[tex]x ^{3} + 5x {}^{2} - 8 r - 20 = 0 \\ x { }^{3} + 5x {}^{2} - 8r - 20(x {}^{3} + 5x {}^{2} ) = 0 - (x {}^{3} + 5x {}^{2} ) \\ - 8r - 20 = - (x {}^{3} + 5x {}^{2} ) \\ \\ - 8r - 20 + 20 = - (x {}^{3 } + 5x {}^{2} ) + 20 \\ \\ - 8r = x {}^{3} - 5x {}^{2} + 20 \\ \\ [/tex]
hope it is helpful
Find the area and perimeter
for each polygon.
Answer:
5. P = 23 m
A = 15 [tex]m^{2}[/tex]
6. P = 24.4 in
A = 15.3 [tex]in^{2}[/tex]
Step-by-step explanation:
Area formula of a triangle is A = 1/2 bh
Area formula of a parallelogram is A = bh
5. The height of a triangle is perpendicular to the base.
A = 1/2 * 10 * 3
A = 15 [tex]m^{2}[/tex]
6. The height of the parallelogram is also perpendicular to the base.
A = 9 * 1.7
A = 15.3 [tex]in^{2}[/tex]
Perimeter means you add all the side lengths.
5. The side lengths are 5m, 8m, and 10m. Adding those together, you get 23m.
6. A parallelogram has congruent opposite sides. That means your side lengths are 9 in, 3.2 in, 9 in and 3.2 in. Adding those together, you get 24.4 in.
A radar unit is used to measure speeds of cars on a miter way the speed are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr what is the probability that’s a car picked at random is traveling at more than 100 km/hr
Using the normal distribution, there is a 0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 90, \sigma = 10[/tex]
The probability that’s a car picked at random is traveling at more than 100 km/hr is one subtracted by the p-value of Z when X = 100, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 90}{10}[/tex]
Z = 1
Z = 1 has a p-value of 0.8413.
1 - 0.8413 = 0.1587.
0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.
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PLEASE HELP Find the value of x.
X
15
12
Answer: x = 9
Step-by-Step Solution:
Hypotenuse = 15 units
Base = 12 units
Altitude = x units
Using Pythagoras Theorem,
=> Hypotenuse^2 = Base^2 + Altitude^2
(15)^2 = (12)^2 + x^2
225 = 144 + x^2
225 - 144 = x^2
81 = x^2
x^2 = 81
x = √81
=> x = 9
Therefore, Altitude = 9 units
David rented a truck for one day. There was a base fee of $17.99, and there was an additional charge of 84 cents for each mile driven. David had to pay $250.67 when he returned the truck. For how many miles did he drive the truck?
Answer:
277 miles
Step-by-step explanation:
JOHN RICHARDS BORROWED $875 AGAINST HIS CHARGE ACCOUNT ON SEPTEMBER
12 AND REPAID THE LOAN ON OCTOBER 14 (32 DAYS LATER). IF THE INTEREST RATE
IS 0.04273% PER DAY, HOW MUCH INTEREST DID JOHN PAY ON THE LOAN AND WHAT
AMOUNT DID HE PAY THE BANK WHEN HE REPAID THE LOAN
Using simple interest, it is found that:
John paid $12 in interest for the loan.The total amount that he paid the bank was of $887.Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t units of time in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.For this problem, the parameters are given as follows:
A(0) = 875, r = 0.0004273, t = 32.
Hence the amount paid is given by:
A(32) = 875 x (1 + 0.0004273 x 32) = $887.
The amount of interest is given by:
I = 887 - 875 = $12.
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Select the correct answer. The graph of function f is shown. An exponential function passes through (minus 4, 9), (0, 1), (1, 0), and (5, minus 2). Function g is represented by the table. x -1 0 1 2 3 4 g(x) 24 6 0 -2 Which statement correctly compares the two functions? A. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
The answer choice which correctly draws a comparison between the end behaviours of the functions is; Choice C; They have the same end behavior as x approaches -∞ and same end behavior as x approaches ∞.
Which answer choice correctly compares the end behaviour of the functions?As given in the task content; the graph of the exponential function passes through (-4, 9), (0, 1), (1, 0), and (5, -2).
It therefore follows that as; x reduces (approaches -∞), the y value increases.
And, as x -increases (approaches +∞), the y-value decreases.
For the table, the values can be written as coordinates as follows; (-1,2), (0,4), (1,6), (2, 0), (3,-2).
Consequently, as x reduces (approaches -∞), the y- values decrease.
And, as x increases (approaches +∞), the y-values decrease.
Ultimately, the two functions in discuss can be concluded to have; Choice C.
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The ratio of Sadias age to her fathers age is 3:5. The sum of their ages is 96. What is Sadias age.
Answer:
36 years old
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
sum the parts of the ratio , 3 + 5 = 8
divide the sum of their ages by 8 to find the value of one part of the ratio
96 ÷ 8 = 12 ← value of 1 part of the ratio , then
3 parts = 3 × 12 = 36 ← Sadias age
WILL GIVE BRAINLIEST
HELP PLEASE
Select the correct answer.
The section of paper shown in the pattern below is of a circle. It will be wrapped around a cone. The wrapper will then be painted.
What is the amount of paint needed to paint 100 of these wrappers? Round your answer to the nearest hundred.
Answer:
C
Step-by-step explanation:
Area of a 1/4 sector of a circle = 1/4 * pi r^2
Givens
100 of these quarter sectors
pi = 3.14
r = 12
Solution
You are using area because you are going to paint each one of the sectors. You must cover every cm^2 with paint.
Area = 1/4 * 3.14 * r * r
Area = 1/4 * 3.14 * 12 * 12
Area = 113.25
But there are 100 of them. so the area is
100 * Area = 11325 cm^2
Rounded to the nearest 100 hundreds = 11300 cm^2
Answer:
The answer is 11,300 cm²
Step-by-step explanation:
I got it right on edmentum jope this helps your question.
if a set of test scores has a large range but a small standard deviation, describe what this means about students' performance on the test.
a. Most of students' test scores are around the mean, except that few students got scores much less than the mean.
b. Most of students' test scores are around the mean.
c. Most of students' test scores are around the mean, except for the students who got scores much greater than the mean and a few students who got scores much less than the mean.
d. Most of students' test scores are around the mean, except for the students who got scores much greater than the mean.
Answer:
C
Step-by-step explanation:
Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.
The correct option is:
b. Most of students' test scores are around the mean.
A large range indicates that there is a significant difference between the highest and lowest scores in the set.
On the other hand, a small standard deviation indicates that the data points (test scores) are clustered closely around the mean.
When the range is large but the standard deviation is small, it means that most of the students' test scores are relatively close to the mean, and there are no extreme values that are significantly far from the mean. In other words, the majority of students performed similarly on the test, with only a few outliers having scores much higher or much lower than the mean.
Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.
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Use the ANOVA analysis tool Base on the given data uploaded, will you conclude that the number of bathroom of houses is a significant factor for house price? I your answer is affirmative, then explain how the house price is influenced by the number of bathroom?
help! giving brainlest to best answer!
Answer:
C...........................
What is the next number in the following sequence 0 0 1 2 2 4 3 6 4 8 5
Answer:
10
Step-by-step explanation:
the sequence follows the rule of adding the number and then the number -1 depending on the number before it. for example, you can see in order to get from 2 to 2, it adds 0 or subtracts by 0. After that to get from 2 to 4, you add 2. After that, you subtract 1 from 2 and you subtract that number which is 1 from 4 to get 3 and so on. Following that rule, you get 10 as the next number in the sequence
How many and of which kind of roots does the equation f(x)=x^3+2x^2+4x+8 have?
The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.
What kind of roots does have a cubic equation?
In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.
Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.
The discriminant is described below:
Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² (1)
Where:
There are three distinct real roots for Δ > 0.Real roots with multiplicity greater than 1 for Δ = 0.A real root and two complex roots for Δ < 0.If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:
Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²
Δ = - 1024
The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.
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question is in the image
From the information given, F(x) = 9.3319419 or approximately 9. This is problem relating to math functions
What is the calculation supporting the above answer?Recall that we are given x to be = 16.1
Hence,
[tex]f\left(x\right)=\ 2x^{\frac{1}{4}}\ +\ 3x^{\frac{1}{2}}[/tex] =
2 (16.1) ⁰°²⁵ + 3 (16.1)⁰°⁵
= 32.2⁰°²⁵ + 48.3⁰°⁵
= 2.3821218 +6.9498201
f(x) = 9.3319419
f(x) approximately 9
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solve x^2 + x - 12 = 0
Answer:
x₁ = -4
x₂ = 3
Step-by-step explanation:
x²+ x + 12 = 0
x = {-1±√((1²)-(4*1*-12))} / (2*1)
x = {-1±√(1+48)} / 2
x = {-1±√49} / 2
x = {-1±7} / 2
x₁ = {-1-7} / 2 = -8/2 = -4
x₂ = {-1+7} / 2 = 6/2 = 3
Check:
x₁
-4² + (-4) - 12 = 0
16 - 4 - 12 = 0
x₂
3² + 3 - 12 = 0
9 + 3 - 12 = 0
Absolute value of sqrt(5) - 2.2
0.03607
Step-by-step explanation:Absolute value is the distance of a number from zero. Since distance is always positive, the absolute value is the same number but positive.
Please note, for this problem I have rounded to 5 decimal points because the answer is irrational.
Subtracting
There are 2 different ways to approach this problem. You can either estimate the square root of 5 or plug this question straight into a calculator.
First, we can estimate [tex]\sqrt{5}[/tex] and round to 5 decimal places.
[tex]\sqrt{5}[/tex] ≈ 2.23607Then, take this value and subtract.
2.23607 - 2.2 = 0.03607Absolute Value
Now that we have solved the subtraction problem we have to find the absolute value. As stated above, the easiest way to find absolute value is to simply make the number positive. Since the answer is already positive, this is the final answer.
|0.03607| = 0.03607A normal population has a mean u = 31 and standard deviation = 10. What proportion of the population is less than 30?
The proportion of the population exists less than 30 then
(x< 30) = 0.986.
How to estimate the proportion of the population that exists less than 30?To estimate the z-score using the formula, z = (x - µ)/σ
Where, x be the randomly chosen values = 30
µ be the mean = 31
σ be the standard deviation = 10
Proportion of the population that exists less than 18 = P(x < 30)
Plug in the values into z = (x - µ)/σ, to get z-score.
Substitute the values in the above equation, we get
z = (30 - 31)/10
z = -1/10 = -0.1
Therefore, the value of z = - 0.1.
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Which equation does the graph represent?
Answer:
It is the second answer
Step-by-step explanation:
The standard form of an ellipse is
x^2/a^2 + y^2/b^2 or x^2/b^2 + y^2/a^2 = 1
If the x is the main axis we use the first form. If the y is the main axis we use the second form. We will use the second form.
our a is 3 and our b is 4
x^2/3^2 + y^2/4^2
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.)
The psi that the TPMS would trigger a warning for this car is = 23.36 psi
Calculation of tire pressureThe target tire pressure of the car is = 32 psi (pounds per square inch.)
The Tire pressure monitoring systems (TPMS) warns the car below 27% of 32psi
That is , 27/100 × 32
= 864/100
= 8.64psi
Therefore, 32 - 8.64 = 23.36. When the car is below 23.36psi, TPMS would trigger a warning for this car.
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Complete question:
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.)
At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is above or below?
simplify 12x^6-4x^4+6x^2 over 2x^2
Answer:
6x⁴ - 2x² +3
Step-by-step explanation:
[tex]\frac{12x^6-4x^4+6x^2}{2x^2}=6x^4 - 2x^2 + 3[/tex]
Which statement is true about the voting results?
Answer:
11% more people voted for Candidate B than Candidate A
Step-by-step explanation:
15+6=21
9+23=32
32-21=11
Suppose that Andrea told you that “Blake and I started out with the same number of marbles, but I gave him one of mine. Now Blake has one more marble than me.” Is Andrea’s reasoning incorrect? If so, how can you help Andrea identify her misunderstanding?
Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation 15. Find the probability that a randomly selected adult has an IQ less than 123.
The probability that a randomly selected adult has an IQ less than 123 is ____.
Answer:
.8849 or 88.49% have score ess than 123
Step-by-step explanation:
Answer:
88.49 % have less than 123 (or .8849)
Step-by-step explanation:
123 is 18/15 = 1.2 S.D. ABOVE the mean z-score +1.2
from z- score table +1.2 this is .8849 or 88.49 %
5. Compound Interest - Single Payment: $5000 was invested at 5.2%, compounded semi-annually, for 3 years. What was the investment worth at its maturity? (3)
Answer:
78000
Step-by-step explanation:
5000/1 times 52/10 times 3)1
im just here to help fl vs students Select the statement that describes the expression (one fourth x 8 + 3) ÷ 5.
Add three to the quotient of one fourth and 8, then divide by 5
one fourth times the product of 8 and 3, then divide by 5
Add 3 to the product of one fourth and 8, then divide by 5
Add 3 to the sum of one fourth and 8, then divide by 5
Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which may also be given in the form of a statement. Therefore the required statement in the question is option C. Add 3 to the product of one-fourth and 8, then divide by 5.
Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which can be given in the form of a statement. When a given expression consists of both numbers and alphabets, then it forms an algebraic expression. It can also be given in the form of a statement.
Given in the question:
([tex]\frac{1}{4}[/tex] x 8 + 3) ÷ 5
This can be given in a statement form as; Add 3 to the product of one-fourth and 8, then divide by 5.
The appropriate statement that describes the given expression is: Add 3 to the product of one-fourth and 8, then divide by 5 i.e Option C.
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You and Jake are studying together and after correctly solving a system of equations using
the substitution method the result is 3 3. Jake does not know how to interpret this
result.
In at least one complete sentence, explain to Jake the number of solutions, solution type,
and how the graph of the system of equations would look
Answer: its the 3rd one if im wrong im sorry
:3
For the equation 2x - y = 1, if x = 0, then y = ?
Answer:
y= -1
Step-by-step explanation:
(2) (0) − y = 1
0 + − y = 1
(−y) + (0) = 1
−y = 1
Step 2: Divide both sides by -1
Y = −1
Find the value of b.
Step-by-step explanation:
b + 35° = 180° ( supplementary angle )
b = 180° - 35°
b = 145°
Answer: [tex]\Large\boxed{b=145^\circ}[/tex]
Step-by-step explanation:
Given information
∡1 = 35°
∡b = ?
Total Angle = 180° (Supplementary Angle)
Derived formula from the given information
∡1 + ∡b = Total Angle
Substitute values into the given formula
(35) + b = 180
Subtract 35 on both sides
35 + b - 35 = 180 - 35
[tex]\Large\boxed{b=145^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
ONE HUNDRED LOTTERY TICKETS ARE SOLD FOR $5.00 EACH. ONE PRIZE OF $300
WILL BE AWARDED. STEVE PURCHASES ONE TICKET. FIND HIS EXPECTATION. SHOW ME THE WORK SO I CAN UNDERSTAND THANKS
Steve's expected win from the lottery ticket purchase is $3 because his chance of winning the $300 prize is only 1%.
How are the expected winnings of the lottery determined?The expected winnings for Steve are a function of the probability of some predictable outcomes.
In this situation, the predictable outcome is the size of the lottery prize.
The probability that Steve will win the prize is 1% (1/100), depicting his chance of winning.
Data and Calculations:Sale price per ticket = $5
Lottery prize = $300
Value of lottery prize to Steve if he wins = $295 ($300 - $5)
Probability of winning = 1% (1/100 x 100)
Expected win = $3 ($300 x 1%)
Thus, Steve's expected win is $3, which outweighs the cost of a ticket.
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the tens digit of a 2 digit number is 5 greater than the units digit if you subtract twice the reverse number the result is one fourth the original
Answer:
The original number is 72.
Step-by-step explanation:
Let the number by
[A][B]
The reverse number is
[B][A]
Original number:
A = B + 5
[A][B] - 2[B][A] = [A][B]/4
10A + B - 20B - 2A = (10A + B)/4
8A - 19B = (10A + B)/4
32A - 76B = 10A + B
22A - 77B = 0
22(B + 5) - 77B = 0
22B + 110 - 77B = 0
-55B = -110
B = 2
A = B + 5 = 2 + 5 = 7
The original number is 72.
The reverse is 27.
Let's check.
"the tens digit of a 2 digit number is 5 greater than the units digit"
7 is 5 greater than 2,so 72 looks good so far.
"if you subtract twice the reverse number the result is one fourth the original"
The reverse number is 27. Twice 27 is 2 × 27 = 54.
Subtract 54 from 72: 72 - 54 = 18
18 is 1/4 of 72. It works.
Answer: the original number is 72
