t=number of years = 6
[tex]\begin{gathered} F=p(1+\frac{r}{n})^{nt} \\ 45000=p(1+\frac{0.07}{1})^{1(6)} \\ 45000=P(1+0.07)^6 \end{gathered}[/tex][tex]\begin{gathered} 45000=P(1.07)^6 \\ 45000=P(1.50073) \\ P=\frac{45000}{1.50073} \\ P=29985.4 \end{gathered}[/tex]Therefore the present value deposited today = $29,985.40
find the mode of the data set obtained after multiplying each value by 5
Mode
2 x 5 = 10
6 x 5 = 30
5 x 5 = 25
3 x 5 = 15
7 x 5 = 35
8 x 5 = 40
9 x 5 = 45
2 x 5 = 10
4 x 5 = 20
7 x 5 = 35
4 x 5 = 20
7 x 5 = 35
The mode is 35 because it is repeated 3 times.
Ceasia needs a new pair of basketball shoes for the upcoming season. The price of the shoes she wants is $98.99. The tax on the shoes is 5.2%. What
is the exact price Ceasia will pay for her shoes tax included?
Answer:
$104.14
Step-by-step explanation:
5.2% of $98.99
= $5.15
Price of the shoes + tax
= $98.99 + $5.15
= $104.14
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
a. Why does the image of ray CA line up with rayCE?
The image of ray CA and CE coincide after rotating because, (rotations preserve rays, or we defined our rotations that way)
b. Why does the image of A coincide with E?
Transformations preserve, (angles, distance, or orientation) so the image of point A and point E are the same, (distance, orientation) along the same ray from C and they have to coincide.
c. Complete the explanation to prove triangle CBA is congruent to triangle CDE.
The rotation would also make the image of B, (coincide, equal) with D. So there is a, (magnitude, rigid motion, translation) that takes CBA onto CDE.
a. The images coincide because rotations preserve rays.
b. Transformations preserve distances, so the image of point A and point E are the same distance along the same ray from C and they have to coincide.
c. The rotation would also make the image of B equal with D. So there is a rigid motion that takes CBA onto CDE.
What are rigid transformations?Transformations are classified into rigid and non-rigid, according to the definitions presented as follows:
Rigid transformations preserve the distances.Rigid transformations do not preserve the distances.In this problem, the transformation was a rotation of triangle BAC over vertex C, generating triangle EDC.
A rotation is a rigid transformation, hence the distances are preserved.
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What Goes Around Is Bad Circulation
by c. safos
Pablo did his best to keep quiet. He had pulled his legs behind the door and out of sight. He had folded himself tight behind Amy's closet door and waited. It was cramped, and his knees were in his chest. He could feel the blood pumping into his heart. It made his legs tingle as if ants were crawling on his skin, but he knew it was because his legs were crossed, and the blood was pumping hard.
Suddenly, he heard a sound from the bedroom. This is it, he thought to himself. Now, she'll pay for hiding my video game controller. Amy was settling into her desk and pulling out her homework assignment from her bag.
Pablo was just about to spring forward when he heard his mom's voice call upstairs, "Amy! Get down here and wash these dishes! It's your turn!" She called out again when there was no answer. "Hurry up, I need to help your sister Maya with her homework!"
"Aw, man," Amy called out. She closed her book and walked back downstairs. Her mom's voice still rang in the air.
Pablo decided to wait. While Amy washed dishes, and their mom was helping their younger sister Maya, Pablo would wait. Five minutes turned into ten. Ten minutes turned into twenty.
Just as he was about to give up, Pablo saw Amy return to her desk. This is it! he thought. As she sat down, Pablo flung the closet door open, screamed, "Got you . . . ooohhhhh," and plopped on the ground. He writhed around holding his legs. "They're asleep! They're asleep!" he said over and over.
Amy looked down at her brother and said sharply, "Pablo, please, I'm really busy and don't have time for this."
"You'll pay, Amy! This isn't overrrrr . . . owww," he said as he limped off and out of her room.
8
From what point of view is the story told?
A.
third person limited
B.
first person
C.
second person
D.
third person omniscient
╭┄┈┄────────❥
Answer:
↣ A.) Third person limited
Explanation:
A story told from a third person limited point-of-view, or POV, is defined as a narration that describes the thoughts, feelings, and actions of one character.
. . • ☆ . ° . • °: . * ₊ ° . ☆
I hope this helps!
peachtea ^-^
╰┄┈┄──❥
how do i find each system of equations for these answers x-y=4 2 x+y=5
The value of x and y of system of equations are 3 and -1. A group of equations involving one or more variables is known as a system of equations.
How to solve system of equations ?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.
Solution for x-y=4, 2x+y=5
x - y = 4
2x + y = 5
Substitute 4 = x+ y
2(4+y) + y =5
Simplify
8 + 3y = 5
Isolate y for 8 + 3y = 5 ; y = -1
For x = 4 + y
Substitute y= -1
x= 4-1
x=3
The solutions to the system of equation are :
x =3 , y = -1
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What is the product of (−7)(14) • (−6)? 92 −77 588 −104
The product of (− 7) ( 14 ) multiplied by ( −6 ) will be C. 588.
What is a product?A product simply means the value that's gotten when the numbers are multiplied together. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It should be noted that minus × minus = plus
minus × plus = minus
Therefore, the value of ( −7 ) ( 14 ) • ( −6 ) will be:
= ( -7 ) × 14 × ( -6 )
= 588
Therefore, the value of the product is 588 and this implies that the correct option is C.
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Which of the following is a factor of x³ + 343?
x-7
x² - 14x + 49
x² + 7x +49
x+7
Answer:factor of x³ + 343
Step-by-step explanation: Option D is correct. A factor of an expression is usually referred to as a number or an algebraic expression that divides the known expression. The above algebraic expression needs to be expanded to determine its factor; Mathematically; x³ + 343 = (x + 7) (x² - 7x + 49) Therefore, we can conclude that the factors are (x + 7) (x² - 7x + 49)
I need help with this please I will give brainlist
The inequality represented by the graph attached is y > -3x + 6
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
An inequality is used to show that two numbers or variables are non equal to each other.
The graph attached shows a straight line inequality. It passes through the point (0, 6) and (2, 0). Hence, the straight line has the equation:
y - 6 = [(0 - 6)/(2 - 0)](x - 0)
y - 6 = -3(x)
y = -3x + 6
Based on the dotted line and the shaded region, the inequality is y > -3x + 6
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What is the answer to this
The amount invested at 8% is $26,333.33.
The amount invested at 2% is $8,666.66.
What is simple interest?
Simple compound interest is a method of calculating the amount of interest charged for a fixed rate and total over a fixed period of time. With simple interest, the principal is always the same, unlike compound interest, which adds interest to the previous year's principal to calculate the next year's interest.
interest = principal * rate * time
Given data:
Principal = $35000
Interest = $2280
time = one year.
Let 'x' represent the amount invested at 8%, then '35000-x' represents the amount invested at 2%.
interest = principal * rate * time
2280 = 0.08x + 0.02(35000 - x)
2280 = 0.08x + 700 - 0.02x
2280 - 700 = 0.06x
x = 1580/0.06
x = 26333.33
and
35000 - x = 35000 - 26333.33
x = 8666.66
Hence, The amount invested at 8% is $26,333.33.
The amount invested at 2% is $8,666.66.
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X + 4 = 40
X = 44
23 = x - 6
X = 29
Create your own false statment but not from the one's given
A false statement could be that
"the maximum height attained by the diver was 20 feet
How to calculate the volume of this shape?
(1 litre = 1000 cm^3)
Answer:
it is half of volume of tube.
tube volume = area of circle (πr)× height of tube (h)
volume of tube = π × r × t
1/2 tube volume = 1/2 × π × r × h
what is the perimeter, in meters, of a rectangular garden 6 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide?
The perimeter of the Garden is 76 meters. and the length is 32m.
Area= L × B
(L×6) = 16 × 12
L = [tex]\frac{288}{6}[/tex] = 32m
Therefore L works out to 32 meters.
Perimeter of Garden = 2 × (32+6) = 76 meter.
The area is the quantity that expresses the extent of a place on the plane or on a curved floor. The area of an aircraft area or aircraft location refers to the region of a shape or planar lamina, at the same time as floor vicinity refers back to the region of an open surface or the boundary of a three-dimensional object. the vicinity may be understood as the quantity of cloth with a given thickness that would be essential to fashion a version of the form, or the amount of paint necessary to cover the floor with an unmarried coat. it's miles the two-dimensional analog of the period of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).
vicinity of a form may be measured by evaluating the form to squares of a fixed size. inside the international system of devices (SI), the usual unit of the region is the rectangular meter (written as m²), which is the region of a square whose facets are one meter lengthy. A shape with a place of three square meters would have the same place as 3 such squares. In arithmetic, the unit rectangular is defined to have region one, and the place of any other shape or floor is a dimensionless actual wide variety.
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The piston diameter of a certain hand pump is inch. The manager determines that the diameters are normally distributed, with a mean of inch and a standard deviation of inch. After recalibrating the production machine, the manager randomly selects pistons and determines that the standard deviation is inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the level of significance?.
We fail to reject the null hypothesis and there is no significant evidence for the manager to conclude that the standard deviation has decreased at the α = 0.01
What is standard deviation?
The standard deviation is a statistic that expresses the degree of variation or dispersion among a group of data. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.
The null and alternative hypotheses are:
[tex]H_{0} :[/tex] α = 0.004
[tex]H_{a} :[/tex] α < 0.004
Under null hypothesis, the test statistic is:
[tex]x^{2} = \frac{(n-1)s^{2} }{\alpha ^{2} }[/tex]
= (29 - 1)0.0036² / 0.004²
= 22.68
Now the critical value of x² at 0.01 level of significance for
df = n-1
= 29 - 1
= 28
[tex]x_{critical} ^{2}[/tex] = 48.278
Since the test statics
x² = 22.68 is less than the critical value
[tex]x_{critical} ^{2}[/tex] = 48.278
∴ we fail to reject the null hypothesis and there is not significant evidence for the manager to conclude that standard deviation has decreased at α = 0.01
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y 'varies inversely with x.
If x = 6 and y = 5, find y when x = 3
Answer: y = 2
Good luck!
How the honk do i solve this problem?
a) Tyler ran 0.07 miles farther than Elena in 10 minutes.
b) The paces of each runner are given as follows:
Tyler: 8 minutes per mile.Elena: 8.5 minutes per mile.c) Due to the lower measure of minutes per mile, Tyler ran faster during the run.
What are the equations?For this situation, the input and the output are given as follows:
Input: distance in miles.Output: time in minutes.This situation is represented by a proportional relationship, in this following format:
t = dv.
In which v is the pace in minutes per mile.
From the graph, Tyler runs 1 mile in 8 minutes, hence:
His pace is of 8 minutes per mile.His equation is of y = 8x.Elena's equation is:
y = 8.5x.
Hence her pace is of 8.5 minutes per mile, meaning that she is slower than Tyler, as she takes more time to run a mile.
The distances in 10 minutes are given as follows:
Tyler: 10/8 = 1.25 miles.Elena: 10/8.5 = 1.18 miles.Hence Tyler ran 0.07 miles farther.
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Write an equation of a parabola that opens upward, has a vertex at the origin, and a focus at (0, 1).
The focus of a parabola does not lie on it. Hence, the equation of parabola is given as y² = 2y - x².
What is a parabola?The parabola can be defined as a conic section curve, all of whose points are equidistant from a fixed point called as focus and a fixed line called as directrix.
Given that,
The focus of parabola is (0, 1).
The vertex of parabola is (0, 0).
Suppose, there is one more point on parabola as (x, y).
Since focus of a parabola is equidistant from all the points on parabola.
Use distance formula to find the distance between two points (x₁, y₁) and (x₂, y₂) as √((x₂ - x₁)² + (y₂ - y₁)²) to find the equation of parabola as,
√((x - 0)² + (y - 1)²) = √((0- 0)² + (0 - 1)²)
=> x² + (y - 1)² = 1
=> (y - 1)² = 1 - x²
=> y² - 2y + 1 = 1 - x²
=> y² = 2y - x²
Hence, the equation of the parabola having vertex at origin and focus at (0, 1) is y² = 2y - x².
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