Use this information to find the value of b.
c = 25
s = 9
b = 4c - s2
To find the value of b in the equation 25s = 9b = 4c - s^2, we can substitute the given values and solve using the quadratic equation.
Explanation:To find the value of b, we can use the given information and substitute the values of a, b, and c into the quadratic equation.
The equation is: c = 25s = 9b = 4c - s^2
Substituting the values:
25s = 9b = 4c - s^2
25s = 9b = 4c - s^2
Now we can solve for b:
9b = 4c - s^2
9b = 4(-0.0211) - (9)^2
9b = -0.0844 - 81
9b = -81.0844
b = -81.0844/9
b = -9.01
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Meg is printing a term paper for class at the rate shown in the table below. If the term paper is 60 pages long, how many total minutes will it take to print out? Assume that the printer prints the pages at a constant rate.
Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 7. the hypotheses h0: μ = 75 and ha: μ < 75 are to be tested using a random sample of n = 25 observations. (a) how many standard deviations (of x) below the null value is x = 72.3? (round your answer to two decimal places.) standard deviations (b) if x = 72.3, what is the conclusion using α = 0.01? (round your answers to two decimal places.) test statistic z = critical value z = what can you conclude? reject the null hypothesis. there is sufficient evidence to conclude that the mean drying time is less than 75. do not reject the null hypothesis. there is sufficient evidence to conclude that the mean drying time is less than 75. do not reject the null hypothesis. there is not sufficient evidence to conclude that the mean drying time is less than 75. reject the null hypothesis. there is not sufficient evidence to conclude that the mean drying time is less than 75. (c) what is α for the test procedure that rejects h0 when z ≤ −2.8? (round your answer to four decimal places.) α = (d) for the test procedure of part (c), what is β(70)? (round your answer to four decimal places.) β(70) = (e) if the test procedure of part (c) is used, what n is necessary to ensure that β(70) = 0.01? (round your answer up to the next whole number.) n = specimens (f) if a level 0.01 test is used with n = 100, what is the probability of a type i error when μ = 76? (round your answer to four decimal places.)
A paint drying situation, has the standard deviation 1.93. The detailed solution is given below.
Given :
Standard Deviation, [tex]\sigma = 7[/tex]
Mean, [tex]\mu = 75[/tex]
Sample, n = 25
Solution :
A) We know that,
[tex]z = \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n} }}[/tex] ---- (1)
Now put the values of [tex]\rm x,\;\mu,\;\sigma \;and \;n[/tex] in equation (1) we get,
[tex]z = \dfrac{72.3-75}{\dfrac{7}{\sqrt{25} }}[/tex]
z = -1.93
Therefore, 72.3 is 1.93 standard deviations below the mean.
B) From the above part we know that z = - 1.93.Therefore p-value is,
P(-1.93) = 0.03
Since [tex]\alpha[/tex] = 0.01 and p-value = 0.03, this means that the p-value is greater than the fail to reject the null hypothesis.
C) The p-value for [tex]z\leq -2.8[/tex]
is 0.00256
Therefore, the [tex]\alpha[/tex] for the test procedure that rejects the null hypothesis when [tex]z\leq -2.8[/tex] is 0.0026.
D) For alternate hypothesis,
[tex]\rm \beta (\mu') = P(X>\mu_0-z_1_-_\alpha \frac{\sigma}{\sqrt{n} }|\mu')[/tex]
[tex]\rm = P(-z_1_-_\alpha +\dfrac{\mu_0-\mu'}{\dfrac{\sigma}{\sqrt{n} }})[/tex]
For [tex]\alpha[/tex] = 0.0026
[tex]\rm \beta (70)=1- P(-z_0_._9_9_7_4 +\dfrac{75-70}{\dfrac{7}{\sqrt{25} }})[/tex]
[tex]\rm \beta (70) = 1-P(-2.7949+3.5714)=1-P(0.7765)[/tex]
[tex]\beta (70)=1-0.78128\approx 0.2187[/tex]
E) Now we want n when
[tex]\beta (70) = 0.01[/tex]
[tex]\rm 0.01=1- P(-z_0_._9_9_7_4 +\dfrac{75-70}{\dfrac{7}{\sqrt{n} }})[/tex]
[tex]P(-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }})=0.99[/tex]
[tex]P(-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }})=P(2.3262)[/tex]
[tex]-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }}=2.3262[/tex]
[tex]\rm \sqrt{n} = 7.1695[/tex]
n = 51.4
Therefore we need n = 52.
F)
[tex]\rm p-value = P(\bar{X}\leq \bar{x})[/tex]
[tex]\rm p-value = P(\bar{X}\leq 72.3)=P(z\leq \dfrac{72.3-76}{\dfrac{7}{5}})[/tex]
[tex]\rm p-value = P(z\leq -2.643)[/tex]
[tex]\rm p-value = 0.00411[/tex]
Since p-value is larger that .01 therefore we fail to reject [tex]\mu[/tex] = 76.
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Find the unit rate for 521 miles in 14 hours
The unit rate for 521 miles in 14 hours is 37.2 miles per hour
Given:
Total distance travelled = 521 miles
Total time taken = 14 hours
Unit rate = Total distance travelled ÷ Total time taken
= 521 miles ÷ 14 hours
= 37.214285714285
Approximately, 37.2 miles per hour
Therefore, unit rate for 521 miles in 14 hours is 37.2 miles per hour
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what degree of rotation will cause the triangle below to map onto itself
Answer:
Option A is correct that is [tex]360^{\circ}[/tex]
Step-by-step explanation:
We have been given a triangle we need to tell which one of these is a triangle below to map onto itself.
[tex]360^{\circ}[/tex] rotation is the complete rotation which eventually leads to the same figure which is given.
Option A is correct that is [tex]360^{\circ}[/tex] that will cause the triangle below to map onto itself.
How would you write 5x5x5x5x5x5 in an exponent form, please help me i forgot
The exponent form of the given multiplication 5x5x5x5x5x5 is 5⁶.
What is an exponent expression?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent,"
it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."
The given expression is 5x5x5x5x5x5. The exponent form of the number will be written below,
E = 5x5x5x5x5x5
E = 5⁶
Therefore, the exponent form of the given multiplication 5x5x5x5x5x5 is 5⁶.
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Vinny auto repair charges $75 an hour for labor plus the cost of parts. Mr sellners car was repaired and repaired $50 worth of parts and h hours of labor. The total cost,C, to repair the car is modeled by this function.
C(h)=75h+50
The total cost to repair the car was $650. How many hours of labor were required?
Select the correct answer below.
A.8hours
B.8 2/3 hours
C.9 1/3hours
D.13 hours
What is another way to express 64?
A) 34
B) 64
C) 6.4 x 102
D) 82
Answer:
D) 8²
Step-by-step explanation:
Evaluate each of the choices and see which one is equal to 64.
_____
It helps if appropriate mathematical symbols are used.
Find the largest number which divides 149 and 101 , leaving remainder of 5
The largest number which divides 149 and 101 , leaving remainder of 5 : 48
Further explanationThe division operation is one of the basic arithmetic operations
Common signs used are [tex] \large {\boxed {:}}} [/tex] or [tex] \large {\boxed {\slash}} [/tex]
The division is written by placing the numerator above the denominator with a horizontal line between them or use a slash with the numerator's position and the denominator is parallel
The division is actually an iterative subtraction operation (as many as the number of divisors)
Division is the opposite of multiplying
The general form of division can be stated by:
[tex] \large {\boxed {\bold {divident:divisor=quotient+remainder}} [/tex]
example:
7: 3 = 2 + 1
Division operation statement:
"7 divided by 3 equals 2 remainder 1"
7 = dividend 3 = divisor 2 = quotient 1 = remainderA number have many factors
A common factor is a factor of two / more numbers.
Greatest common factor (GCF or HCF = Highest Common Factor) is the largest of the common factors
The largest number which divides 149 and 101 leaving remainder of 5
Division operation:
149: x = y +5 101: x = z + 5We find the value of x which is the GCF of the numbers 144 and 96
149 - 5 = 144
101 - 5 = 96
We look for GCF from factors of 144 and 96
144: 1, 2, 3, 4, 6, 8, 9, 16, 18, 24, 36, 48, 72, 144 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96GCF of 144 and 96 is 48
Or we can use prime factors:
144: 2⁴ X 3²
96: 2⁵ X 3
GCF = 2⁴ X 3 = 48
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Keywords : Greatest common factor , division, prime factors
what is the greatest common factor for 5 4 and 2
if you flip the graph of the exponential function f(x)=2x over the x axis what is the equation of the new function
Answer:
Option: B is the correct answer.
The equation of the new function g(x) on flipping the function f(x) over the x-axis is:
[tex]g(x)=-2^x[/tex]
Step-by-step explanation:
We are given a graph of the exponential function f(x) which is represented by:
[tex]f(x)=2^x[/tex]
We know that when a graph of a function is reflected or flipped over the x-axis then the the change that take place to the function is that f(x) is transformed to -f(x).
( Since on flipping the function over the x-axis the positive value of the function get changed to negative and the negative value of the function is changed to positive)
Hence, the equation for the new function is:
[tex]g(x)=-f(x)\\\\g(x)=-2^x[/tex]
How does dividing the coins into equal groups help solve the problem
LMN Office Company sells 20 printer cartridges for $240. XYZ Supplies has a box of printer cartridges for $150. The box contains 12 cartridges.
Which company has the least expensive cartridge? choose one of the following
LMN Office Company?
XYZ Supplies?
They are the same?
Not enough information?
The company which has the least expensive cartridge is:
LMN office company.
Step-by-step explanation:LMN Office Company sells 20 printer cartridges for $240.
This means that the cost of 1 printer cartridge is: $ 240/20=$ 12
Also, . XYZ Supplies has a box of printer cartridges for $150.
The box contains 12 cartridges.
This means that the cost of 12 cartridge is: $ 150
Hence, cost of 1 printer cartridge is: $ 150/12=$ 12.5
Hence, the company which has the least expensive cartridge is:
LMN Office Company.
( Since, 12 < 12.5 )
Sean Matthews is a waiter at the Duluxe Lounge. In his first weekly pay in March, he earned $300.00 for the 40 hours he worked. In addition, he reports his tips for February to his employer ($500.00), and the employer withholds the appropriate taxes for the tips from this first pay in March.
Sean Matthews' weekly earnings are subject to payroll taxes, including his tips. The deductions for social security and medicare are split between him and his employer. Understanding how these deductions work can enable him to maximize his total earnings.
Explanation:The subject of the question pertains to Sean Matthews' earnings at the Duluxe Lounge, which involves payroll taxes on his wages and tips. From his regular wages of $300.00 for 40 hours, "payroll taxes" of 6.2% for Social Security and 1.45% for Medicare are deducted. The same deductions also apply to his reported tips of $500.00. These deductions are shared between Sean and his employer, though, it's possible that the employer's share might effectively be passed onto Sean in the form of lower wages.
Learning and understanding these financial procedures can significantly help individuals like Sean to maximise their total earnings.
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$736 will be his Net take home.
Net pay is the money you have left when your paycheck makes its way to you and all of the required taxes are taken out. To find Sean's net pay, both his earned wages and the reported tips will be considered for tax deductions.
Calculate total earnings for the week:
Wages = $300.00.
Total earnings = Wages + Tips = $300.00 + $500.00 = $800.00.
Assume a tax rate (federal, state, and other taxes) of 2%
Tax deductions = $800.00 x 2% = $16.00.
Calculate net pay:
Net pay = Total earnings - Tax deductions = $800.00 - $16.00 = $736.00.
complete question:
Sean Matthews is a waiter at the Deluxe Lounge. In his first weekly pay in March, he earned $300.00 for the 40 hours he worked. In addition, he reports his tips for February to his employer ($500.00), and the employer withholds the appropriate taxes for the tips from this first pay in March.Calculate his net take-home pay assuming the employer withheld federal income tax (wage-bracket, married, 2 allowances), social security taxes, and state income tax (2%).
What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?
y = –3/4x + 8
y = –3/4x + 6
y =4/3 x – 8
y= 4/3x - 6
Step 1
Find the slope of the given line
Let
[tex]A(-4,4)\ B(4,-2)[/tex]
we know that
the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-2-4}{4+4}[/tex]
[tex]m=\frac{-6}{8}[/tex]
[tex]m=-\frac{3}{4}[/tex]
Step 2
Find the slope of the line perpendicular to the given line
we know that
if two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=-\frac{3}{4}[/tex] ------> slope of the given line
Find the value of m2
[tex]m2=-1/m1[/tex]
substitute
[tex]m2=-1/(-3/4)[/tex]
[tex]m2=\frac{4}{3}[/tex]
Step 3
Find the equation of the line
we know that
the equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{4}{3}[/tex]
x-intercept is equal to [tex]6[/tex] --------> is the point [tex](6,0)[/tex]
substitute in the formula
[tex]y-0=\frac{4}{3}(x-6)[/tex]
[tex]y=\frac{4}{3}x-8[/tex]
therefore
the answer is the option
[tex]y=\frac{4}{3}x-8[/tex]
Each of 5 birdwatchers reported seeing 15 roseate spoonbills in a day. If they each reported seeing the same nunber of roseate spoonbills over 14 days, how many would be reported?
A line passes through the points (2, –2) and (–6, 2). The point (a, –4) is also on the line. What is the value of a?
Answer:
The value of a=6[/tex]
Step-by-step explanation:
step 1:-
col linearity of three points :-
We know that slopes of two parallel lines are equal.If two lines having the same slope pass through a common point ,then two lines will coincide . Hence ,If A,B,C are three points in the X Y- plane, then they will lie on a line,
that is three points are col linear if and only if Slope of AB= slope of BC
step 2:-
Since the given three points are col-linear, we have
Slope of AB= slope of BC
given points are A(2,-2) ,B(-6,2) and C(a,-4)
Step 3 :-
Slope of AB= slope of BC
[tex]\frac{2-(-2)}{-6-2} =\frac{-4-2}{a+6}[/tex]
[tex]\frac{-1}{2} =\frac{-6}{a+6}
by cross multiplication
we get \\a+6=12\\
Step 4:-
The value of a=6[/tex]
What inequality represents the graph?
The inequality that represents the graph is y < x.
Explanation:The inequality that represents the graph is y < x. This inequality represents the region below the line that forms the graph. In this case, the line starts at the origin and has a slope of 1, meaning that for every increase of 1 unit on the x-axis, the y-coordinate increases by 1 unit as well.
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k-20/5=11j ; solve for k
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.7 years, and standard deviation of 2.5 years. if you randomly purchase one item, what is the probability it will last longer than 8 years?
First let us calculate for the z score using the formula:
z = (x – u) / s
where x = 8, u is the mean = 12.7 years, s is the standard deviation
z = (8 – 12.7) / 2.5
z = -1.88
From the standard probability tables, the p value at z = -1.88 is:
P = 0.0301 = 3.01%
An apartment building has the following distribution of apartments: 1st floor 1 bed room 3, two bedroom 1, 3 bedroom 1, 2nd floor 1 bedroom 2, 2 bedroom 2, 3 bedroom 2, 3rd floor 1 bedroom, 2 bedroom 4, 3 bedroom 1. If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms
Final answer:
The probability that an apartment is on the 2nd floor or has 2 bedrooms is 0.7727 or 77.27%.
Explanation:
To find the probability that an apartment is on the 2nd floor or has 2 bedrooms, we need to determine the total number of apartments that satisfy either of the conditions.
On the 2nd floor, there are 2 apartments with 1 bedroom, 2 apartments with 2 bedrooms, and 2 apartments with 3 bedrooms. This gives us a total of 2 + 2 + 2 = 6 apartments on the 2nd floor.
Out of the total distribution of apartments, there are 3 apartments with 1 bedroom, 4 apartments with 2 bedrooms, and 4 apartments with 3 bedrooms. This gives us a total of 3 + 4 + 4 = 11 apartments with 2 bedrooms.
The probability of an apartment being on the 2nd floor or having 2 bedrooms is given by:
Probability = (Number of apartments on the 2nd floor + Number of apartments with 2 bedrooms) / Total number of apartments
Probability = (6 + 11) / (6 + 1 + 1 + 2 + 2 + 2 + 1 + 2 + 4 + 1) = 17 / 22 = 0.7727 or 77.27%
One of the zeros of the polynomial function is 2.
f(x)=x4−3x3−23x2+75x−50
What is the factored form of the function?
f(x)=(x−5)(x+5)(x−2)2f(x)=(x−5)(x+5)(x−2)(x−1)f(x)=(x−5)(x+5)(x−2)(x+1)f(x)=(x−5)(x+5)(x−1)2
Answer:
Heres the correct answer. Hope this helps anyone who needs it!!!
Step-by-step explanation:
The polynomial function is one that involves only non-negative number powers of x, unlike a polynomial, cubic, or quartic function, and further calculation can be defined as follows:
Given:
[tex]\bold{f(x)=x^4-3x^3-23x^2+75x-50}[/tex]
To find:
Solution:
[tex]\to \bold{f(x)=x^4-3x^3-23x^2+75x-50}[/tex]
Let [tex]\bold{x=2}[/tex]
[tex]\to \bold{f(2)=2^4-3(2)^3-23(2)^2+75(2)-50}\\\\\to \bold{f(2)=16-3(8)-23(4)+75(2)-50}\\\\\to \bold{f(2)=16-24-92+150-50}\\\\\to \bold{f(2)=166-166}\\\\\to \bold{f(2)=0}\\\\[/tex]
So the factor is [tex]\bold{(x-2)}[/tex].
[tex]\to \bold{(x-5)(x-2)(x-1)(x+5)}\\\\[/tex]
Therefore, the final answer is "[tex]\bold{ f(x)=(x-5)(x-2)(x-1)(x+5)}\\\\[/tex]".
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what is the value of x in the proportion below ?
180 Kilometers / 3 hours = 540 Kilometers / X
Answer: 9 hours
Step-by-step explanation:
Given proportion : [tex]\frac{\text{180 Kilometers}}{\text{3 hours}}=\frac{\text{540 Kilometers }}{x}[/tex]
To find the value of x , we need to multiply 3x hours and divide 180 Kilometers on both the sides, we get
[tex]\text{x}=3\times\frac{540}{180}\text{hours}\\\\\Rightarrow\ x=3\times3\\\\\Rightarrow\ x=9\text{ hours} [/tex]
Hence, the value of x = 9 hours.
The equation of this type of line is y = kx. What is special about k?
Answer:
C
Step-by-step explanation:
k is the slope of the line
The equation of the line is y = kx. Therefore, the special thing about k is that it is the slope of the line.
Equation of a lineUsing a slope intercept equation,
y = kx + b
where
k = slope of the lineb = y-interceptTherefore, the y-intercept of the line y = kx is zero.
What is special about k is that it is the slope of the line y = kx.
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The cost to mail a first-class letter is $0.47 for the first ounce. Each additional ounce costs $0.22. Fractions of an ounce are rounded up to the next whole ounce. How much would it cost to mail a letter that weighs 2.7 ounces? pleaseee
A rectangle has a width of 44 centimeters and a perimeter of 180 centimeters what is the rectangle length
Farmer Dave builds a crate to hold vegetables. the volume of the crate is 48 cubic feet. the base area of the crate is 16 square feet. what is the height of the crate
Answer:
the answer is 3
Step-by-step explanation:
just got it right on iready
A line has a slope of mc013-1.jpg and passes through the point (–5, 4). Which is the equation of the line?
Answer:
y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].
Step-by-step explanation:
Given : Graph of slope [tex]\frac{-3}{4}[/tex] and passes through the point (–5, 4).
To find : Which is the equation of the line.
Solution : we have given that point ( -5 ,4)
By equation of line ([tex]y-y_{1}) = m (x -x_{1})[/tex]
y - 4 = [tex]\frac{-3}{4}[/tex]( x +5).
y - 4 = [tex]\frac{-3x}{4}[/tex] +[tex]\frac{-15}{4}[/tex].
On adding 4 both sides we get,
y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{-15}{4}+4[/tex].
y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{-15 +16}{4}[/tex].
y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].
Therefore, y = [tex]\frac{-3x}{4}[/tex] + [tex]\frac{1}{4}[/tex].
When referring to the normal probability distribution, there is not just one; there is a "family" of normal probability distributions?
Final answer:
There is a family of normal probability distributions, each representing different populations or sets of data with varying mean and standard deviation values.
Explanation:
Yes, there is a family of normal probability distributions. The normal distribution is a continuous probability distribution that can take on different forms depending on the mean and standard deviation. The family of normal distributions is characterized by different mean and standard deviation values, which result in different shapes of the distribution curve.
For example, the standard normal distribution has a mean of 0 and a standard deviation of 1, and its curve is symmetrical around the mean. Other normal distributions may have different means and standard deviations, resulting in curves that are shifted or stretched.
Each normal distribution in the family represents a different population or set of data, and knowing the specific mean and standard deviation allows us to calculate probabilities and make statistical inferences.
X2+4x-3/X4-5X2+4 what is the domain of this function