Answer: t = 4.87s
Step-by-step explanation: The vertical position y is given by
[tex]y = -16t^{2}+380[/tex]
If y at the base of the cliff equals 0, then equation is
[tex]-16t^{2}+380=0[/tex]
[tex]-16t^{2}=-380[/tex]
[tex]t^{2}=\frac{-380}{-16}[/tex]
[tex]t=\sqrt{\frac{380}{16}}[/tex]
[tex]t=\sqrt{23.75}[/tex]
t = 4.87
Since it is time we want, the negative value of the square root can be ignored. So, at the base of the cliff, the rock will hit the ground after 4.87 seconds.
The formula below represents Celsius temperature C as a function of Fahrenheit temperature F.
C (F) = 5/9 (F - 32), where F greaterthanorequalto -459.6
(a) Find the inverse function of C.
(b) What does the inverse function of C represent?
A. The inverse represents the temperature F corresponding to a temperature C.
B. The inverse represents the temperature 1/C corresponding to a temperature C.
C. The inverse represents the temperature 1/F corresponding to a temperature C.
D. The inverse represents the temperature C corresponding to a temperature F.
(c) Determine the domain of the inverse function.
a. all real numbers
b. C greaterthanorequalto 0
c. C lessthanorequalto -273.1
d. C greaterthanorequalto -273.1
(d) If the temperature is 90 degree C, what is the corresponding temperature in degrees Fahrenheit?
Answer:
The inverse represents the temperature F corresponding to a temperature C.
The domain of the inverse function is all real numbers.
194°F
Step-by-step explanation:
Let C= y
y= 5/9 (F - 32),
F= 9/5y + 32
But y= C, hence;
F= 9/5 C +32
The inverse represents the temperature F corresponding to a temperature C.
Given;
F= 9/5 C +32
The domain of the inverse function is all real numbers.
Given C= 90°
F= 9/5 C +32
F= 9/5 (90°) +32
F= 194°F
Write an equation in point slope form for the line through the given point with the given slope. (4,-6);m=3/5
Answer:
y+6 = 3/5(x-4)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y --6 = 3/5( x-4)
y+6 = 3/5(x-4)
48% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 300 found that 45% of the readers owned a particular make of car. Is there sufficient evidence at the 0.02 level to support the executive's claim?
Answer:
There is no sufficient evidence to support the executive claim
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.48[/tex]
The sample proportion is [tex]\r p = 0.45[/tex]
The sample size is [tex]n = 300[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
The null hypothesis is [tex]H_o : p= 0.48[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.48[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1 - p )}{n} } }[/tex]
=> [tex]t = \frac{0.45 - 0.48 }{ \sqrt{ \frac{0.48 (1 - 0.48 )}{300} } }[/tex]
=> [tex]t = -1.04[/tex]
The p-value is mathematically represented as
[tex]p-value = 2P(z > |-1.04|)[/tex]
Form the z-table
[tex]P(z > |-1.04|) = 0.15[/tex]
=> [tex]p-value = 2 * 0.15[/tex]
=> [tex]p-value = 0.3[/tex]
Given that [tex]p-value > \alpha[/tex] we fail to reject the null hypothesis
Hence we can conclude that there is no sufficient evidence to support the executive claim
Solve this quadratic equation using the quadratic formula. 5 - 10x - 3x2 = 0
Answer:
x = (-5 ± 2√10) / 3
Step-by-step explanation:
5 − 10x − 3x² = 0
Write in standard form:
-3x² − 10x + 5 = 0
Solve with quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ -(-10) ± √((-10)² − 4(-3)(5)) ] / 2(-3)
x = [ 10 ± √(100 + 60) ] / -6
x = (10 ± 4√10) / -6
x = (-5 ± 2√10) / 3
Step-by-step explanation:
[tex]5 - 10x - 3 \times 2 = 0[/tex]
[tex]multiply \: the \: numbers \\ \\ 5 - 10 x- 6 = 0[/tex]
[tex]collect \: like \: terms \\ \\ 5 - 6 - 10x[/tex]
[tex] - 1 - 10x = 0[/tex]
[tex] - 10x = 1[/tex]
[tex]divide \: both \: sides \: of \: the \: equation \: by \: - 10[/tex]
[tex]x = - \ \frac{1}{10} [/tex]
[tex]alt \: form \: = \\ \\ = 0.1 \\ x = - 10 {}^{ - 1} [/tex]
Hope this helps. :)
write the desimale 3.17 in word form
Answer:
There are multiple ways this can be said :
Three and seventeen hundredthsThree-point seventeenThree-point one sevenHow many more pumpkins have a mass between 9 and 12 kg than between 0 and 3 kg?
Answer:
According to the graph, there are 6 pumpkins with the mass of 9kg to 12kg and 4 pumpkins with the mass of 0kg to 3kg.
In order to find how many pumpkins more, you have to subtract it so it will be 6 pumpkins - 4 pumpkins = 2 pumpkins.
Therefore, there are 2 more pumpkins with the mass of 9 to 12kg compared to the pumpkins with the mass of 0 to 3kg.
Answer:
2
Step-by-step explanation:
Write the number shown in standard notation. 1.02 x 10 First Correct answer gets Brainliest
Answer:
1.02×10¹ = 10.2
Step-by-step explanation:
We have given a number in scientific notation as follows 1.02×10¹
We need to convert it into standard notation.
1 is in ones place, 0 is in tenths place and 2 is in hundredths place.
[tex]1.02\times 10^1=\dfrac{102}{100}\times 10\\\\=\dfrac{102}{10}\\\\=10.2[/tex]
So, the standard notation of 1.02×10¹ is 10.2
Which figure shows △MNP reflected over the y-axis to form △M`N`P`?
Answer:
The answer is in the picture below
Step-by-step explanation:
Hope this helps!
Figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.
What is the reflection of an image?The reflection operator geometrically repositions image elements, or pixel values, in such a way that they are reflected about a user-specified image axis or image point and placed in a new position in a matching output image.
In the given image option fourth is showing the correct reflection of the triangle △MNP over the y-axis to the form △M`N`P'.
It is observed that every point of the triangle MNP is at the same distance from the y-axis as every point of the triangle M'N'P'.
Therefore, figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.
To know more about the reflection of an image follow
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The profit that a business made during a year is $536,897,000. If the business divides the profit evenly for each share, estimate how much each share made if there are 10,995,000 shares.
sara quiere guardar 48 manzanas y 36 duraznos en cajas con el mismo numero de frutas de cada tipo en cada caja cuantas cuantas frutas pude guardar teniendio en cuenta que nesecita el mayor numero de cajas posibles
Answer:
Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.
Step-by-step explanation:
Se requiere el menor número posible de manzanas y duraznos para obtener el mayor número de cajas. Puesto que no se considera cortar fruta alguna en porciones y sabiendo que hay más manzanas que duraznos, se determina la razón mínima de manzanas por duraznos:
[tex]x = \frac{48\,manzanas}{36\,duraznos}[/tex]
[tex]x = \frac{4 manzanas}{3\,duraznos}[/tex]
Se requiere 4 manzanas por cada 3 duraznos. Entonces, cada caja debe contener 3 duraznos y 4 manzanas. El número máximo de cajas es:
[tex]n = \frac{48\,manzanas}{4\,\frac{manzanas}{caja} } = \frac{36\,duraznos}{3\,\frac{duraznos}{caja} }[/tex]
[tex]n = 12\,cajas[/tex]
Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.
Your forecasted income statement shows sales of $1,362,000, cost of goods sold at $830,000, depreciation expense of $310,000, and a forecasted free cash flow of $470,200. What are your forecasted earnings? What is your tax rate?
Answer:
Forecasted earning = $160,200
Tax rate = 27.84%
Step-by-step explanation:
The calculation of forecasted earning and tax rate is shown below:-
Earnings before income and taxes = Sales - Cost of goods sold - Depreciation Expense
= $1,362,000 - $830,000 - $310,000
= $222,000
So,
Forecasted Free cash flow = Net Income + Depreciation
$470,200 = Net Income + $310,000
Net Income = $470,200 - $310,000
= $160,200
Now, the Tax rate is
Net Income = EBIT × (1 - Tax Rate)
$160,200 = $222,000 × (1 - Tax rate)
(1 - Tax rate) = $160,200 ÷ $222,000
(1 - Tax rate) = 0.721622
Tax rate = 27.84%
to find the distance between a point x and an inaccessible point z, a line segment xy is constructed. measurements show that xy=966 m, angle xyz=38°24', and angle yzx=94°6'. find the distance between x and z to the nearest meter.
Answer:
[tex]\approx \bold{602\ m}[/tex]
Step-by-step explanation:
Given the following dimensions:
XY=966 m
[tex]\angle XYZ[/tex] = 38°24', and
[tex]\angle YZX[/tex] = 94°6'
To find:
Distance between points X and Z.
Solution:
Let us plot the given values.
We can clearly see that it forms a triangle when we join the points X to Y, Y to Z and Z to X.
The [tex]\triangle XYZ[/tex] has following dimensions:
XY=966 m
[tex]\angle XYZ[/tex] = 38°24', and
[tex]\angle YZX[/tex] = 94°6'
in which we have to find the side XZ.
Kindly refer to the image attached.
Let us use the Sine rule here:
As per Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{XZ}{sin\angle Y} = \dfrac{XY}{sin\angle Z}\\\Rightarrow \dfrac{966}{sin94^\circ6'} = \dfrac{XZ}{sin38^\circ24'}\\\Rightarrow XZ=\dfrac{966}{sin94^\circ6'} \times sin38^\circ24'\\\Rightarrow XZ=\dfrac{966}{0.997} \times 0.621\\\Rightarrow XZ=601.69 \m \approx \bold{602\ m}[/tex]
A researcher found a study relating the distance a driver can see, y, to the age of the driver, x. When researchers looked at the association of x and y, they found that the coefficient of determination was r = 0.542 Select two conclusions that the researcher can make from this data.
a.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
b.) The correlation coefficient, r, is -0.736.
c.) About 74% of the variation in the driver's age is explained by a linear relationship with the distance that the driver can see.
d.) About 46% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
e.) The correlation coefficient, r, is -0.458.
f.) The correlation coefficient, r, is -0.271.
Answer: a.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
b.) The correlation coefficient, r, is -0.736.
Step-by-step explanation:
The coefficient of determination is denoted [tex]R^2 \ or \ r^2[/tex] which gives the percent of the variance in the dependent variable that is predictable from the independent variable.
Given, [tex]r^2= 0.542[/tex]
That means 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
Also, [tex]r=\sqrt{0.542}\approx\pm0.736[/tex] , where r determines the correlation coefficient.
As driver;s age increases the distance he can see decreases, so there is a negative correlation between them.
So r= -736.
Hence, The correlation coefficient, r, is -0.736.
So, the correct options are a.) and b.)
Let f(x) = 1/x+2 and g (x) = 1/x-3. Find (f/g) (x). Assume all appropriate restrictions to the domain. help!!!!
Answer:
x ≠ -2 or 3
Step-by-step explanation:
No denominator can be zero, so ...
x +2 ≠ 0
x ≠ -2
__
x -3 ≠ 0
x ≠ 3
__
g(x) ≠ 0 . . . . . true for all x; no restriction needed for this
__
The appropriate restrictions are x ∉ { -2, 3 }.
The following data shows marks obtained by students in a mathematics test; 6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,68 a. construct a frequency distribution table data using a discrete values 0, 1, 2,............. 10 b. State the modal score of the distribution c. if a student is chosen at random, what is the probability that a student scored more than 5 means d. Using assumed mean of 6, calculate the arithmetic mean score of the distribution
Data
6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,8
Answer:
(a) shown in the attachment
(b) 0.54
(c) 5.32
Step-by-step explanation:(a) The frequency distribution table has been added to this response.
The table contains four columns:
First column (x): The discrete values of the marks
Second column (f): The corresponding frequency of the marks
Third column (d) : The difference between each mark(x) and the assumed mean(A). i.e d = x - A (Where A = 6 from the question)
Fourth column (fd): The product of the first column and the third column. i.e f * d
(b) From the table, it can be deduced that the modal score is 6
This is because the score 6 has the highest number of frequency which is 6
(c) If a student is selected at random, the probability P(>5), that the student scored more than 5 is given as follows;
P( >5 ) = [The sum of frequencies of marks greater than 5] / [Total frequency]
P( >5 ) = [6 + 4 + 2 + 3 + 1] / [28]
P( >5 ) = 15 / 28 = 0.54
Therefore, the probability that the student scored more than 5 is 0.54
(d) To get the arithmetic mean, M, from the assumed mean A = 6, we use the following relation;
M = A + [∑fd / N] -----------(*)
Where
N = total frequency = 28
A = 6
∑fd = sum of the items on the fourth column = -19
Substitute these values into equation (*)
M = 6 + [-19 / 28]
M = 149 / 28
M = 5.32
Therefore, the arithmetic mean is 5.32
A rectangular box has a length of 9 inches, width of 5 inches, and hight of 1 foot. Find the volume of the box in cubic inches.
Answer:
[tex]45^{3}[/tex] inches
Step-by-step explanation:
To calculate the volume of a rectangular prism(or in this case, the rectangular box), you need to multiply the length, width and height together.
length x width x height
9 x 5 x 1
= [tex]45^{3}[/tex] inches
Hayley is 5feet 5 inches tall. What is tis i metres to the nearest centimetre
Answer:
It might be 168 centimetres
Step-by-step explanation:
The valve was tested on 210 engines and the mean pressure was 5.0 pounds/square inch (psi). Assume the population standard deviation is 0.9. The engineer designed the valve such that it would produce a mean pressure of 4.9 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
1.6101529
Step-by-step explanation:
Given the following :
Number of samples (n) = 210
Sample mean (x) = 5
Population standard deviation = 0.9
Population mean (m) = 4.9
Since the standard deviation of the population is known, we can use the z statistic
Z = (x - m) / standard error
Standard error = sd / √n
Standard error = 0.9 / √210
Standard error = 0.9 / 14.491376
Standard error= 0.0621059
Z statistic = (5 - 4.9) / 0.0621059
Z statistic = 0.1 / 0.0621059
Z statistic = 1.6101529
The number of foxes in a national forest had grown by 1160 in the past year If the number of foxes at the beginning of the year was 5800 by what percent did it increase
Answer:
5800-1160=4640
1160×100÷4640=25
=25%
**WILL GIVE BRAINLIEST** Absolute Value Question. PLEASE HELP QUICK.
Cross multiply the numbers in the matrix:
1 *2 + 5*x = -13
Simplify:
2 + 5x = -13
Subtract 2 from both sides:
5x = -15
Divide both sides by 5
X = -15/5
X = -3
Because it’s absolute value it needs to be positive so x = 3
2y + 18 y + 39 Find y
Answer:
Step-by-step explanation: 2y+18 = y+39
y=21
Answer:
y = 21
Step-by-step explanation:
In the figure , 2y + 18 and y + 39 are opposite interior angles . We know that opposite interior angles are equal , so
2y + 18 = y + 39
=> 2y - y = 39 - 18
=> y = 21
1) You are attending the first Lil Baby concert after quarantine. There are two levels, one level
that is standing room only. The dimensions of the room are 62 feet by 31 feet. 15 people fit in a 3
feet by 6 feet space. Upstairs there can be 80 people. How many people can attend? (Note: It
helps if you make a sketch of the problem).
Answer:
Total number of people in the concert
= 186
Step-by-step explanation:
There are 80 people in level 2
Then in level one
The dimensions of the room are 62 feet by 31 feet.
15 people fit in a 3 feet by 6 feet space.
Area of the room= 62*31= 1922 feet²
area of 15 people space= 3*6= 18 feet²
To know how many 15 people we get in the 2nd level
=Area of room/area of 15 people space
= 1922/18
= 106.77
= 106 (we round down because this is human being.)
Total number of people in the concert
= 106+80
= 186
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.) (c) The manufacturer’s recommended correct inflation range is 27 psi to 31 psi. Assume the tires’ average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire’s inflation is within the recommended range? (Round your intermediate calculations and final answer to 4 decimal places.)
Answer:
(a) At 21.46 psi, the TPMS trigger a warning for this car.
(b) The probability that the TPMS will trigger a warning is 0.0001.
(c) The probability that the tire’s inflation is within the recommended range is 0.6826.
Step-by-step explanation:
We are given that tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).
(a) It is stated that TPMS warns the driver when the tire pressure of the vehicle is 26% below the target pressure.
So, the TPMS trigger a warning for this car when;
Pressure = 29 psi - 26% of 29 psi
= [tex]29-(0.26 \times 29)[/tex] = 21.46 psi
At 21.46 psi, the TPMS trigger a warning for this car.
(b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.
Let X = The pressure at which TPMS will trigger a warning
So, X ~ Normal([tex]\mu=29, \sigma^{2} =2^{2}[/tex])
Now, the probability that the TPMS will trigger a warning is given by = P(X [tex]\leq[/tex] 21.46)
P(X [tex]\leq[/tex] 21.46) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{21.46-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -3.77) = 1 - P(Z < 3.77)
= 1 - 0.9999 = 0.0001
The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.
(c) The manufacturer’s recommended correct inflation range is 27 psi to 31 psi.
So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)
P(27 psi < X < 31 psi) = P(X < 31 psi) - P(X [tex]\leq[/tex]27 psi)
P(X < 31 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{31-29}{2}[/tex] ) = P(Z < 1) = 0.8413
P(X [tex]\leq[/tex] 27 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{27-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -1) = 1 - P(Z < 1)
= 1 - 0.8413 = 0.1587
Therefore, P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.
At 21.46 psi, the TPMS trigger a warning for this car.
The probability that the TPMS will trigger a warning is 0.0001.
The probability that the tire’s inflation is within the recommended range is 0.6826.
Given that,
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.
Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).
We have to determine,
At what psi will the TPMS trigger a warning for this car.
What is the probability that the TPMS will trigger a warning.
What is the probability that the tire’s inflation is within the recommended range.
According to the question,
It is stated that TPMS warns the driver when the tire pressure of the vehicle is 26% below the target pressure.So, the TPMS trigger a warning for this car when;
Pressure = 29 psi - 26% of 29 psi
[tex]Pressure = 29- (0.26 \times 29) = 21.46psi[/tex]
At 21.46 psi, the TPMS trigger a warning for this car.
Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.
Let X = The pressure at which TPMS will trigger a warning
So, X ~ Normal [tex]\mu = 29, \sigma^2 = 2^2\\[/tex]
Now, the probability that the TPMS will trigger a warning is given by = P(X≤ 21.46).
[tex]P(X\leq 21.46) = P (\dfrac{X-\mu}{\sigma}\leq \dfrac{21.46-29}{2}) = P(Z\leq -3.77) = 1-P(Z<3.77) \\\\= 1-0.9999 = 0.0001[/tex]
The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.
The manufacturer’s recommended correct inflation range is 27 psi to 31 psi.
So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)
[tex]P(27psi<X<31psi) = P(X<31psi)-P(X\leq psi)\\\\P(X<31psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{31-29}{2}) = P(Z<1) = 0.8413\\\\P(X<27psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{27-29}{2}) = P(Z\leq -1) = 1-P(Z<1) = 0.8413\\[/tex]
Therefore, , P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.
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Julio ran 1 1/2 miles In 15 minutes. What is his unit rate in miles per minute?
Answer:
= 0.1 miles per minute
Step-by-step explanation:
= 1.5 miles / 15 min.
= 0.1 miles per minute
If the computed minimum sample size n needed for a particular margin of error is not a whole number, round the value of n (up or down) to the next (smaller or larger) whole number.
a) down; smaller
b) down; larger
c) up; larger
d) up; smaller
Answer:
The correct option is c.
Step-by-step explanation:
The margin of error is the range of values lower than and more than the sample statistic in a confidence interval. It is the number of percentage point by which the sample result will differ from the population result.
The general formula to margin of error is:
[tex]MOE=CV\times\frac{SD}{\sqrt{n}}[/tex]
Here,
CV = critical value
SD = standard deviation
n = sample size
Now, if the computed minimum sample size needed for a particular margin of error is not a whole number, then round the value of n up to the next larger whole number.
Thus, the correct option is c.
Data for price and thickness of soap is entered into a statistics software package and results in a regression equation of ŷ = 0.4 + 0.2x.
What is the correct interpretation of the slope if the price is the response variable and the thickness is an explanatory variable?
A. The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.
B. The price of the soap decreases by $0.40, on average, when the thickness increases by 1 cm.
C. The price of the soap increases by $0.40, on average, when the thickness increases by 1 cm.
D. The price of the soap decreases by $0.20, on average, when the thickness increases by 1 cm.
Answer: A. The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm
Step-by-step explanation:
Given the following :
Regression equation : ŷ = 0.4 + 0.2x
Price is the response variable (ŷ)
Thickness is the explanatory variable (x)
Relating the equation given to the regression model:
ŷ = c + mx
Here c = intercept ; y = response variable ;x = explanatory variable and m = slope or gradient.
Hence, mx = 0.2x
Where m = 0.2
The slope means :
Change in y / change in x
Changes in the response variable with respect to change in the explanatory variable.
The slope is positive meaning an increase in the thickness will result in a corresponding increase in price.
With a 0.2 gradient value, that means there is an $0.2 average increase in price of soap as the thickness increases by 1 cm.
Answer:
The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.
Step-by-step explanation:
Simplify: (x-3) (x-3)
Answer:
x^2 -6x +6
Step-by-step explanation:
Square of a difference (can be found in IM2)
Formula: a^2 -2ab +b^2
x= a; 3= b
(x -3)(x -3)
Plug in to formula.
x^2 -2(x)(3) +3^2
Simplify.
x^2 -6x +6
Answer:
[tex](x - 3)^{2}[/tex]
Write -5 less than p as an expression
Answer:
the answer is -5 -p
Step-by-step explanation:
the reason why this is, because negative 5 is less than (-) the variable p.
geometric mean between 8 and 1/4
Answer:
√2
1.414
Step-by-step explanation:
ⁿ√x₁*x₂*x₃*...*xₙ
√8*1/4
√2
1.414
The geometric mean between 8 and 1/4 is; 1.414.
According to the question:
We are required to determine the geometric mean between 8 and 1/4.In essence, the geometric mean can be evaluated as follows;
Geometric mean = √(8×1/4)G.M = √2G.M = 1.414Read more on geometric mean:
https://brainly.com/question/2292573
Assignment
Modeling Real-World Problems with Composite Functions
A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which
represents the situation, where x is the original cost of the item(s)?
Of(x) = 0.35x represents the discount price and g(x) = 0.07x represents the price after taxes. The total price would
be (fog)(x) = 0.35(0.07x) = 0.0245x.
Of(x) = 0.65x represents the discount price and g(x) = 0.07x represents the price after taxes. The total price would
be (fºg)(x) = 0.65(0.07x) = 0.0455x
f(x) = 1.07x represents the price after taxes and g(x) = 0.65x represents the discount price. The total price would
be (fºg)(x) = 1.07(0.65x)= 0.6955x.
Of(x) = 1.07x represents the price after taxes and g(x) = 0.35x represents the discount price. The total price would
be (fºg)(x) = 0.35(1.07x)=0.3745x.
Answer:
Total Price = 1.07(0.65x)= 0.6955x.
Step-by-step explanation:
The discount percentage is, d% = 35%.
The sales tax percentage is, s% = 7%.
The variable x represent the original cost of the item(s).
The discount is subtracted from the original amount.
So, the discounted amount will be, 0.65x.
And the sales tax is added to the original amount.
So, the value of tax plus price will be, 1.07x.
Then the final price of the item(s) will be:
Total Price = 1.07(0.65x)= 0.6955x.
Answer:
It's C for those on edgenuity
Step-by-step explanation: