The dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3
Rectangular Box with Square base
Volume v = a²b = 12
S = Surface area = 2a² + 4ab
v = a²b = 12
b = 12/a²
S = 2a² + 4ab = 2a² + 4a(12/a²) =2a² + 48/a
S'(a) = 4a -48/a² = 0
4a³ = 48
a = 12^ 1/3
b = 12/a² = 12/12^ 2/3 = 12^ 1/3
Therefore, the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3
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Compare and Explain: Are they equivalent?
Jenny is comparing the cost of two packages of socks. One package has 8 pairs of socks for $12. Another package has 3 pairs of socks for $6. Are the rates equivalent?
Express your answer as a polynomial in standard form.
f(x)= -3x+5
g(x)=x^2+2x+15
Find: (g∘f)(x)
Answer: [tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]
=====================================================
Explanation:
The notation (g∘f)(x) is the same as g(f(x))
We'll start with the outer function g(x). Then replace each x with f(x). Afterward plug in f(x) = -3x+5 for the right hand side only.
This is what the steps look like
[tex]g(\text{x})=\text{x}^2+2\text{x}+15\\\\g(f(\text{x}))=(f(\text{x}))^2+2f(\text{x})+15\\\\g(f(\text{x}))=(-3\text{x}+5)^2+2(-3\text{x}+5)+15\\\\g(f(\text{x}))=9\text{x}^2-30\text{x}+25-6\text{x}+10+15\\\\g(f(\text{x}))=9\text{x}^2-36\text{x}+50\\\\[/tex]
Therefore,
[tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]
You can use tools like WolframAlpha, GeoGebra, and Desmos as ways to confirm the answer.
"6 more than 7 times the amount of 10"
Answer: 76
Step-by-step explanation:
Based on the given conditions, formulate: 6+10*7
Calculate the product or quotient: 6+70
Calculate the sum or difference: 76
help 100 points i need help asap
Answer:
Unclassified
Step-by-step explanation:
Which questions would you like answered?
the honda civic hybrid gets 46 miles per gallon in city driving and 51 mpg in highway driving. the car is driven 621 miles in 13 gallons of gasoline. how many miles were driven in the city and how many were driven on the highway?
The distance driven in city is 386.4 miles and same in highway is 213.6 miles.
Let the distance driven in city be x and driven in highway be y.
Now given that the mileage in city is 46 miles per gallon and in highway same is 51 miles per gallon.
The car is driven 621 miles in 13 gallon.
So suitable system of linear equations in two variables to solve this is,
x+y = 621 ……(1)
x/46+y/51 = 13 …….(2)
From (2) we get,
51x+46y = 30498
5x+46(x+y) = 30498
5x+46*621 = 30498
5x = 30498-28566
5x = 1932
x = 386.4
So from (1) we get,
y = 621-x = 621-386.4 = 213.6
Hence the car drove 386.4 miles in city and 213.6 miles in highway.
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PLEASE HELP ME WITH GEOMERY
The blanks in this two-column proof should be completed (filled) as follows:
Statements Reasons_______________
m∠RST = 5x° and m∠UVW = 7x° Given
∠RST and ∠UVW are supplementary
m∠RST = 5x° + m∠UVW = 180 definition of supplementary angles
5x + 7x = 180 substitution property of equality
12x = 180 addition property of equality
x = 15 division property of equality
What is a supplementary angle?In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this context, we can logically deduce that the sum of angles RST and UVW are supplementary angles:
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what is the best point estimate for the population's standard deviation if the sample variance is 49.7? round your answer to one decimal place, if necessary.
Using the relation between standard deviation and variance it is concluded that the standard deviation for the population for the given variance is 7.1
What is the relation between standard deviation and sample variance?In statistics, the two most crucial metrics are variance and standard deviation. While the variance is a measurement of how data points vary from the mean, standard deviation is a measure of the distribution of statistical data.
The square root of the variance yields the standard deviation, i.e.
Standard deviation = [tex]\sqrt{variance[/tex]
Given that sample, the variance is 49.7 and we have to calculate the standard deviation.
Standard deviation (σ) = [tex]\sqrt{variance[/tex]
= [tex]\sqrt{49.7}[/tex]
= 7.0498
=7.1
Hence, the standard deviation for the population for the given variance is 7.1
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3* + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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the sample regression line a. is estimated by the population regression line. b. maximizes the sum of the squared differences between the data points in a sample and the sample regression line. c. shows the actual (or true) relation between the dependent and independent variables. d. is used to estimate the population regression line. e. connects the data points in a sample.
The simple regression line is used to estimate the population regression line.
We are asked about, the simple regression line
We have options:
a. is estimated by the population regression line.
b. maximizes the sum of the squared differences between the data points in a sample and the sample regression line.
c. shows the actual (or true) relation between the dependent and independent variables.
d. is used to estimate the population regression line.
e. connects the data points in a sample.
From the above options, Option (d) is the correct one i.e. is used to estimate the population regression line.
The simple regression line is used to estimate the population regression line.
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it takes a hose 3 minutes to fill a rectangular aquarium 8 inches long, 11 inches wide, and 13 inches tall. how long will it take the same hose to fill an aquarium measuring 26 inches by 33 inches by 35 inches?
It takes almost 5.7 hours the same hose to fill an aquarium measuring 26 inches by 33 inches by 35 inches.
First, we must determine how quickly the hose operates.
By dividing the volume of the first aquarium by the length of time it took to fill it, we may determine that.
The following formula can be used to determine the volume of the first aquarium: V =L*B*H
where the aquarium's length is L and its width is B
Its height is H.
Thus, the first aquarium's volume is:
V =L*B*H = 3*8*11 = 264 inches^3
We have the filling rate as:
264/3 inches ^3 per minute,
Let's now determine the second aquarium's volume.
The first formula is what we employ.
The volume is as follows:
V =L*B*H = 26*33*35 = 30030 inches ^3
Now, we divide the capacity of the second aquarium by the pace of the first aquarium to obtain the amount of time.
According to mathematics, that is:
30030 * 3/264 = 341.25 minutes = 5.7 hours approximately
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Transformation of functions f(x)=-7(x-8)^2 +2
Answer:
Step-by-step explanation:
I think this is the answer you were looking for but im not 100% sure
Can anyone write the equation of the graph?
The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.
How to Determine the Equation of the Graph of an Absolute Value Function?The equation that represents the absolute value function is expressed in in vertex form as y = a|x – h| + k, here, the vertex of the graph of the absolute value function is (h, k), while the value of a determines if the graph opens up or opens down.
The point (3, 5) is the vertex of the graph, therefore:
(h, k) = (3, 5)
Plug in h = 3 and k = 5 into, y = a|x – h| + k:
y = a|x - 3| + 5
Find the value of a, by substituting the values of the coordinates of a point on the graph, (x, y) = (5, 7), into the equation y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 = 2a + 5
2 = 2a [subtraction property]
1 = a [division property of equality]
a = 1
Substitute the value of a into the equation y = a|x - 3| + 5:
y = |x - 3| + 5 [equation of the graph].
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Make d the subject of the formula h=d/3+2
Answer:
d = 3h - 6
Step-by-step explanation:
h = [tex]\frac{d}{3}[/tex] + 2 ( multiply through by 3 to clear the fraction )
3h = d + 6 ( subtract 6 from both sides )
3h - 6 = d
simplify (-5)∧5(-5)∧-6
Answer:
-5 with the exponet of 11
Answer:
-1/5 or -0.2 if you are going by fraction or decimal
The probability that a male’s foot is between 10 and 12. 5 inches is ___%
P(10
The probability of a foot of male being between 10 and 12. 5 inches is 59%.
Define the term normal distribution?The normal distribution approximates any real-valued random distribution which clusters around one single mean value. A cumulative frequency is a procedure that determines if the total amount of information in such a data set is less than and equal to a specific value.The z score of the distribution is found as-
z = (x - μ)/σ
In which,
μ = mean = (11)
σ = standard distribution (1.5)
The likelihood that a male's foot measures between 10 and 12. 5 inches.
P(10 < x < 12.5)
For x = 10
z = (10 - 11) / 1.5
z = -0.67
check the p-value fro z score table.
p (z = -0.67) = 0.2514
For x = 12.5
z = (1.5 - 11)/1.5
z = 1
p (z = 1) = 0.8413
P(10 < x < 12.5) = 0.8413 - 0.2514
P(10 < x < 12.5) = 0.5899
P(10 < x < 12.5) = 58.99%
P(10 < x < 12.5) = 59%.
Thus, the likelihood of a male's foot being between 10 and 12. 5 inches is 59%.
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The complete question is attached in figure.
Marcus wants to save $378 in order to buy a new electronic
keyboard. He plans to save $15. 75 every week from his paycheck. Write and solve an
equation to find how many weeks Marcus will need to save.
Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.
Define the meaning of the equation?A mathematical assertion in which you use mathematical symbols to demonstrate that two sums are equal.
As per specified data-
Marcus wishes to save $378 so that he can purchase a new electronic keyboard.Every week, he saves $15.75 from his paycheck.Let 'x' be the number of weeks required to complete the amount.
The equation becomes.
378 = 15.75x
For the number of week required.
x = 378/15.75
x = 24
Thus, Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.
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Expand & simplify: (7-3x)(2x-4)(x+1)
Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. If she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account?
PLEASE ANSWER ILL DO ANYTHING. Like give brainliest mark, etc.
Sherry needs to invest 2000$ in mutual fund and 13200$ in bond to earn 548$ at the end of the year.
What is percentage?A percentage is just one of the many ways that a number, ratio, or fraction can be expressed. It is a number or ratio expressed as a fraction of 100.
Given:
Sherry has 15200$ to invest in mutual funds and in bonds.
Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.
Here we need to find how much does she need to invest in each type of account if she wants to earn 548 at the end of the first year.
Here we have total amount = 15200$
So, let us consider x be the amount invested in mutual funds, then the amount invested in bonds will be 15200 - x.
It can be written in the following matrix
[x 15200-x ]
We know that the total amount earned at the end of the year is 548.
So, it can be written as
amount invested x percentage = final amount
[tex]\left[\begin{array}{cc}x&15200-x\\\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}1/100\\4/100\\\end{array}\right][/tex] = 548
We can simply it as
[x*1/100 + (15200 - x)*4/100] = 548
⇒ x/100 + 60800/100 - 4x/100 = 548
⇒ x + 60800 - 4x = 54800
⇒ -3x = 54800 - 60800
⇒ -3x = -6000
⇒ x = 2000
⇒ 15200 - 2000 = 13200
Therefore, Sherry invests 2000$ in mutual funds and 13200$ in bond to earn 548 at the end of the year.
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in a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that
In a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that For every unit increase in x1, the predicted mean of Y rises by 2 units holding [tex]x_{2}[/tex] constant.
Given data,
Slope b1 = +2
Mutiple regression which means,
Use multiple linear regression to determine the relationship between two or more independent variables and one dependent variable.
The value of the dependent variable at a specific level of the independent variables (For instance, the crop's anticipated yield at specific levels of temperature, rainfall, and fertilizer application).
[tex]y = b_{0} +b_{1}x_{1}+b_{2}x_{2}+b_{3}x_{3}+....[/tex]
[tex]b_{1}[/tex]=2 means
The estimated mean of Y increases by 2 units for each increase of 1 unit of [tex]x_{1}[/tex], holding [tex]x_{2}[/tex] constant.
Hence, the expected mean of Y increases by two units for every unit increase in x1.
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Which statement is true? All decimals are rational. All rational numbers can be written as the quotient of Integers
The statement that is true is All rational numbers can be written as the quotient of Integers
What are rational numbers ?Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.
In a rational number, the denominator cannot be zero.
Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers
Quotients refers to the end product of division example 2 ÷ 1 = 2/1
2/1 is the quotient, both 2 and 1 are integers
All decimals are rational - A counter example to this is √2
It has decimal and not a rational number because it cannot be represented as a fraction
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The statement that is true is All rational numbers can be written as the quotient of Integers
What are rational numbers ?
Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.
In a rational number, the denominator cannot be zero.
Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers
Quotients refers to the end product of division example 2 ÷ 1 = 2/1
2/1 is the quotient, both 2 and 1 are integers
All decimals are rational - A counter example to this is √2
It has decimal and not a rational number because it cannot be represented as a fraction
Find a rational function that has vertical asymptotes x= -4 and x= 2 and x-intercept (3,0). Write equation and show work
Step-by-step explanation:
to create a vertical asymptote (a tangent of the curve in infinity) at x = n we define e.g.
f(x) = 1/(x - n)
the cost x gets to n, the much closer the function gets to 1/0 and infinity.
so, the part to get us the asymptote at x = -4 is
1/(x + 4)
the part to get us the asymptote at x = 2 is
1/(x - 2)
and the part that gives us a zero solution at x = 3 is
(x - 3)
because that is what the point (3, 0) is : when x = 3. then y = 0.
now we only need to multiply all 3 parts to combine them :
f(x) = 1/(x + 4) × 1/(x - 2) × (x - 3)
The relationship between the number of crocodiles and the number of alligators is not proportional across all lakes. Only two of the lakes have crocodiles and alligators in the same proportion. Which two lakes are they?
There are two lakes that have crocodiles and alligators in the same proportion.The two lakes are Lake Winnipeg and Lake Champlain.
This is the only lakes where this is the case, making them the only lakes with a proportional relationship between the number of crocodiles and the number of alligators. crocodiles and alligators have been known to live in the same body of water, but they are usually not found in the same proportion. In these two lakes, however, they are found in equal numbers.
Crocodiles and alligators are both reptiles that belong to the same order, which is why they can live in the same environment and in the same proportion.It is most likely because these lakes have a warm climate which is suitable for these reptiles.
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A baseball diamond is a square that measures 90ft on each side. Write and expression for the distance from 2nd base to home plate in square root form using a^2+b^2=c^2, then give the answer rounded to the nearest tenth
If a baseball diamond is a square that measures 90ft on each side. The expression for the distance from 2nd base to home plate in square root form isc =√ (90)² + (90)² and the distance is 127ft.
How to find the distance?Using the Pythagoreans theorem formula
c= √ a²+b²
Where:
c = length of hypotenuse
a and b = length of the sides of the right triangle
Let plug in the formula
c =√ (90)² + (90)²
c =√ 8100 +8100
c =√16200
c = 127.3
c = 127 ft (Approximately)
Therefore the distance is 127ft.
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g(x) = x-2
What is the Parent function and transformation
The parent function is y = x ; shift 2 units downwards.
Given,
In the question:
The function is :
g(x) = x - 2
Now, According to the question ;
Let's know
What is the Parent function and transformation?
The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. Reflection. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.
According to the above statement is;
g(x) = x -2
Hence, The parent function is y = x ; shift 2 units downwards.
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Greta sells advertising space for her school yearbook. Last year, a quarter-page ad cost $110.
This year, Greta's teacher asks her to mark down the price by 15% to attract more sponsors.
Greta wants to know the price after the markdown.
☐ Let q equal the price of a quarter-page ad after the markdown.
Which equation can you use to find q?
q=110-0.15(15)
q=110 +0.15(110)
q=110 - 0.15(110)
q=110 +0.15(15)
The equation that could be used to find q is q = 110-0.15(110) where q equal the price of a quarter-page ad after the markdown.
According to the question,
We have the following information:
Cost of a quarter-page ad cost = $110
Mark down in the price = 15%
Now, q represents the price of a quarter-page ad after the markdown.
(Note that when we remove the sign of % means that the number has to be divided by 100.)
So, the equation will be the difference of the markdown price from the original price:
q = 110-(15/100)110
q = 110-0.15*110
q = 110-0.15(110)
Hence, the correct option is the third one.
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You measure containers for international shipments. The height of the standard container is 6 feet and 7 inches. Which of the following is closest to its height in meters?
The emissivity of a surface coated with aluminum oxide can be approximated to be 0. 15 for radiation at wavelengths less than 5 μm and 0. 9 for radiation at wavelengths greater than 5 μm. Determine the average absorptivity of this surface at 1040. 00 K
For emission of a surface, the average absorptivity of this surface at 1040 K is 0.899705900025.
Knowing that ε1 =0.15 and ε2 = 0.9, we first solve for the average emission, e, as follows:
ε = ε1 [tex]f_λ[/tex] [ λT] + ε2 [1- [tex]f_{λ}[/tex](λT)]
is also solved for reference in calculating fλ
(λ*T) = (5 μm)(1040 K)
= 5200 μm K
[tex]f_{λ}[/tex]= 0.0003921333 when referencing this to a blackbody function.
Moving on, we solve for T1040 using the equation above:
ε = ε1 [tex]f_{λ}[/tex][λT] + ε2[1 -[tex]f_{λ}[/tex]( λT)]
=0.9 + (0.15-0.9)0.0003921333
=0.899705900025
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find an equation for the perpendicular bisector of the line segment whose endpoints are (9,-5) and (-5,-1)
The equation y = (13 / 4) · x - 19 / 2 represents the perpendicular bisector of the line segment.
How to find the equation for the perpendicular bisector of a line segmentIn this problem we need to determine the equation of the line perpendicular to a line segment whose endpoints are known. The equation of the line is represented by a first grade polynomial of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.And the relationship between the slopes of two perpendicular lines:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.And the slope of the original line can be found by the secant line formula:
m = Δy / Δx
And the midpoint of a line segment between two endpoints is defined below, necessary for the location of the bisector:
M(x, y) = 0.5 · A(x, y) + B(x, y)
Where:
M(x, y) - MidpointA(x, y), B(x, y) - EndpointsFirst, find the slope of the line segment by secant line formula:
m = [- 1 - (- 5)] / (- 5 - 9)
m = - 4 / 13
Second, find the slope of the perpendicular bisector by the slope relationship between two perpendicular lines:
m' = - 1 / m
m' = - 1 / (- 4 / 13)
m' = 13 / 4
Third, determine the midpoint of the line segment by the midpoint formula:
M(x, y) = 0.5 · (9, - 5) + 0.5 · (- 5, - 1)
M(x, y) = (4.5, - 2.5) + (- 2.5, - 0.5)
M(x, y) = (2, - 3)
Fourth, find the intercept of the perpendicular bisector by means of the equation of the line:
b = y - m' · x
b = - 3 - (13 / 4) · 2
b = - 3 - 26 / 4
b = - 3 - 13 / 2
b = - 19 / 2
The equation for the perpendicular bisector is y = (13 / 4) · x - 19 / 2.
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in rocky mountain national park, many mature pine trees along highway 34 are dying due to infestation by pine beetles. scientists would like to use a sample of size 200 to estimate the proportion of the approximately 5000 pine trees along the highway that have been infested. describe how to select a systematic random sample of 200 pine trees along highway 34.
The given alternate possible way given in the question is not good as the sample does not follow the conditions of the definition of SRS in the study.
SRS is a group or sample size of "n" objects in a population of "n" objects in which all the possible samples would have equal chances to occur or happen.
In the alternate case, There 200 trees sample is taken from near the highway, that can have fewer chances to be infected or can have more infected.
The fact that the sample was not taken randomly and has not been selected in such a way that each tree has equal chances to happen.
The SRS is not possible to obtain as it does not follow the term and conditions of SRS.It creates a bias in the study.Hence we get the required answer.
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There are some sweets in a jar
The sweets are red or orange or blue or yellow.
Hannah is going to take at random a counter from the bag.
The table shows cach of the probabilities that the counter will be blue or will be yellow.
Colour
Probability
red
orange
blue
0.5
yellow
0.2
There are 20 blue sweets in the jar.
The probability that the sweet Hannah takes will be red is twice the probability that the
sweet will be orange.
(a) Work out the number of red sweets in the jar.
the mom
the number of Red sweets=14
Let the probability of getting a red sweet be = P(R)
Let the probability of getting a Blue sweet be = P(B)
Let the probability of getting an orange sweet be = P(O)
Let the probability of getting a yellow sweet be = P(Y)
Let the number of Red sweets be represented as = n(R)
Let the number of Yellow sweets be represented as = n(Y)
Let the number of Orange sweets be represented as = n(O)
Let the number of Blue sweets be represented as = n(B)
Let the total number of sweets in the jar be represented as = n(T)
P(B) = 0.5
P(E) = 0.2
P(R) = 2 x P(O)
The formula of probability =
Number of the Sweets of a color/Total number of sweets in the jar
then,
P(B)=n(B)/ n(T)
P(B)=0.5 (Given in question)
n(B)=20 (Given in question)
So,
0.5 = 20/n(T)
5/10 = 20/n(T)
5/10 x 1/20 = 1/n(T)
cross multiplying
n(T)=10/5 x 20
dividing 10 by 5 =2
n(T) = 2 x 20
n(T) = 40
P(Y)=0.2 (Given in question)
Applying the formula of probability
P(Y) = n(Y)/n(T)
putting values
0.2=n(Y)/40
2/10=n(Y)/40
2/10 x 40 =n(Y)
Dividing 40 by 10 = 4
n(Y)= 2 x 4
n(Y)= 8
P(R)=2P(O)
Applying the formula of probability
n(R)/n(T)=2n(O)/n(T)
Cancelling out n(T) with n(T)
So,
n(R)=2 x n(O) -(i)
n(T) = n(O)+n(R)+n(B)+n(Y)
putting values
40=n(O)+n(R)+20+8
40=n(O)+n(R)+28
40-18=n(O)+n(R)
From -(i)
22=2n(O)+n(O)
22=3n(O)
n(O)=22/3
Since,
n(R)=2xn(O)
n(R)=2x22/3
n(R)=44/3
n(R)=14.6
the number of Red sweets=14.6
Learn more about Probability at:
brainly.com/question/13932428