Answer:
. Onusko made 60 cookies for a bake sale. She sold 2/3 of them and gave 3/4 of the remaining cookies to the students working at the sale. How many
Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
The product of 3 and the difference of 5 and a number.
The sentence "5 is subtracted from the square of a number" represented as an algebraic expression is x² -5.
Algebraic expressions: what are they?
A group of integers or variables combined using the operations +, -, o, or constitute an expression. algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.Given,
Let the number be x and 3 is subtracted from a number.
Represent it in expression.
Step 2
3 is subtracted from a number means 3 is subtracted from x.
Here we have to subtract 3 from x. It can be represented as = x - 3
Let the number be x.
In this exercise, you're required to write an algebraic expression to represent the word problem (sentence). Also, the number would be denoted by the letter x and no need for further simplification of the algebraic expression.
Translating the word problem (sentence) into an algebraic expression, we have;
Square of a number (x) = x²
Subtracting 5 from the the square of x, we have x² -5 .
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.Solve 2x−1<4 or −5x−3>−3 and write the solution in interval notation.
The interval notation is { 5/ 2 < x > 0 }
How to determine the valueGiven the inequalities;
2x−1<4−5x−3>−3To determine the value of x, we have;
2x - 1 < 4
collect like terms
2x < 4 + 1
2x < 5
Make 'x' the subject
x < 5/ 2
−5x −3 > −3
collect like terms
-5x > -3 + 3
-5x > 0
x > 0
Thus, the interval notation is { 5/ 2 < x > 0 }
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9x = 7x + 22 need help
Answer:
x=11
Step-by-step explanation:
9x=7x+22
9x-7x=22
2x=22
2x/2=22/2
x=11
Nine hundred ninety two hundred thousandths wrote in decimal form
Answer:
I think the answer is 9.920 please be careful with your answer I think it 9.920 because it says nine hundred and ninety two thousands so therefor the decimal need to be in between 9 and 9 I hope you get this correct!
step-by-step explanation:
Please help on the middle!!
Answer: I just points so rate this a 10
Step-by-step explanation:
Answer:
owi4w85e963696w95witote5iw47e
If y’all can’t se it just zoom in because that’s the best I can get it please help me thank u please don’t comment on my stuff just for points I really need help with this
Answer:
the answer is 42
Step-by-step explanation:
you add 217+153+88=458
500-458=42
the distance between two cities on a map measures 3.75 inches. the scale shows that 2 inches is equal to 50 miles . how many miles apart are the cities
all real numbers greater than or equal to 55
The set notation of the numbers is {x | x < 50 ∪ x > 50}
How to determine the set notation of the numbers?The set is given as
The set of all real numbers less than 50 or greater than 50
Let the number be represented by x
So, we have
x less than 50 or x greater than 50
When represented as an inequality, we have
x < 50 or x > 50
Using set notation, we have
{x | x < 50 ∪ x > 50}
Hence, the set notation of the numbers is {x | x < 50 ∪ x > 50}
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Fill in all missing terms and select all missing descriptions.
Answer:
Add all like terms
12s = 0
s = 0
Step-by-step explanation:
8s + 6 + 4s = 6
12s + 6 = 6
-6 -6
12s = 0
÷12 ÷12
s = 0
I hope this helps!
Ettwice is three times as old as mavis. the sum of their age is 60. how old each
the answer to your question is Ettwice is 45 years old and Mavis is 15 years old. hope this helps
Step-by-step explanation:
15 * 3 = 45
45 + 15 = 60
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 20. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 80 and 120? (b) What percentage of people has an IQ score less than 60 or greater than 140? (c) What percentage of people has an IQ score greater than 160?
Using the Empirical Rule, the percentages are given as follows:
a) 68%.
b) 5%.
c) 0.15%.
What does the Empirical Rule state?It states that, for a normally distributed random variable, approximately:
68% of the values in the distribution are within 1 standard deviation of the mean.95% of the values in the distribution are within 2 standard deviations of the mean.99.7% of the values in the distribution are within 3 standard deviations of the mean.For item a, 80 and 120 are within one standard deviation of the mean, hence:
68% of people has an IQ score between 80 and 120.
For item b, the bounds are within two standard deviations of the mean, hence 5% of the observations are outside this interval, that is:
5% of people has an IQ score less than 60 or greater than 140.
For item c, 160 is three standard deviations above the mean. Considering the symmetry of the normal distribution, 0.3/2 = 0.15% of people has an IQ score greater than 160?.
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NO LINKS!! Please help me with these problems. Part 10a1
y = √(x - 2)
Answer:
Domain: [2, ∞)Range: [0, ∞)Continuity: Function is continuous on its domain [2, ∞).Minimum point at (2, 0).Increasing function: (2, ∞)Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.Step-by-step explanation:
Given function:
[tex]y=\sqrt{x-2}[/tex]
DomainThe domain is the set of all possible input values (x-values).
As the square root of a negative number cannot be taken, the domain of the given function is restricted.
[tex]x-2\geq 0 \implies x\geq 2[/tex]
Therefore, the domain of the given function is [2, ∞).
RangeThe range is the set of all possible output values (y-values).
As the square root of a negative number cannot be taken, the range of the given function is restricted.
Therefore, the range of the given function is [0, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Therefore, the function is continuous on its domain [2, ∞).
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & = \sqrt{x-2}\\& = (x-2)^{\frac{1}{2}\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{1}{2}(x-2)^{-\frac{1}{2}}\\ & = \dfrac{1}{2\sqrt{x-2}}\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{1}{2\sqrt{x-2}} &= 0\\\dfrac{1}{2} &\neq 0\end{aligned}[/tex]
Therefore, there are no stationary points.
As the domain is restricted and f(x) ≥ 0, the minimum point of the function is at point (2, 0).
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & > 0 \\ \dfrac{1}{\sqrt{x-2}} & > 0\\ \textsf{If $\frac{1}{a} > 0$ then $a > 0$}: \\ \implies \sqrt{x-2} & > 0\\ x-2 & > 0\\ x & > 2\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & < 0 \\ \dfrac{1}{\sqrt{x-2}} & < 0\\ \textsf{If $\frac{1}{a} < 0$ then $a < 0$}: \\ \implies \sqrt{x-2} & < 0\\ \textsf{As $\sqrt{x}\geq 0$, no solution.}\end{aligned}[/tex]
Therefore:
The function is increasing in the interval (2, ∞).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.
Answer:
Domain: [2, ∞)
Range: [0, ∞)
Continuity: Function is continuous on its domain [2, ∞).
Minimum point at (2, 0).
Increasing function: (2, ∞)
Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.
An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population.
Find the probability that the sum of the 95 values is less than 7,450. (Round your answer to 4 decimal places)
The probability that the sum of the 95 values is less than 7450 is 0.1002
Given Data :
An unknown distribution has a
Mean (μ) = 80
Standard Deviation (σ) = 12
Sample Size (n) = 95
is drawn from the population.
∑X ≈ N (95 * 80, [tex]\sqrt{95}[/tex] * 12)
= N (7600, 116.96)
The Probability that the sum of the 95 values is less than 7450 is given as follows :
P(∑x < 7450) = P [(∑x - μ) / s] < [(7450 - 7600) / 116.96
= P(Z < -1.282) = 0.1 (From Z table)
Hence, the probability that the sum of the 95 values is less than 7450 is 0.1002
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The length of a rectangle is 1 fr more than double the width, and the area of the rectangle is 45 ft^2. Find the dimensions of the rectangle.
The length and width of rectangle is 10 feet and 4.5 feet.
This problem is related to the area and perimeter of plane figures. We have to find the dimensions of the rectangle using the data given.
Given, the length is 1 feet more than twice the width.
Let the width be a feet.
So, length = (2a+1) feet
Now according to question,
[tex](2a+1)(a)=45\\[/tex]
⇒ [tex]2a^{2} +a-45=0[/tex]
On solving the above quadratic equation we get a=4.5 feet.
So, length = 10 feet.
The dimension of rectangle is 10 feet × 4.5 feet.
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Lucia walked of the length of the Tremont Trail before
stopping for a rest. How far had Lucía walked on the trail?
Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail
We are told in the question that
Linda walked 3/4 of the length of the Tremont Trail before stopping for a rest.
From the question, the length of the Tremont Trail = 3 1/2 miles
Hence, the distance (how far )Linda has walked =
3/4 of 3 1/2 miles
= 3/4 × 3 1/2 miles
= 3/4 × 7/2 miles
= 21/8 miles
= 2 5/8 miles or 2.625 miles
Therefore, Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail.
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The length of a rectangle is 1 in. less than 3 times the width. If the perimeter of the rectangle is 46 in., find the length and the width.
[tex] \Large {\mathbb {SOLUTION: }}[/tex]
[tex] \: \: \text{L = 3w - 1}[/tex]
[tex] \: \: \text{P=46}[/tex]
[tex] \: \: \text{2(3w-1) + 2w = 46}[/tex]
[tex] \: \: \text{6w - 2 + 2w = 46}[/tex]
[tex] \: \: \text{8w = 48}[/tex]
[tex] \: \: \text {W = 6 }[/tex]
[tex] \: \: \text{L = 17}[/tex]
[tex] \: \: \text{Applying the inequalities:}[/tex]
[tex] \: \: \text{L>=17 and w=6}[/tex]
[tex] \: \: \text{The perimeter is at least 46.}[/tex]
A shopkeeper allows a discount of 10% on the marked price of an article.What was the marked price of the article which costs him 1800 and makes profit of 15%.
Answer:
$243 is his profit
Step-by-step explanation:
Answer: $4100
Step-by-step explanation:
discount = [tex]\frac{1800}{90}[/tex]×100 = 2000
profit = [tex]\frac{115}{100}[/tex]×2000 = 2300
market price = 2300 + 1800 = 4100
Two angles are complementary if their sum is 90°. A larger angle measures three degrees less than
twice the measure of the smaller angle. If x represents the measure of the smaller angle and these two
angles are complementary, find the measure of each angle.
Answer:
31 and 59
Step-by-step explanation:
We can figure this out by putting the words into an equation
"three degrees less than twice the measure of the smaller angle"
we know the smaller angle = x, so:
twice the smaller angle=2x
3 degrees less=-3
you then put those into an equation where they all add up to equal 90 and simplify
x+2x-3=90
3x-3=90
3x=93
x=31
you then plug that into the equation we would have for the second angle:
2x-3
2(31)-3
62-3
59
the first angle would be 31 and the second angle would be 59
:D
You buy a new computer for $1500. The value of the computer decreases by 6% every year. How much is the computer worth after 4 years?
Answer: Your computer will be worth $1,171.12
Step-by-step explanation:
[tex]a_n = 1500(0.94)^4\\a_n=\boxed{1171.12}[/tex]
If 7cakes cost $6.30 what is the cost of 12 such cakes
Answer:
$10.8
Step-by-step explanation:
First, to determine the price of one cake divide 6.30/7
You will determine one cake costs 90 cents.
So, multiply 0.90 by 12, and you get $10.8
what is (8^5)^4 (answer must include an exponent )
Answer:
[tex]8^{20}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](8^5)^{4}[/tex] = [tex]8^{5(4)}[/tex] = [tex]8^{20}[/tex]
Please help!!!!!!! thx xxx
Start by dividing both sides by G, giving us
[tex]\frac{F}{G}=\frac{m_{1} m_{2} }{d^{2} } }[/tex]. Multiply both sides by d^2. [tex]\frac{F}{G}(d^{2})=m_{1} m_{2}[/tex].
Finally, divide both sides by m2.
[tex](\frac{F}{G}\div{m_{2}}) (\frac{d^{2} }{m_{2} } )=m_{1}[/tex]
Hope this helps! This was a tough problem for me too.
The governor of state A earns $49,485 more than the governor of state B. If the total of their salaries is $288,035, find the salaries of each.
need to find a and b
Answer:
a) $168,760
b) $119,275
Step-by-step explanation:
For this, I believe you do $288,035 - $49,485. This equals $238,550.
Then divide this by 2 to get the salary for state B, which is $119,275 .
$168,760 remains, so it's the salary for state A.
Answer:
Governor of state A = 168,760
Governor of state B = 119,275
Step-by-step explanation:
A = 49485 + B Eq. 1
A + B = 288035 Eq. 2
A = Earns of governor of state A
B = Earns of governor of state B
Replacing Eq. 1 in Eq. 2:
(49485+B) + B =288035
2B + 49485 = 288035
2B = 288035 - 49485
2B = 238550
B = 238550/2
B = 119275
From eq. 1
A = 49485 + 119275
A = 168760
Check:
from eq. 2:
A + B = 288035
168760 + 119275 = 288035
The perimeter of a rectangle is 32 m. The length is 4 m more than two times the width. Find the length and the width of the rectangle.
The length of the rectangle is 12 meters and its width is 4 meters.
A rectangle is a four sided figure, whose opposite sides are equal and the angle formed by any two adjacent sides is 90 degrees.
Here, we are given that the perimeter of the rectangle is 32 meters.
Let the length of the rectangle be L and breadth or width be B
We known that perimeter of a rectangle = 2(L + B)
Now, it is given that the length is 4 m more than two times the width
⇒ L = 4 + 2B
Thus, the area of the perimeter will be-
Perimeter = 2(4 + 2B + B)
⇒ 32 = 2(4 + 2B + B)
32/2 = 4 + 2B + B
16 = 4 + 3B
16 - 4 = 3B
12 = 3B
or 3B = 12
B = 12/3
B = 4
Thus, the width of the rectangle is 4 meters.
Therefore, L = 4 + 2(4)
L = 4 + 8
L = 12
Thus, the length of the rectangle is 12 meters.
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Oscar buys a bag of cookies that contains 7 chocolate chip cookies, 8 peanut butter cookies, 9 sugar cookies and 7 oatmeal cookies.
What is the probability that Oscar reaches in the bag and randomly selects a peanut butter cookie from in the bag and randomly selects a peanut butter cookie from
the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie?
Give your answer as a fraction, or accurate to at least 4 decimal places.
The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how probable an event is to do, or how likely it's that a proposition is true. The probability of an event is a number between 0(zero)(zero) and 1(one), where, roughly speaking, 0(zero) indicates the impossibility of the event and 1(one) indicates certainty.The more advanced the probability of an event, the more likely it's that the event will do.These generalities have been given a self-evident fine formalization in probability proposition, which is used extensively in areas of study similar to statistics, mathematics, wisdom, finance, gambling, artificial intelligence, etc.
P(sugar | oatmeal) = (7/25)(6/24) = 0.07
The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.
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HELPP!!
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 15 gallons of water. Ryan used 6.8 gallons to water his garden in June and 5 and one-eighth gallons in July. How much water is left in the barrel?
1.) 3.075 gallons
2.) 5.125 gallons
3.) 5.178 gallons
4.) 16.675 gallons
Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:
1.) 3.075 gallons.
How to find the remaining amount of water in the barrel?
To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.
We have that:
The initial amount was of 15 gallons.The amount used was of: 6.8 + 5 + 1/8(relative to the one-eight) = 11.925 gallons.Hence the remaining amount is:
15 - 11.925 = 3.075 gallons.
Which means that option 1 is correct.
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Answer: 3.075 gallons
Step-by-step explanation:
Rewrite the following statement using a number in scientific notation.
My new music player has a capacity of gigabytes 400. (Recall that giga means billion.)
My new music player has a capacity of _ enter your response here bytes.
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
4 x 10¹¹
Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
400 billion in scientific notation = 4 x 10¹¹
We can complete the sentence as,
My new music player has a capacity of 4 x 10¹¹
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How many times larger is (1.143 x 101) than (9 x 10−1)?
0.127
7.87
10.287
12.7
how did you get your answer?
(1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7
Calculating magnitudeFrom the question, we are to determine the factor by which 1.143 × 10¹ is larger than 9 × 10⁻¹
To determine how many times larger the number is, we will divide 1.143 × 10¹ by 9 × 10⁻¹
Carrying out the division operation
(1.143 × 10¹) ÷ (9 × 10⁻¹)
= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)
= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)
= 0.127 × (10¹ ⁻ ⁽⁻¹⁾)
= 0.127 × (10¹ ⁺ ¹)
= 0.127 × (10²)
= 0.127 × 10²
= 12.7
Hence, (1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7
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For the equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the equation.
For the linear function x - y = 3, three ordered pairs are given as follows:
x = 3, y = 0.x = 1, y = -2.x = 0, y = -3.Using points (3,0) and (0,-3), the graph of the function is given at the end of the problem.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the function is:
x - y = 3.
In standard notation:
y = x - 3.
Hence three pairs of points are given as follows, replacing the value of x in the equation to find y.
x = 3, y = 0.x = 1, y = -2.x = 0, y = -3.The graph of the function is given at the end of the answer.
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Use f(x) = |x|
f(x) is shifted down 4 and right 3 to create h(x)
Which answer shows the correct function for h(x)
The function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -
(y - 4) - |x - 3| = 0
What is Modulus function?The modulus function can be written as follows -
|x| = x [for x ≥ 0]
|x| = - x [for x < 0]
Given that a function f(x) = |x| which is shifted down by 4 units and right by 3 units. Therefore, we can write -
y = f(x) = |x|
Change in y - coordinate = y + 4.
Change in x - coordinate = x - 3.
We will plot the graph of h(x) after the doing the given changes in the coordinates.
Now, we have -
y = |x|
y - |x| = 0
Change in y - coordinate can be written as -
(y + 4) - |x| = 0
Change in x - coordinate can be written as -
(y - 4) - |x - 3| = 0
Now, the graph of both f(x) and and h(x) is attached at the end.
Therefore, the function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -
(y - 4) - |x - 3| = 0
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