Answer:
Solve algebraicallyEliminate y:
x² - x - 6 = x + 2x² - 2x = 8x² - 2x + 1 = 9(x - 1)² = 3²1) x - 1 = 3 ⇒ x = 4 ⇒ y = 62) x - 1 = -3 ⇒ x = -2 ⇒ y = 0The solution is:
(-2, 0), (4, 6)Solve graphicallySee the attached
Answer:
[tex]thank \: you[/tex]
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker
Discounted price = $60
Discount = 60%
Let the usual price be x.
So, x - (60% of x) = $60
=> x - [(60/100) × x] = $60
=> x - (60x/100) = $60
=> x - (3x/5) = $60
=> (5x/5) - (3x/5) = $60
=> 2x/5 = $60
=> 2x = $60 × 5
=> 2x = $300
=> x = $300/2
=> x = $150
So, the usual price is $150.
If the length of a leg of a right triangle is 25 and the length of the hypotenuse is 35, what's the length of the other leg, to the nearest tenth?
Answer:
24.5
Step-by-step explanation:
using Pythagorean theorem
[tex]a^{2} +b^{2} =c^{2} \\[/tex]
Since we know the hypotenuse, we can change up the theorem into [tex]c^{2} -b^{2} =a^{2}[/tex]
[tex]35^{2} -25^{2} =a^{2}[/tex]
1225-625=[tex]a^{2}[/tex]
[tex]\sqrt{a^{2} } =24.5[/tex]
Find the missing side. Round your answer to the nearest
Please help me
Answer:
Step-by-step explanation:
The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,450. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 570 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.)
Answer:
The manufacturer should advertise 11720 pages.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 12450, standard deviation of 570:
This means that [tex]\mu = 12450, \sigma = 570[/tex]
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time?
They should advertise the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 12450}{570}[/tex]
[tex]X - 12450 = -1.28*570[/tex]
[tex]X = 11720[/tex]
The manufacturer should advertise 11720 pages.
If two events, A and B, never occur at the same time they are _____.
complementary
compound
simple
disjoint
Answer:
Disjoint is the correct answer.
Mr. Plaggenier divided Camp Greenfield into 5 squads for an athletic scrimmages. Each squad competes against each of the other 4 squads 2 times. The scrimmage lasts 2 hours. If only one pair of teams competes at a time and all of the competitions take the same amount of time, how long is each competitions?
A)6 min.
B) 8 min.
C) 10 min.
D) 12 min.
Answer: (a)
Step-by-step explanation:
Given
There are 5 squads for an athletic scrimmages
If each team played 2 matches
Total no of matches will be
[tex]\Rightarrow \dfrac{5(5-1)}{2}\times 2=20\ \text{matches}[/tex]
So, 20 matches are played in 2 hours
Each match takes
[tex]\Rightarrow \dfrac{120}{20}=6\ \text{minute}[/tex]
Option (a) is correct.
A jar contains 11red marbles, 12 blue marbles and 6 white marbles. Four marbles from the jar are selected. With each marble being replaced after each selection. What is the probability that the first red marble chosen is on the 5th selection?
Answer:
Red on the 5th draw = 0.0907
Step-by-step explanation:
The first to fourth selections are all the same.
Blue + white = 12 + 6 = 18
The total number of marbles is 11 + 12 + 6 = 29
P(~ red) for the first four times = (18/29)^4 = 0,1484
Now on the 5th time, the first red is 11/18
So the Probability is 0.1484 * 11/18 = 0.0907
30 POINTS PLEASEEEEEEEEEEEE HELP
Answer:
Solution given:
f(x)=5x-3
let
y=f(x)
y=5x-3
interchanging role of x and y
x=5y-3
x+3=5y
y=[tex]\frac{x+3}{5}[/tex]
$o,
f-¹(x)=[tex]\frac{x+3}{5}[/tex]
we conclude that
f-¹(x)≠g(x)
Each pair of function are not inverses.
g(x)=x/5+3
let g(x)=y
y=x/5+3
interchanging role of x and y
x=y/5+3
x-3=y/5
doing crisscrossed multiplication
5(x-3)=y
y=5x-15
g-¹(x)=5x-15
So
g-¹(x)≠f-¹(x)
Each pair of function are not inverses.
Given that,
→ f(x) = 5x-3
Then y = f(x),
→ y = 5x-3
Now we can interchange role of x and y,
→ x = 5y-3
Then use the cross multiplication,
→ x+3 = 5y
→ y = x+3/5
Now the inverse is,
→ f-¹(x) = x+3/5
We can go to the conclusion that,
→ f-¹(x) ≠ g(x)
So, each pair of function is not inverse.
Help me again? Thanks to whomever does! Please show work!
Answer: See Below
Step-by-step explanation:
Concept:
Here, we need to know the idea of alternative interior angle, alternative exterior angle, and corresponding angles.
Alternative interior angle: a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
Alternative exterior angle: a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
Corresponding angle: A pair of angles that occupy the same relative position at each intersection where a straight line crosses two others.
All three kinds of angles above occur to be congruent (equal) when the lines are parallel to each other.
If you are still confused, please refer to the attachment below for a graphical explanation
Solve:
PART ONE
a) Name two pairs of alternative exterior angles: ∠1 and ∠7 / ∠2 and ∠8
b) Name two pairs of corresponding angles: ∠1 and ∠5 / ∠2 and ∠6
c) Name two pairs of alternative interior angles: ∠4 and ∠6 / ∠3 and ∠5
PART TWO
a) If the measure of angle 7 is 52°, what is the measure of angle 1?
As we can see from above, ∠1 and ∠7 are alternative exterior angles. They are part of parallel lines, thus according to the properties, they are equal.m∠1 = m∠7 = 52°b) If the measure of angle 8 is 112°, then what is the measure of angle 3?
As we can see from the figure given, ∠8 and ∠7 are linear pairs or supplementary angles, which adds up to 180°.m∠7 = 180 - m∠8 = 180 - 112 = 68°As we can see from the figure given, ∠7 and ∠3 are corresponding angles.They are part of parallel lines, thus according to the properties, they are equal.m∠3 = m∠7 = 68°Hope this helps!! :)
Please let me know if you have any questions
IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15.
(a) Find the IQ scores that represent the bottom 35%.
(b) Find the IQ score that represents the 3rd Quartile.
(c) Find the IQ score for the top 5%.
Answer:
a) IQ scores of 94.2 and below represent the bottom 35%.
b) An IQ score of 110.1 represents the 3rd quartile.
c) IQ scores of 124.7 and higher are in the top 5%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
(a) Find the IQ scores that represent the bottom 35%.
The 35th percentile and below, in which the 35th percentile is X when Z has a p-value of 0.35, so X when Z = -0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.385 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = -0.385*15[/tex]
[tex]X = 94.2[/tex]
IQ scores of 94.2 and below represent the bottom 35%.
(b) Find the IQ score that represents the 3rd Quartile.
This is the 100*3/4 = 75th percentile, which is X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 0.675*15[/tex]
[tex]X = 110.1[/tex]
An IQ score of 110.1 represents the 3rd quartile.
(c) Find the IQ score for the top 5%.
IQ scores of at least the 100 - 5 = 95th percentile, which is X when Z has a p-value of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 1.645*15[/tex]
[tex]X = 124.7[/tex]
IQ scores of 124.7 and higher are in the top 5%.
Find the number that comes after 144five
Answer:
The number that comes after 144five is:
= 200five.
Step-by-step explanation:
Adding 1 to 144 base 5 will result in:
144
+ 1
= 200
b) To obtain the next number that comes after 144five, add 1five to 144five. Since the numbers are in base 5, 1five added to 4five will result in 0 with 1 carried backward. When 1 is added to the next 4, the result will be 0 with 1 carried backward. 1 added to 1 = 2, all in base 5. Figures in base 5 cannot exceed 4. The usual numbers for a base 5 operation are 0, 1, 2, 3, and 4.
the measures of three angles of a triangle are given by (8x-10), (2x), and (3x-5). What is the measure of the larges tangle
9514 1404 393
Answer:
110°
Step-by-step explanation:
The sum of angles of a triangle is 180°.
(8x -10) +(2x) +(3x -5) = 180
13x -15 = 180
13x = 195
x = 15
The largest angle is ...
8x -10 = 8(15) -10 = 110 . . . . degrees
Let x represent the regular price of any book in the store. Write an expression that can be used to find the sale price of any book in the store.
Answer:
.
e
Step-by-step explanation:
.
find find the equation of straight line find the equation of straight line joining the points 3 4 and 5 7
I need help with answering this equation
Answer:
in this case it is just multiplying the two items together
the THIRD CHOICE...
3x(x^2-5x-9)
3x^3 -15x^2 -27x
Step-by-step explanation:
Answer:
3x^3-15x^2-27x
Step-by-step explanation:
the function f (gx) means you have to substitute the function of gx in the function of fx were there's x
3x(x^2-5x-9)
3x^3-15x^2-27x
I hope this helps
Economists have found that the amount of corruption in a country's government is correlated to the gross domestic product (GDP) per capita of that country. This can be modeled by y=1400(1.05)^x where x is the corruption score and y is GDP per capita in dollars. Corruption scores range from 0 to 100 with 0 being highly corrupt and 100 being least corrupt.
What does the y-intercept of this function represent?
A. the corruption score needed for a GDP per capita of zero
B. the increase in GDP per capita for every increase of one in corruption score
C. the GDP per capita of a country with a corruption score of zero
D. the GDP per capita necessary to decrease the corruption score by one
Economists found that amount of corruption in a country is correlated to the Gross domestic products of the country.
Whenever there is high corruption in a country it leads to great negative impacts on the economic growth of that country.
The equation represents the the corruption score for every dollar per capita rise.
The slope of the equation will represent the GDP per capita of a country with corruption score of zero.
The correct answer is C.
C. The GDP per capita of a country with a corruption score of zero.
Noah charges $20 for each lawn that he mows.
Answer:
m = 20 * n
Step-by-step explanation:
The money that he earns is equal the amount earned per lawn times the amount of lawns that he mows
m = 20 * n
Answer:
60 = 3 x 20
Step-by-step explanation:
60 = m
3 = c
20 = n
Find the measure of each side of this triangles. Answer in exact form.
Answer:
[tex]sin(0)=opposite/hypotenuse,cos(0)=adjacent/hypotenuse[/tex]
[tex]sin(60)=\frac{x}{8\sqrt{5} } ,\:\:cos(60)=\frac{y}{8\sqrt{5} }[/tex]
[tex]\frac{\sqrt{3} }{2} =\frac{x}{8\sqrt{5} } \:\:\:\:\frac{1}{2} =\frac{y}{8\sqrt{15} }[/tex]
[tex]2x=8\sqrt{5} \times\sqrt{3} \:\;\:\:2y=1\times8\sqrt{15}[/tex]
[tex]2x=\frac{8\sqrt{15} }{2} \:\:\:\:2y=8\sqrt{15}[/tex]
[tex]x=8\sqrt{15} /2\:\:\: y=8\sqrt{15} /2[/tex]
[tex]x=4\sqrt{15}[/tex] [tex]y=4\sqrt{15}[/tex]
OAmalOHopeO
The image is attached below. Thank you
Use the drawing tools to form the correct answer on the graph.
Plot function g on the graph
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
same as the person above plato 2022'
PLEASE HELP QUICKLY
Determine whether the given sequence could be arithmetic. If so, identify the first difference and the next term.
-6, -11, -16, -21, -26.....
Answer:
The first difference is -5. The next term is -31.
Step-by-step explanation:
If you find the difference between -6 and -11, then you get -5.
And, all the other ones also have differences of -5, so basically, the next term is -31.
Thanks! Please mark me Brainliest!
Answer:
It could be arithmeticIf so, then the first difference is -5 and the next term is -31===================================================
Explanation:
Pick any term and subtract off the previous term
term2 - term1 = -11 - (-6) = -11 + 6 = -5term3 - term2 = -16 - (-11) = -16 + 11 = -5term4 - term3 = -21 - (-16) = -21 + 16 = -5term5 - term4 = -26 - (-21) = -26 + 21 = -5No matter what we picked, we end up with the same result which is -5. This is the common difference aka first difference.
If this pattern keeps up forever, then the sequence is arithmetic.
And if the pattern keeps up, then the next term would be
term6 = term5 + (common difference)
term6 = -26 + (-5)
term6 = -31
Note: Adding -5 is the same as subtracting 5.
moses is inviting 10 friends to a party each friend wants 4 cookies and each box has 10 cookies how many boxes should moses get?
Answer:
4
Step-by-step explanation:
Since each friend wants 4 cookies, and there are 10 friends, there are 10 x 4 = 40 cookies total Moses should buy. Since each cookie box has 10 cookies in it, he should buy 40/10 = 4 total cookie boxes.
Find the intersection of the line and the circle given below
y=-x-3
x^2+y^2=17
Answer:
There are two points of intersection
(-4,1) and (1,-4)
Step-by-step explanation:
Answer:
the guy above me is correct
Step-by-step explanation:
multiplication between exponentiation number 648
Answer:
648 is the sum of consecutive prime numbers 317 and 331.
The sixth root of 648 begins with 2.941682753. Notice all the digits from 1 to 9 appear somewhere in those nine decimal places. OEIS.org states that 648 is the smallest number that can make that claim.
From Archimedes-lab.org I learned some powerful facts about the number 648:
16² – 17² + 18² – 19² + 20² – 21² +22² – 23² + 24² – 25² + 26² – 27² + 28² – 29² + 30² – 31² + 32² = 648
48² – 47² + 46² – 45² + 44² – 43² +42² – 41² + 40² – 39² + 38² – 37² + 36² – 35² + 34² – 33² = 648
(1^2)(2^3)(3^4) = 648
18² + 18² = 648
(6^3) + (6^3) + (6^3) =648
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Print the puzzles or type the solution on this excel file: 10 Factors 2015-10-12
—————————————————————————————————
648 is a composite number.
Prime factorization: 648 = 2 x 2 x 2 x 3 x 3 x 3 x 3, which can be written 648 = (2^3) x (3^4)
The exponents in the prime factorization are 3 and 4. Adding one to each and multiplying we get (3 + 1)(4 + 1) = 4 x 5 = 20. Therefore 648 has exactly 20 factors.
Factors of 648: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
Factor pairs: 648 = 1 x 648, 2 x 324, 3 x 216, 4 x 162, 6 x 108, 8 x 81, 9 x 72, 12 x 54, 18 x 36, or 24 x 27
Taking the factor pair with the largest square number factor, we get √648 = (√324)(√2) = 18√2 ≈ 25.455844122…
HELP
1) Determine the sum of row 19 in Pascal's triangle
Answer: 262144
Step-by-step explanation: You can calculate & draw it out. Then, add the values in the second-to-bottom row of the picture below.
262144 if I'm correct....
Which graph shows the solution set for 2 x + 3 greater-than negative 9? A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded.
Step-by-step explanation:
A number line going from negative 8 to positive 2. An open circle is at negative 6. Everything to the right of the circle is shaded
A pharmacist wants to make 36ml of a 65% hydrogen peroxide solution. how many pls of 75% hydrogen peroxide must he mix with 57% hydrogen peroxide to make the desired solution?
Answer:
16 mls of the 75% solution and 20 mls of the 0.57% solution.
Step-by-step explanation:
Set up a system of equations:
Let x = volume of 75% solution and y be volume of 57% solution
0.75x + 0.57y = 36*0.65
0.75x + 0.57y = 23.4.......(1)
x + y = 36.........(2)
From equation (2):
y = 36 - x
Substituting this into equation(1):
0.75x + (0.57(36 - x) = 23.4
0.75x + 20.52 - 0.57x = 23.4
0.18x = 23.40 - 20.52 = 2.88
x = 2.88/0.18
x = 16
so from equation (2): y = 36-16 = 20.
solve each question please thank you
Answer:
SURE
Step-by-step explanation:
I need help with this
Answer:
[see below]
Step-by-step explanation:
Reflection over the x axis is: [tex](x,y)\rightarrow(x,-y)[/tex]
(0, -2) - > (0, 2)
(5, -1) - > (5, 1)
(2, -4) - > (2, 4)
A'B'C' should be (0,2), (5,1) and (2,4). (Or option B)
Hope this helps.
A principal P is to be invested at continuous compound interest of 1.9% to yield $50,000 in 20 years. What is the approximate value of P to be invested?
You may need to delete the dollar sign and/or the comma when typing in the answer.
=======================================================
Work Shown:
[tex]A = P*e^{rt}\\\\50,000 = P*e^{0.019*20}\\\\50,000 = P*e^{0.38}\\\\P = \frac{50,000}{e^{0.38}}\\\\P \approx 34,193.0704606\\\\P \approx 34,193.07\\\\[/tex]
Side note: the 'e' is a special constant roughly equal to 2.71828...
Julio has a net pay of $ 537.00 each paycheck. He pays $ 142.00 in pre-tax deductions and taxes each paycheck. What is Julio's gross income before the tax deductions?
Answer:
Julio's gross income before the tax deductions is $ 405.
Step-by-step explanation:
Given that Julio has a net pay of $ 537.00 each paycheck, and he pays $ 142.00 in pre-tax deductions and taxes each paycheck, to determine what is Julio's gross income before the tax deductions the following calculation must be performed:
547 - 142 = X
405 = X
Therefore, Julio's gross income before the tax deductions is $ 405.
