Answer:
x² = 81 , x = ± 9
x² - 18x = 7 : x = 9 ± √(22)
Step-by-step explanation:
x² = 81
simply take the square root of both sides
x = ± 9
x² - 18x = 7
This question is a bit more complicated as there is a variable with a power as well as a variable with no power. To solve for x we are going to have to put the equation in quadratic form then solve using the quadratic equation
x² - 18x = 7
put the equation in quadratic form by subtracting 7 from both sides so that the equation is equal to 0
x² - 18x - 7 = 0
we can now solve for x using the quadratic equation
recall the quadratic equation : [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
where the value of a,b and c are derived from the equation
remember the equation is in quadratic form ax² + bx + c = 0
so ax² + bx + c = 0 : x² - 18x - 7 = 0
knowing this we can assign variables, a = 1 , b = -18 and c = -7
now we plug in the variables into the quadratic equation
recall equation : [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
a = 1 , b = -18 and c = -7
plug in values
[tex]x=\frac{-(-18)+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}[/tex]
remove parenthesis
[tex]x=\frac{18+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}[/tex]
simplify exponent
[tex]x=\frac{18+\sqrt{324-4(1)(-7)} }{2(1)}[/tex]
simplify multiplication in square root and on denominator
[tex]x=\frac{18+\sqrt{324+28} }{2}[/tex]
simplify addition
[tex]x=\frac{18+\sqrt{352} }{2}[/tex]
simplify radical
[tex]x=\frac{18+4\sqrt{22} }{2}[/tex]
simplify fraction
[tex]x=9+or-\sqrt{22}[/tex]
and we are done!
Julian is a manager at a clothing store for teens. he is analyzing the order for next season. data for the previous 10 years suggests that teens are willing to spend an average of $75 for a pair of designer jeans with a standard deviation of $5. however, julian thinks the average may have changed due to a recession. he finds that the last three seasons of data show that teens spent an average of $68 on a pair of jeans. therefore, he performed a hypothesis test to see if the recent average is the same. julian used a significance level of 5% to perform the test. which of the following statements is valid based on the results? julian’s data shows that the recent seasons’ average jean price is not $75. julian’s data shows that he should order fewer jeans than before. julian’s data shows that the recent seasons’ average jean price is still $75. julian’s data is inconclusive, so he should order the same number of jeans.
Julian’s data shows that the recent seasons’s average jeans price is not $75.
Julian is a manager at a clothing store for teens.
He is analyzing the order for next season.
What is the average price?
The average price is the mean price of an asset or security observed over some period of time
data for the previous 10 years suggests that teens are willing to spend an average of $75 for a pair of designer jeans with a standard deviation of $5.
however, Julian thinks the average may have changed due to a recession.
The answer is A).
Julian’s data shows that the recent seasons’s average jeans price is not $75.
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Answer:
Julian’s data shows that the recent seasons’ average jeans price is not $75.
Step-by-step explanation:
edge 2022
please help me asap! Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. A multiple-choice question has five answer options of which two options are correct. What is the probability of randomly choosing the correct pair of answer options? The probability of choosing the correct pair of answer options is .
Using the combination formula, it is found that there is a 0.1 = 10% probability of randomly choosing the correct pair of answer options
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 2 answers are chosen from a set of 5, hence the total number of options is given by:
[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
Only one pair is correct, hence the probability of randomly choosing the correct pair of answer options is given by:
p = 1/10 = 0.1 = 10%.
More can be learned about the combination formula at https://brainly.com/question/25821700
8. Dimensions and Construction. The Space Needle is 605 feet (184m)
tall, the rough equivalent of 60 stories, though it only has a few
Moors. The outdoors observation deck, along with a cafe and
historical information can be found at 520 feet (158m). The
observation deck is circular, with a 138 foot (42m) diameter.
observation deck
a) What is the Circumference of the observation
deck? Use the formula C=21tr = d.
Round your answer to the nearest tenth.
Answer:
A
Step-by-step explanation:
it a because it there the right answer
What is the equation of the line passing through the point (2,3) and perpendicular to the line y = 2x+7
Answer:
[tex]y =\dfrac{-1}{2}x +4[/tex]
Step-by-step explanation:
Equation of the line: y = mx +b
y = 2x + 7
m = 2
Slope of the perpendicular line = [tex]-\frac{1}{m}[/tex]
[tex]\sf m_1 =\dfrac{-1}{2}[/tex]
Equation of the perpendicular line:
[tex]y= \dfrac{-1}{2}x + b[/tex]
This line is passing throught (2 ,3). Substitute the x & y coordinate in the above equation and now we can obtain the value of b (y-intercept)
[tex]\sf 3 = \dfrac{-1}{2}*2+b\\\\3 = -1 + b\\[/tex]
3 + 1 = b
4 = b
Equation:
[tex]y =\dfrac{-1}{2}x +4[/tex]
It costs a zoo $3 to feed the kookaburras for 4 hours. Write an equation relating the total cost y to the number of hours x.
Answer:
y=0.75x
Step-by-step explanation:
$3 for every 4 hours
$0.75 for every hour
y=0.75x
The equation relating the total cost (y) to the number of hours (x) is y = 0.75x.
The equation that relates the total cost (y) to the number of hours (x) can be derived from the given information. We know that the cost is $3 for 4 hours of feeding kookaburras.
The cost is proportional to the number of hours, and we can represent this relationship using a linear equation:
Cost = Rate × Hours
In this case, the rate is the cost per hour, which is $3 / 4 hours = $0.75 per hour.
Therefore, the equation relating the total cost (y) to the number of hours (x) is:
y = 0.75x
Here, "y" represents the total cost, and "x" represents the number of hours. This equation reflects the linear relationship between the total cost and the number of hours of feeding kookaburras in the zoo.
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Which statistical measure is not strongly affected by a few outliers in the data?.
Answer: Median
The median is not affected by large or small outliers.
The mean on the other hand is affected by outliers. The more distant the outlier, the more skewed the mean will be.
For example, home prices will have a larger than normal mean because of very rich mansions which are far above the average group. This is why the median home price is a more useful measure of center.
Please answer the following??????/
Answer:
I would be 3 8/10
Step-by-step explanation:
hope this helps
A poll worker analyzing the ages of voters found that mu = 65 and sigma = 5. what is a possible voter age that would give her zx = 1.14? round your answer to the nearest whole number. 59 66 71 90
A poll worker analyzing the ages of voters found that μ = 65 and σ = 5. The possible voter age that would give her zx = 1.14 is 71.
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of a population
N = number of observations of population
X = mean
μ = population mean
It is given that the random variable,
X = The ages of voters
μ = The analysis is having mean of 65
Standard deviation = 5
X = normal (65,5) Now, we will convert it into Z-score concept ,
Z = x - 65/ 5
z = 1.14
X = 65 + 5z
So, X = 65 + 5(1.14)
= 65 + 5.7
= 70.70
Therefore, We can also write it by rounding off the value,i.e.=71
The possible voter age that would give her zx = 1.14 is 71.
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Answer:
C, 71
Step-by-step explanation:
quiz edge
Help me with this one too Have a good day
Answer:
So, a.0, b.1/10, c.81, d.1/64
Step-by-step explanation:
Part A, anything raised to the power of zero is equal to zero. So suppose we have a constant, b, and we raise it to the power of zero, so b^0, it'll always be 0.
Part B, a negative power essentially means that you'll have to inverse the number. Once again, if we have a constant, b, and we raise it to the power of -1, it'll end up being 1/b. So b^-1 = 1/b.
Part C, its simply just multiplying 3 with itself four times.
Part D, as mentioned before, anything raised to a negative power means that you need to inverse the number. So 4^-3 is equal to 1/4^3, meaning that its just 1/64.
For what value of c does the following system not have a solution.
1/2x+1/5y=2
5x+2y=c
Answer:
The answer is 3. 1. There is '0' point of intersection, that means they do not intersect. This only possible when the lined are parallel to each other.
'c' can be any real number except 4 for which the considered system would have no solution.
When does a system of linear equation have no solution?When both the lines(represented by both the equations) are parallel and not coincident, then that system of linear equations have no solutions as there is no common point on both line.
If they are coincident (lying over each other), then there will have infinite solution since in that case, they will have infinite points in common.
Thus, if two lines are not in any of above case, they intersect at single point and in that case, the considered system of equation has unique single solution.
How to get the slope intercept form of a straight line equation?If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
[tex]y = mx +c[/tex]
Parallel lines(non-coincident) have same slope but different y-intercept.
Converting these equations to slope-intercept form, we get:
For first line:
[tex]\dfrac{1}{2}x + \dfrac{1}{5}y = 2\\\\ \dfrac{1}{5}y = 2 - \dfrac{1}{2}x\\\\y = 10 - \dfrac{5}{2}x\\\\y = -\dfrac{5}{2}x + 2[/tex]
and
For second line:
[tex]5x + 2y = c\\\\y = \dfrac{1}{2}c - \dfrac{5}{2}x\\\\y = -\dfrac{5}{2}x + \dfrac{c}{2}[/tex]
For no-solution, we need both lines to stay parallel but not coincident so that there is no common point (solution of this system) between those two lines.
Thus, we get:
[tex]2 \neq \dfrac{c}{2}\\\\\text{Multiplying 2 on both the sides}\\\\c \neq 4[/tex]
Since 'y' assumes real numbers assumingly, so 'c' can be any real number except 4 for which the considered system would have no solution.
Below is image attached of those parallel lines when c = 10.
Thus, 'c' can be any real number except 4 for which the considered system would have no solution.
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Giselle made several apple and peach pies. She bought peaches for $4 per pound and apples for $2 per pound. If Giselle spent $60 to buy 24 pounds of fruit, how many pounds of peaches did she buy?
The number of pounds of peaches is 6 pounds and the number of pounds of apples is 18 pounds
Given:
cost of peaches per pound = $4
cost of apples per pound = $2
Total amount spent = $60
Total pounds bought = 24
let
x = number of peaches
y = number of apples
x + y = 24 (1)
4x + 2y = 60 (2)
multiply (1) by 2
2x + 2y = 48 (3)
4x + 2y = 60 (2)
subtract (3) from (2)
4x - 2x = 60 - 48
2x = 12
x = 12/2
x = 6
substitute x = 6 into (1)
x + y = 24 (1)
6 + y = 24
y = 24 - 6
y = 18
Therefore, the number of pounds of peaches is 6 pounds and the number of pounds of apples is 18 pounds
What are the solutions to the equation y = 4x2 +5x−6?
Answer:
Option D: x = -2; x = 3/4
Step-by-step explanation:
Hello!
We can factor this expression and then find the zeroes to find our solutions.
Factor:We have to factor by grouping. Multiply the 1st and last term, 4x² and -6 is -24x², and find two factors that equal to -24x² and add up to the second term, 5x. 8x and -3x work for this.
y = 4x² + 5x - 6y = 4x² + 8x - 3x - 6y = 4x(x + 2) - 3(x + 2)y = (4x - 3)(x + 2)Zero-Product PropertyNow, set the equation equal to zero.
0 = (4x - 3)(x + 2)Remember, if two numbers, a and b, multiply to 0, either a or b or both numbers must be zero. So now we set both factors to zero, hence the zero-product property.
4x - 3 = 04x = 3x = 3/4And the next one:
x + 2 = 0x = -2The solutions are x = -2, and x = 3/4, or Option D
What is the answer for 4/7x5/3x3/4= ?
Answer:
[tex]\frac{x^{2} }{21}[/tex]
Step-by-step explanation:
1. Combine multiplied terms into a single fraction
2. Eliminate quotient in numerator
3. Multiply the numbers
Solution: [tex]\frac{x^{2} }{21}[/tex]
Answer:
When we multiply 4\7, 5\3 and 3\4, then the answer will be 5\7.
Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. which of the following equations models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds? assume that right of center is a positive distance and left of center is a negative distance. d = 9 cosine (startfraction pi over 4 endfraction t) d = 9 cosine (startfraction pi over 2 endfraction t) d = 18 cosine (startfraction pi over 4 endfraction t) d = 18 cosine (startfraction pi over 2 endfraction t)
The expression that models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds is d=9cosine[(π/2)t] option second is correct.
What is the frequency?It is defined as the number of waves that crosses a fixed point in one second, known as frequency. The unit of frequency is per second.
The pendulum takes 2 seconds to swing a horizontal distance of 18 inches from right to left.
For swing back from left to right, it takes again 2 seconds to cover a horizontal distance of 18 inches.
The total time to complete the one cycle = 4 seconds
Thus, the frequency is the reciprocal of the time
f = 1/4
The expression for the angular speed is:
w = 2πf
w = 2π(1/4)
w = π/2
The distance of the pendulum from the center A = half the horizontal
distance of 18 inches
A = 18/2
A = 9 inches
We know the cosine function for the pendulum is given by:
d = Acosine(wt)
d = 9cosine(πt/2) or
d = 9cosine[(π/2)t]
Thus, the expression that models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds is d = 9cosine[(π/2)t]
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Enter an expression that shows the sum of exactly two terms that is equivalent to 6m + 3n + 8m + 5n
Answer: 14m+8n
Step-by-step explanation:
Simplify the expression
6m+3n+8m+5n
6m+8m+3n+5n
14m+8n
It is the same expression except that it is simplified and contains only 2 terms
Last month, korey’s comics had $4,350 in net sales with a gross profit of $3,320 and a net income of $1,850. calculate korey’s net profit margin. a. 42.5% b. 55.7% c. 76.3% d. 179.5% please select the best answer from the choices provided a b c d
Korey’s gross profit margin last month will be equal to 55.7%.
What is the gross profit margin?
The gross profit margin is a profitability ratio. Profitability ratios measures the efficiency with which a company generates profit from its asset. Gross profit margin measures the return on sales.
Gross profit margin = net income / gross profit
$1850 / 3320 = 0.557 = 55.7%
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Answer:
The answer is actually a. 42.5%
Step-by-step explanation:
Correct on edg. 2022
If a person with an hourly pay of $9.50 per hour gets a 20% raise, what is the new hourly pay?
ONLY ANSWER IF YOU KNOW THE ANSWER (15 POINTS HELP PLEASE)
CORRECT ANSWER WILL GET BRAINLEST AND LINKS WILL BE REPORTED
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A number cube with six sides numbered 1 through 6 is rolled. The probability of rolling a 5 is 1/6.
What is the probability of not rolling a 5?
Enter your answer as a fraction, in simplest form, in the box.
Answer:
The probability of all events occurring is 1
(1/6)+p=1
p=1-1/6
p=5/6
The probability of not rolling 5 is 5/6
Or you could have just said there are five numbers other than 5 out of the six so:
5/6
Point JJ is located at (-4,5) on the coordinate plane. Point J is reflected over the x-axis to create point J′. What ordered pair describes the location of J'?
Answer: (-4, -5) in 3rd Quadrant
Step-by-step explanation: Reflection across x axis only flips the sign of y coordinate
Will name brainliest!
Answer:
B as the number of molecules increases the volume increases
Step-by-step explanation:
The sum of three numbers is 78. The third number is 7 more than the first. The second number is 3 times the third. What are the numbers?
Answer:
10+51+17=78
Step-by-step explanation:
Alright, so at first I just took a random number and kept on working it out until I got the exact answer as 78. Finally, i got the third number as 17. Now, i know the third number is 7 more than the first so I have to subtract 17 and 7, 17-7=10. So the first number is 10. Ok, now i know that the second number is 3 times the third number (17) so you should multiply, 17x3=51. 51 is the 2nd number.
1st number=10
2nd number=51
3rd number=17
Add them, 10+51+17=78.
Answer:
First number = 10Second number = 51Third number = 17Step-by-step explanation:
In the question we are given ,
Sum of three numbers is 78Third no. is 7 more than firstSecond no. is 3 times thirdSo , we are assuming that ,
Let first no. be xThird no. be x + 7 ( because in question it is given that third number is 7 more than the first number ) .Second no. be 3 ( x + 7 ) ( because in the question it is given that second no. is three times the third )We are finding the solution by adding all these term and equating it with 78 because sum of these three numbers is equal to 78 .
Here we go ,
[tex] \longrightarrow \: x + 3(x + 7) + x + 7 = 78[/tex]
Step 1 : Solving the bracket part :
[tex] \longrightarrow \: \blue{x }+ \blue{ 3x} + \red{21} + \blue{ x} + \red{7 }= 78[/tex]
Step 2 : Adding like terms :
[tex] \longrightarrow \:5x + 28 = 78[/tex]
Step 3 : Transposing 28 to right hand side :
[tex] \longrightarrow \:5x = \green{78} - \green{28}[/tex]
Step 4 : Subtracting 28 from 78 :
[tex] \longrightarrow \:5x = 50[/tex]
Step 5 : Transposing 5 to right hand side :
[tex] \longrightarrow \:x = \cancel \frac{50}{5} [/tex]
Step 6 ; Cancelling 50 with 5 :
[tex] \longrightarrow \: \purple{\boxed{x = 10}}[/tex]
Therefore value of ,
x [ first number ] = 103(x + 7 ) [ second number ] = 51x + 7 [ third number ] = 17Verification :
We are verifying our answer by adding the three numbers and it must be equal to 78 .
10 + 51 + 17 = 7861 + 17 = 7878 = 78L.H.S = R.H.SHence , Verified.Therefore , our answer is correct .
#Keep LearningOn their birthdays, employees at a large company are permitted to take a 60-minute lunch break instead of the usual 30 minutes. Data were obtained from 10 randomly selected company employees on the amount of time that each actually took for lunch on his or her birthday. The company wishes to investigate whether these data provide convincing evidence that the mean time is greater than 60 minutes. Of the following, which information would NOT be expected to be a part of the process of correctly conducting a hypothesis test to investigate the question, at the 0. 05 level of significance?
Answer:
Given that the p-value is greater than 0.05, rejecting the null hypothesis and concluding that the mean time was not greater than 60 minutes
Step-by-step explanation:
I got it right on AP Classroom
Find the volume.
B1=36
B2= 24
Height=38
Length=20
Answer:
V= 22800 unit^3
Step-by-step explanation:
hope this helps :)
19. Select all the measures that are equivalent to 10 meters.
0. 01 kilometer
B)
1000 millimeters
100 millimeters
0 1000 centimeters
0. 1 kilometer
100 centimeters
Help I don’t know!
Answer:
10 meters is equivalent to 1000 cm and 0.01 kilometers
Step-by-step explanation:
Write one statistical question(your data needs to have variability),that you could ask the students in your class that would result in numerical data
Answer:
ask your classmates what is there shoe sizes are
Step-by-step explanation:
What’s the volume of the figure?
Answer:
ans below
Step-by-step explanation:
when rectangle is rotated, hemisphere is formed with r =12cm
volume = 2/3πr^3
= 1152π cm^3
100 pts help pls
Is this triangle acute, right, or obtuse?
acute
right
obtuse
Thus its an obtuse angle triangle.
=============================
Acute triangle means they measure less than 90°
Right triangle means a triangle with 90°
Obtuse triangle has one angle greater than 90°
Obtuse
Check one angle is streched like it's greater than 90°
Hence one angle is greater than 90 i.e obtuse.So
it's an obtuse triangle
7/10 of the books sold by the used book store had hardback covers. 2/3 of those had been repaired. What part of the books sold had repaired hardback covers?
Answer:
7/15
Step-by-step explanation:
2/3 of those means 2/3 of the 7/10 books sold by the used book store
2/3 of 7/10 means 2/3 * 7/10 = 14/30 = 7/15
Hope this helps :)
Have a nice day!
Help me stop bots plsss not bots
Pls help algebra 1
A clerk earns $125 per day, plus a commission equal to
10% of her sales, s. The clerk earns less than $180 on
Monday
Enter an inequality that represents all possible values for
the clerk's sales, s, on Monday.
Answer:
0.1s + 125 < 180