Answer:
The two solutions are
5 and 9
-5 and -9
Step-by-step explanation:
Let x and y be the numbers
x-y = 4
x*y = 45
Using substitution
x = 4+y
(4+y)y =45
4y + y^2 = 45
Subtract 45 from each side
y^2 +4y -45 =0
Factor
(y - 5) ( y+9) = 0
Using the zero product property
y -5 =0 y+9 =0
y=5 y = -9
Now we can find x
y=5
x = 4+y
x =4+5
x=9
y = -9
x = 4+y
x = 4+-9
x = -5
The two solutions are
5 and 9
-5 and -9
5. Please help and show work
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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What’s the answer?
5x + 12(19 - x) = 19(1678)
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:
Which equation best represents the graph shown below? Explain in detail how you arrived at your answer by stating each of the mathematical transformations necessary to produce the graph.
please I need help
In the graph we have a parabola, and its equation is y = (x - 2)^2 - 3
How to find the equation of the graphed function?
In the graph, we can see a parabola.
We only need to identify 3 parts, which are the two x-intercepts (if it has) and the y-intercept.
Remember that if the vertex and the y-intercept. Remember that if the vertex is (h, k) and the leading coefficient is a, then we can write the equation as:
y = a*(x - h)^2 + k
In the image we can see that the vertex is (2, -3), then:
y = a*(x - 2)^2 - 3
And the y-intercept is y = 1, then if we evaluate in x = 0 we should get y = 1, replacing that we get:
1 = a*(0 - 2)^2 - 3
1 = a*4 - 3
1 + 3 = a*4
4/4 = a = 1
Then the quadratic equation is y = (x - 2)^2 - 3
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A bowl filled with lollipops is 3/4 full. 2/3 of these lollipops are green. What fraction of the full bowl are the green lollipops?
Answer:
1/12
Step-by-step explanation:
All you need to do is subtract 3/4 by 2/3, the difference of those two numbers is 1/12.
please help, Solve K-PRT for R.
Answer:
r = [tex]\frac{k}{pt}[/tex]
Step-by-step explanation:
I think that you mean
K = PRT Divide both sides by pr
[tex]\frac{k}{pr}[/tex] = [tex]\frac{prt}{pr}[/tex] On the right sides the pr's on the top and bottom cancel each other out and you are left with
r = [tex]\frac{k}{pr}[/tex]
Is there a difference between [tex]-\frac{x}{y}[/tex] and [tex]\frac{-x}{-y}[/tex] ?
Do they mean different things?
There is a difference between the expressions -x/y and -x/-y
How to determine if there is a difference between the expression?The expressions are given as:
-x/y and -x/-y
When the expression -x/-y is evaluated, we have:
-x/-y = x/y
This means that
-x/y = -x/y
-x/-y = x/y
When the above expressions are compared, we can see that both expressions are not equal
Hence, there is a difference between the expressions -x/y and -x/-y
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Which linear equation represents the information shown in the table?
x y
–6 –1
0 0
12 2
Question 21 options:
y = –1/4x
y = 6x
y = 1/6x
y = –2x
Answer:
Only one equation fits all the information on the table which is:
y = 1/6x
Answer:
y = 1/6x
Step-by-step explanation:
To find the equation, let's see if each option works by plugging in x into each equation.
y = –1/4x
Plug -6 into x
y = –1/4(-6)
y = 1.5
y = –1/4x doesn't work because we didn't get -1.
y = 6x
Plug -6 into x
y = 6(-6)
y = -36
y = 6x doesn't work because we didn't get -1.
y = 1/6x
Plug 1/6x into x
y = 1/6(-6)
y = -1
Let's see if the other x values work.
Plug 0 into x
y = 1/6(0)
y = 0
Plug 12 into x
y = 1/6(12)
y = 2
y = 1/6x works.
y = –2x
Plug -6 into x
y = –2(-6)
y = 12
y = -2x doesn't work because we didn't get -1.
y = 1/6x is the only linear equation that worked and got all y values, so that is your answer.
Hope that helped and have a lovely rest of your day!
What are Conic Sections and how are they formed?
Answer:
In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type.
Conic sections are formed on a plane when that plane slices through the edge of one or both of a pair of right circular cones stacked tip to tip.
What is the fractional equivalent of the repeating decimal _
0.5
Answer:
B. 5/9
Step-by-step explanation:
You can just divide 5 and 9 and you get the repeating decimal
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
A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410410 minutes, the monthly cost will be \$71.50$71.50. If the customer uses 720720 minutes, the monthly cost will be \$118.00$118.00. Use your equation to find the total monthly cost if 687687 minutes are used.
The required cost is $ 101.22.
This problem can be solved by unitary method.
Given that monthly cost of customer if he uses 410 minutes is $71.
So, cost per minute = [tex]\frac{71}{410}[/tex]
=$ 0.17
And if the customer uses 720 minutes then the cost is $118.
So, cost per minute is = [tex]\frac{118}{720}[/tex]
=0.16
Now if he uses 687 minutes then for 410 minutes cost incurred will be
= 410 × 0.17
= $ 69.7
And for next 197 minutes cost incurred will be = 197 × 0.16
= $ 31.52
Total cost for 687 minutes = $(69.7 + 31.52)
= $ 101.22
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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
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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determine the range of the following graph. PLEASE HELP MEEE
Answer:
-5 ≤ y ≤ 5
Step-by-step explanation:
Hello!
The range is the set of y-values that the graph passes through.
Since the endpoints of the graph are filled in, meaning they include the values they end on, we use the ≥ or ≤ symbols to write the inequality for the range.
The minimum y-value is -5, and the maximum y-value is 5.
The inequality for the range would be -5 ≤ y ≤ 5.
If x > 3,, which of the following is equivalent to
1
1
1
+
x+ 2 x+3
?
I
If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].
As per the question statement, we are provided with a mathematical expression in the form of a fraction which goes as [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex].
We are required to calculate an equivalent simplified form of the above mentioned expression.
To solve this question, we simply have to add the fractions in the denominator part and then perform a reciprocal of the overall fraction, and simplify it further in that format only, to obtain our final desired answer. The process is shown below as:
[tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}]\\=\frac{1}{\frac{(x+3)+(x+2)}{(x+2)(x+3)} } \\=\frac{1}{\frac{(2x+5)}{(x+2)(x+3)} }\\=\frac{(x+2)(x+3)}{(2x+5)} \\=\frac{x^{2}+3x+2x+6 }{2x+5} \\=\frac{x^{2}+5x+6 }{2x+5}[/tex]
Hence, If (x > 3), then the simplified form of the expression [tex][\frac{1}{(\frac{1}{x+2})+(\frac{1}{x+3})}][/tex] will be equivalent to [tex][\frac{x^{2}+5x+6 }{2x+5}][/tex].
Expression: In Mathematics, expressions are mathematical statements that have at least two terms, comprising of numbers or variables, or both, and being connected by an operator in between.To learn more about Expressions, click on the link below.
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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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How do I solve this problem?
On Friday, 4/7 of Parkden School chose pasta for lunch, 1/5 chose pizza and the rest chose salad. What fraction of the pupils chose salad?
Answer:
i think is 7/12
because if 4/7 chose pasta,1/5 chose pizza then we add 7+5=12 then we sudstract 12-4-1 = 7.
hope that helps
every year from 2002 to 2014 either joey chestnut of california or takeri kobayashi of japan won the contest. in the five of those years both men completed and the results od the rivalry are shown in the table below. ( after the tie in 2008 joey chestnut won in aan overtime) because the condition of the year natter this is a matched pairs situation witht he twi men going against each year. in a matched pair situation we ise the summary statistica of difference between paris of values
Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?
m - 4 = -7m - 8
-8 - 3m = 4 - m
-3m - 8 = 4 - m
-15m = -4m
-7m - 8 = m - 4
-8 - 7m = -4 + m
You can have multiple answers
The equation equivalent to -2m - 5m - 8 = 3 + (-7) + m is
-7m - 8 = m - 4. Option E
This is further explained below.
Which of the following equations are equivalent to -2m - 5m - 8 = 3 + (-7) + m?Generally, the equations equivalence is mathematically given as
-2m - 5m - 8 = 3 + (-7) + m
Therefore
-7m - 8 = 3 + (-7) + m
When we write the equation such that the variable appears on the right-hand side first, we get the following:
-7m - 8 = m - 4
In conclusion, The equation equivalent to -2m - 5m - 8 = 3 + (-7) + m is
-7m - 8 = m - 4.
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Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 19 of the 59 boxes on the shelf have the secret decoder ring. The other 40 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that both of them have the secret decoder ring?
The probability that both of the boxes one would select had the decoder ring is 9.9%.
Given, the store manger gives the surety that 19 out of 59 boxes on the shelf have the secret decoder ring.
The boxes on the shelf which have a different gift inside is = 40 boxes.
If one randomly selects two boxes from the shelf to purchase, the probability that both of them have the secret decoder ring = ?
You can imagine that someone used invisible link to label each box with a number, and knows that boxes number 1 through 19 have decoder rings, while boxes number 20 through 59 have other gifts.
There are 59×58/2
= 3422/2
= 1711 possible sets of two boxes that one could select, but there are only 19 × 19/2
= 342/2
= 171 possible sets of two boxes with decoder rings.
The fraction of possible pairs of boxes where both boxes have the secret decoder ring is:
= 171/1711
= 0.099 = 9.9%
Hence there is 9.9% probability that both of the boxes one might select had a decoder ring.
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A town's employment statistics show that 855 of its residents were unemployed last month. This is a decrease of 25% from the previous month. How many residents were unemployed in the previous month?
7. Alicia and Dexter are each walking on a straight path. For a particular -second window of time, each has their velocity (in feet per second) measured and recorded as a function of time. Their respective velocity functions are plotted in .
Figure 1.4.14. The velocity functions and for Alicia and Damon, respectively.
Determine formulas for both and .
What is the value and meaning of the slope of ? Write a complete sentence to explain and be sure to include units in your response.
What is the value and meaning of the average rate of change of on the interval ? Write a complete sentence to explain and be sure to include units in your response.
Is there ever a time when Alicia and Damon are walking at the same velocity? If yes, determine both the time and velocity; if not, explain why.
Is is possible to determine if there is ever a time when Alicia and Damon are located at the same place on the path? If yes, determine the time and location; if not, explain why not enough information is provided.
(a) The formula for velocity functions is:
f(t)=0.4t+4
g(t)=0.9t
(b) The slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec². The slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².
(c) Damon is accelerating with 0.9 ft/sec² in intervals [4,8].
(d) Both are walking at a velocity of 7.2 ft/sec at t=8 sec.
What is velocity?
The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.(a) For Alicia,
m=(Δv/Δt)=(8-4)/(10-0)=4/10=0.4
f(t)=0.4t+4
for Damon,
m=(Δv/Δt)=(9-0)/(10-0)=9/10=0.9
g(t)=0.9t
The formula for velocity functions is:
f(t)=0.4t+4
g(t)=0.9t
(b) Value and meaning of the slope is
m for Alicia =0.4
Slope is determined (Δv/Δt)=(8-4)/(10-0)=4/10=0.4 ft/sec².
So, the slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec².
m for Damon=0.9
Slope is determined (Δv/Δt)=(9-0)/(10-0)=9/10=0.9 ft/sec².
So, the slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².
(c) Value and meaning of the average rate of change on the interval:
the average rate of change of Δ on the interval [4,8] =
[tex]\frac{Velocity\ at\ 8\ sec - Velocity\ at\ 4\ sec}{Time\ interval\ (8-4)\ sec}[/tex]
=(7.2-3.6)/(8-4)=(3.6/4)=0.9 ft/sec²
So, Damon is accelerating with 0.9 ft/sec² in intervals [4,8].
(d) Let both are walking with the same velocity at t sec.
So, Let's equate their velocities
0.4t+4=0.9t
t=4/0.5 = 8 sec
The velocity of Alicia at 8 sec = 0.4(8)+4 = 7.2 ft/sec
The velocity of Damon at 8 sec = 0.9(8) = 7.2 ft/sec
So, both are walking at a velocity of 7.2 ft/sec at t=8 sec.
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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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Please help on the middle!!
Answer: I just points so rate this a 10
Step-by-step explanation:
Answer:
owi4w85e963696w95witote5iw47e
Okay so for context there's 4 pounds of pears 3 pounds of grapes 6 pounds of pineapple and 3 pounds of oranges
OKAY NOW FOR THE ACTUAL QUESTION
Jorge wants to bring 2 pounds total of this fruit salad to a potluck dinner, how much of each ingredient should he use?
The total amount of each ingredient are as follows;
Pears = 1/2 pound
Grapes = 3/8 pounds
Pineapple = 3/4 pounds
Oranges = 3/8 pounds
How to Solve Ratio Problems?
We are given the amounts of fruits as;
4 pounds of pears
3 pounds of grapes
6 pounds of pineapple
3 pounds of oranges
Now, total pounds of fruits = 4 + 3 + 6 + 3 = 16 fruits
Ratio of pears = 4/16 = 1/4
Ratio of grapes = 3/16
Ratio of pineapple = 6/16 = 3/8
Ratio of oranges = 3/16
Thus. amount of each ingredient required are;
Pears = 1/4 * 2 = 1/2 pound
Grapes = 3/16 * 2 = 3/8 pounds
Pineapple = 3/8 * 2 = 3/4 pounds
Oranges = 3/16 * 2 = 3/8 pounds
Thus, the total amount of each ingredient are as follows;
Pears = 1/4 * 2 = 1/2 pound
Grapes = 3/16 * 2 = 3/8 pounds
Pineapple = 3/8 * 2 = 3/4 pounds
Oranges = 3/16 * 2 = 3/8 pounds
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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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$2,000 is the average price of a square foot. How much would you have to pay if you want to buy a 2 bedroom (1,200 sq ft) apartment in Manhattan ?
Answer:
$2,400,000
Step-by-step explanation:
Just multiply them together
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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