1 gallon (gal) = 128 fluid ounce (fl oz)
1 hour (hr) = 60 minutes (min)
Convert 1 fl oz/min to gal/hr.
[tex]\dfrac{1\,\rm fl.oz}{1\,\rm min} \times \dfrac{1\,\rm gal}{128\,\rm fl.oz} \times \dfrac{60\,\rm min}{1\,\rm hr} = \dfrac{60}{128} \dfrac{\rm gal}{\rm hr} \approx \boxed{0.47 \dfrac{\rm gal}{\rm hr}}[/tex]
Find the total surface area of the cylinder shown. Leave the answer in terms of π. A cylinder with radius 4.25 inches and height 6 inches. SA=2πrh+2πr2
Answer:
[tex]87.125\pi in^{2} or 87\frac{1}{8}\pi in^{2}[/tex]
Step-by-step explanation:
Given Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex],
and also given r = 4.25 inches and h = 6 inches.
Let's Substitute r and h into the formula to find the total surface area.
Surface Area of Cylinder = [tex]2\pi (4.25)(6)+2\pi (4.25)^{2} \\=51\pi +36.125\pi \\=87.125\pi in^{2} or 87\frac{1}{8} \pi in^{2}[/tex]
What term is used to describe the problem of using variables that strongly correlate with one another in a multiple linear regression model
Multicollinearity is used to describe the problem of using variables that strongly correlate with one another in a multiple linear regression model.
Multiple linear regression refers to a statistical technique that is used to predict the outcome of a variable based on the value of two or more variables. It is sometimes known simply as multiple regression, and it is an extension of linear regression. The variable that we want to predict is known as the dependent variable, while the variables we use to predict the value of the dependent variable are known as independent or explanatory variables.
Multicollinearity, also known as collinearity, is a phenomena in statistics when one predictor variable in a multiple regression model can be linearly predicted from the others with a high level of accuracy. In this case, minor adjustments to the model or the data may cause the multiple regression's coefficient estimates to fluctuate unpredictably. Multicollinearity only impacts calculations pertaining to specific predictors; it has no impact on the predictive capability or reliability of the model as a whole, at least within the sample data set. In other words, a multivariate regression model with collinear predictors can show how well the entire set of predictors predicts the outcome variable, but it might not provide accurate information about any particular predictor or about which predictors are redundant with respect to another predictor.
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Identify the pair of points that can represent an increasing function that has a greater rate of change than that of the function y = 8/5x + 3/5
Answer:
Step-by-step explanation:
Find the first four terms of the sequence given by the following. an= 4(2)^n-1 n=1, 2, 3...
Answer + Step-by-step explanation:
an= 4(2)ⁿ⁻¹
First term (n = 1) :
a1= 4(2)¹⁻¹ = 4(2)⁰ = 4×(1) = 4
Second term (n = 2) :
a2= 4(2)²⁻¹ = 4(2)¹ = 4×(2) = 8
Third term (n = 3) :
a3= 4(2)³⁻¹ = 4(2)² = 4×(4) = 16
Fourth term (n = 4) :
a4= 4(2)⁴⁻¹ = 4(2)³ = 4×(8) = 32
can anyone slove this with formula ( operations with rational number)
How do you solve the expression 1x + 4 ≤ 8?
1x + 4 ≤ 8
x + 4 ≤ 8
x ≤ 8 - 4
=x ≤ 4
HELP FAST!! PLEASE will give brainliest!
Answer:
22
Step-by-step explanation:
3*sqrt 25 + 7
3*5 + 7
15+7
22
A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. four marbles from this jar are selected, with each marble being replaced after each selection. what is the standard deviation of x, the number of draws until the first red marble?
0.4852
0.9704
2.0770
1.5172
The PMF of [tex]X[/tex] is almost geometric in nature. Let [tex]p=\frac{11}{29}[/tex]. Then
[tex]P(X = x) = \begin{cases} p & \text{if }x = 0 \\ (1-p)p & \text{if }x = 1 \\ (1-p)^2 p & \text{if }x = 2 \\ (1-p)^3p & \text{if }x = 3 \\ (1-p)^4 & \text{if }x = 4 \\ 0 & \text{otherwise}\end{cases}[/tex]
Compute the first moment/expected value.
[tex]E(X) = \displaystyle \sum_x x\, P(X=x) \\\\ ~~~~~~~~ = 0\cdot p+1\cdot(1-p)p + 2\cdot(1-p)^2p + 3\cdot(1-p)^3p + 4\cdot(1-p)^4 \approx 1.39349[/tex]
Compute the second moment.
[tex]E(X^2) = \displaystyle \sum_x x^2\, P(X=x) \\\\ ~~~~~~~~ = 0\cdot p+1\cdot(1-p)p + 4\cdot(1-p)^2p + 9\cdot(1-p)^3p + 16\cdot(1-p)^4 \approx 4.01103[/tex]
Compute the variance.
[tex]V(X) = E(X^2) - E(X)^2 \approx 2.06921[/tex]
The standard deviation is the square root of the variance.
[tex]\sqrt{V(X)} \approx \boxed{1.43848}[/tex]
1. The perimeter of a rectangular fram is 24 centimeters. It is 4 1/2 centimeters wide. How long is it?
Answer:
7.5 cm
Step-by-step explanation:
The perimeter of a rectangle is the sum of the length of all its sides.
Perimeter of rectangle= 2(length +breadth)
Given: perimeter= 24 cm, breadth= 4.5 cm
Substitute the given information into the formula:
24= 2(length +4.5)
Divide both sides by 2:
length +4.5= 12
Subtract 4.5 from both sides:
length
= 12 -4.5
= 7.5
Thus, the rectangle is 7.5 cm long.
Which of the following equations results in infinitely many solutions?
7y + 15 - 2y = 7(y + 3)
7y +3-2y = 5(y + 3)
7y + 15 = 5(y + 3)
7y + 15 - 2y = 5(y + 3)
Answer:
7y + 15 - 2y = 5(y + 3)
Step-by-step explanation:
So two equations have infinitely many solutions, when they are exactly the same equation, in their most simplified form, for example: 2x = 3x-x which simplifies to 2x=2x. So in the options, three of the options have the same equation on the right side, so I'll distribute the 5. [tex]5(y+3) = 5y+15[/tex]. Now let's look at the options:
7y + 3-2y
5y+3 (this is not the same as 5y + 15)
7y + 15 (this is not the same as 5y + 15)
7y + 15 - 2y
5y + 15 = 5y + 15 (this is the same)
Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 4r and height 4h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?
Answer:
The surface area of Cylinder B is 16 times the surface area of Cylinder AStep-by-step explanation:
Note: It is assumed we are looking at the total surface area (but the answer would be same for both cases)
GivenCylinders A with radius - r, height - h,Cylinder B with radius - 4r, height - 4h.To find The ratio of total surface areas of cylinder B to ASolutionTotal surface area of cylinder A is:
[tex]S_A = 2\pi r(h + r)[/tex]Total surface area of cylinder B is:
[tex]S_B = 2\pi(4r)(4r + 4h) = 8\pi(4)(r + h) = 32\pi(r + h)[/tex]Find the ratio of areas:
[tex]\cfrac{S_B}{S_A} =\cfrac{32\pi(r+h)}{2\pi(r+h)} =16[/tex]A sample of neon gas at 50.°c and a volume of 2.5 l is cooled to 25°c. what is the new volume? use the formula: v1 t1 = v2 t2 2.3 l 2.7 l 5.0 l 32.3 l
The new amount of neon gas when the temperature drops is 2.30L.
Charles's law
Charles's law states, "The volume occupied by a particular amount of gas is directly proportional to its absolute temperature.
Initial temperature of gas T₁ = 50 ° C = 323.15K
Initial volume of gas V₁ = 2.5L
Final temperature T₂ = 25 ° C = 298.15K
Final capacity V₂ =? Neon gas, substitute the given value into the above equation:
V₁ / T₁ = V₂ / T₂
V₂ = V₁T₂ / T₁
V₂ = (2.5L × 298.15K) ) / 323.15K
V₂ = 2.30 l
Therefore, the new volume when the temperature of the neon gas drops is 2.30l.
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Answer:
A. 2.3
Step-by-step explanation:
An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic Step 1 of 2: Suppose a sample of 2676 new car buyers is drawn. Of those sampled, 642 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places. AnswerHow to Enter 2 Points Tables Keypad Keyboard Shortcuts An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2: Suppose a sample of 2676 new car buyers is drawn. Of those sampled, 642 preferred foreign over domestic cars. Using the data, construct the 98 % confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places, Answer low to Enter) 2 Points T Tables Keypad Keyboard Shortcuts Lower endpoint Upper endpoint:
The proportion of people who preferred foreign cars than domestic cars is 0.24 and the confidence interval for the population proportion of new cars over domestic cars of 98% confidence interval is (641.955,642.045).
Given sample size of 2676 and number of people preferred foreign cars than domestic cars is 642.
We have to calculate the proportion of people who preferred foreign cars than domestic cars and the confidence interval which shows the confidence interval of 98%.
Number of people prefer foreign cars than domestic cars=642
Sample size=2676
Proportion=642/2676
=0.2399
=0.24 (After rounding off)
Now we will find confidence interval.
X=642
n=2676
z value for the confidence interval 98% is 2.33
Confidence interval =X± z*s/[tex]\sqrt{n}[/tex]
Upper =642+2.33*1/[tex]\sqrt{2676}[/tex] (we have taken s=1)
=642+0.045
=642.045
Lower=642-2.33*1/[tex]\sqrt{2676}[/tex]
642-0.045 (putting values in formula given above)
=641.955
Hence the proportion of people preferred foreign cars than domestic cars is 0.24 and the confidence interval is (641.955,642.045).
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3. Write an expression that would help you
solve the problem below.
Hunter cuts a 32 foot long piece of wood
into x pieces.
How long is each piece of wood?
Solve: How long is each piece of wood if
Hunter cuts the original piece into 8
pieces?
Answer:
How long is each piece of wood?
Expression = 32/x
Solve: How long is each piece of wood if
Hunter cuts the original piece into 8
pieces?
32/8 = 4 foot
The ages and grades of some of the 19 girls on a club soccer team are
shown in the table.
O A.
15 years old
2
9th grade
10th grade
Which two-way frequency table correctly shows the marginal frequencies?
9th grade
10th grade
16 years old
0
10
15 years 16 years
old
old
2
0
7
10
Total
2
17
Answer:
Other answer is wrong. The answer is this choice
The table C correctly shows the marginal frequencies.
What is two ways frequency table?A two-way table is a way to display frequencies or relative frequencies for two variables.
One of the variables is represented using rows and the other one using columns.
They are used to see if there is any relationship between the two variables.
Given that, the ages and grades of some of the 19 girls on a club soccer team are shown in the given table.
We need to select the table showing the correct marginal frequencies.
So, we see that,
Table A and Table D add up to a total of 21 girls.
The question says there are 19 girls, so those two are eliminated.
Table B's data doesn't even add properly so that is eliminated too.
This leaves Table C.
Hence, the table C correctly shows the marginal frequencies.
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The complete question is attached.
There are 400 students at a sports camp. Two hundred students play soccer, 100 students play baseball, and 100 students play basketball. Which circle graph could be used to display this data? A circle graph. About 60 percent is soccer, 15 percent is baseball, 25 percent is basketball. A circle graph. About 25 percent is soccer, 25 percent is baseball, 50 percent is basketball. A circle graph. About 50 percent is soccer, 25 percent is baseball, 25 percent is basketball. A circle graph. About 33 percent is soccer, 33 percent is baseball, 33 percent is basketball.
Answer:
C. About 50 percent is soccer, 25 percent is baseball, 25 percent is basketball.
Step-by-step explanation:
400 students at a sports camp.
200 play soccer, which is 50% or half of the students at the sports camp.
100 play baseball, which is 25% or a quarter of the students at the camp.
100 play basketball, which is also 25% or a quarter of the students at the camp.
So, the circle graph that shows soccer 50%, baseball 25%, and basketball 25%, is the answer.
Hope this helps!
If not, I am sorry.
A triangle with vertices at A(0,0), B(0,4), and C(6,0) is dilated to yield a triangle with vertices at A(0,0), (B(0,10), and C (C(15,0). The origin is the center of dilation. What is the scale factor of the dilation
The required scale factor for the dialed triangle is given by SF= 6.28
A triangle with vertices at A(0,0), B(0,4), and C(6,0) is dilated to yield a triangle with vertices at A(0,0), (B(0,10), and C (C(15,0).
The scale factor is defined as the ratio of modified change in length to the original length.
Since, the height and base of the triangle is y coordinate of B and x coordinate of c is given by 4, 6
Area of triangle =1/2(base x height)
= 1/2 (4 x 6)
= 4.8
Similarly, for dilated triangle
Area of dilated triangle = 30
Now, scale factor(SF) = area of dilated triangle \ area of triangle
SF = 30/4.8
SF = 6.25
Thus, the required scale factor is SF = 6.25
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What is the product of the matrices [tex]\left[\begin{array}{ccc}-3&3&0\end{array}\right] \left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex] ?
Answer:
24
Step-by-step explanation:
(-3 * -3) + (3*5) + (0 * -2) = 24
Measure of arc CF
please help
And number 9
I’ll give brainiest answer to whoever helps first
Thank youuuu
Answer:
Step-by-step explanation:
The measure of an angle formed by a Secant and a tangent drawn from the outside point of a circle is half the difference of the intercepted arcs.
[tex]\sf \angle E =\dfrac{arc \ CF - arc \ DF}{2}[/tex]
[tex]\sf53 =\dfrac{arc \ CF-41}{2}[/tex]
53*2 = arc CF - 41
106 = arc CF - 41
106 + 41 = arc CF
[tex]\sf \boxed{\bf \ arc \ CF = 147^\circ}[/tex]
9) If two secants inside a circle, then the angle formed is equal to the half of the sum of intercepted arcs.
[tex]\sf 5x - 7 = \dfrac{27+119}{2}\\\\ 5x - 7 = \dfrac{146}{2}[/tex]
5x - 7 = 73
5x = 73 + 7
5x = 80
x = 80/5
[tex]\sf \boxed{\bf \ x = 16^\circ }[/tex]
Quadrilateral ABCD is a rectangle.
If BDC = 7x + 1 and ADB=9x - 7, find BDC.
[tex]\huge\boxed{45^\circ}[/tex]
See the attached diagram.
Together, angles BDC and ADB form a right angle, which is 90 degrees.
The angles are split straight down the middle, meaning they're equal to each other. This means each one is equal to half of 90 degrees, which is 45 degrees.
Judy is a single woman, 25 years old. Her take home pay is $2314.92/month. She also earns $48 interest per month on her savings account. Judy rents a 1-bedroom apartment for $825/month. She does not own a car and uses public transportation to travel to and from work. Judy also has a student loan for which she repays $258/month.
The monthly budget plan for Judy includes all of her income and expenses, the total balance is $ 2362.92 and she spends $ 1083.
What is the monthly budget?A monthly budget is a personal spending plan that you use to track your monthly income and costs.
The given data in the problem is;
Home pay = $2314.92/month.
Interest earned = $48 / month
House rent = $825/month
EMI of student loan = $258/month
Total earning per month = $2314.92 + $48
Total earning per month = $ 2362.92
Amount she spends per month = $825/month + $258
Amount she spends per month = $ 1083
Hence, the total balance will be $ 2362.92 and she spend $ 1083.
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Solve on the interval [0,2%):
2 cos²x+3cosx+1=0
Answer:
Step-by-step explanation:
Necesito ayuda en esto!!
1. f(x)= x²+3
2. f(x)= x²+1
3.f(x)= x²+4
4. f(x)= -x²-1
Por favor,ayúdenme
Answer:
they are no instructions so no answers either.
Step-by-step explanation:
am sorry I can't help you, the question might not have been complete. please do contact me when it's.
Consider the equality xy=k. Write the following inverse proportion: y is inversely proportional to x. When y = 2, x = 14.
2/1 = k/14
1/k = 14/2
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1.}[/tex]
[tex]\mathbf{\dfrac{2}{1} = \dfrac{k}{14}}[/tex]
[tex]\huge\textbf{Cross multiply the given numbers}\\\huge\textbf{you have listed.}[/tex]
[tex]\mathbf{2\times14 = k \times1}[/tex]
[tex]\mathbf{2\times14 = 1\times k}[/tex]
[tex]\mathbf{28 = 1k}[/tex]
[tex]\mathbf{1k = 28}[/tex]
[tex]\huge\textbf{DIVIDE 1 to BOTH SIDES}[/tex]
[tex]\mathbf{\dfrac{28}{1} = \dfrac{1k}{1}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{k = \dfrac{28}{1}}[/tex]
[tex]\mathbf{k = 28}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{k = 28}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathbf{\dfrac{1}{k} = \dfrac{14}{2}}[/tex]
[tex]\huge\textbf{Cross multiply the given numbers}\\\huge\textbf{you have listed.}[/tex]
[tex]\mathbf{1\times 2 = 14\times k}[/tex]
[tex]\mathbf{2 = 14k}[/tex]
[tex]\mathbf{14k = 2}[/tex]
[tex]\huge\textbf{DIVIDE 14 to BOTH SIDES}[/tex]
[tex]\mathbf{\dfrac{14k}{14} = \dfrac{2}{14}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{k = \dfrac{2}{14}}[/tex]
[tex]\mathbf{k = \dfrac{2\div2}{14\div2}}[/tex]
[tex]\mathbf{k = \dfrac{1}{7}}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{k = \dfrac{1}{7}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitritr1040:)}[/tex]A combination lock like the one shown has three dials. Each of the dials has numbers ranging from 0 to 4. How many different combinations are possible with the lock?
If combination requires 3 numbers ranging from 0 to 4 then number of combinations is 10.
Given A combination lock contains three numbers from 0 to 4.
Combinations refers to a technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Total numbers available to be selected are 5 from 0 to 4.
In this 0 is also included because it is also a number.
Numbers to be filled in the combination lock =3
So to calculate the combinations we need to use nCr formula in which n=5 and r=3.
Combinations=5C3
=5!/3!*(5-3)!
=5!/3!*2!
=5*4*3!/3!*2!
3! will be cancelled from numerator and denominator
=5*4/2
=10
Hence the number of possible combinations are 10.
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Pls heeeelp!!!!!!!!!!!!!!!
The area of a parallelogram is simply its base (6.1 miles) multiplied by its height (2.6 miles).
Substitute the values into the formula for area.
[tex]A=6.1\cdot2.6[/tex]
Multiply.
[tex]A=\boxed{15.86}[/tex]
Note that the answer is given in square miles ([tex]\text{mi}^2[/tex]) since both of the measurements used are in miles.
simplyfy it -25 + 14 ÷ (5 – 3)
Step-by-step explanation:
-25 + 14 ÷ (5-3)
= -25 + 14 ÷ (2)
= - 25 + 7
= - 18
• Your equation
[tex] - 25 + 14 \div (5 - 3)[/tex]
• Solving
[tex] - 25 + 14 \div (2)[/tex]
• Dividing the terms.
[tex] - 25 + 7[/tex]
• Answer = -18
Hope it helps you!
The functions fand g are defined as follows.
g(x) = -2x³-5
f(x)=2x-3
Find f(5) and g(-2).
Simplify your answers as much as possible.
ƒ(s) = 1
s(-2) = 0
3
X
5
?
Answer:
f(5)
-2(5)-3
-10-3=-13
g(-2)
-2(-2)^3-5
-2(-8)-5
16-5=11
Step-by-step explanation:
Select the correct answer.
What are the domain and range of f(x) = -log5(x + 2)?
A.
domain: x > -2; range: all real numbers
B.
domain: x > 2; range: all real numbers
C.
domain: x > -2; range: all positive real numbers
D.
domain: x > 2; range: all positive real numbers
The correct option is A.
domain: x > -2; range: all real numbers
Which is the domain and range of the given function?
Here we have a logarithmic function.
Remember that the argument of a logarithm must be larger than zero, in this case the argument is:
x + 2
So we must have:
x + 2 > 0
x > -2
Then the domain is: x > -2.
And the range of any logarithmic function is the set of all real numbers.
Then the correct option is A.
domain: x > -2; range: all real numbers
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Write an equation to model this proportional relationship, where x represents the length of the rectangle and y represents the width of the rectangle.
When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle.
[tex]x\propto \frac{1}{y} [/tex]
We know that the area of a rectangle is given by the product of the length and width of the rectangle.
Area = Length*Width
In this given problem,
The length of the rerectanglctangle is represented by x
and the width of the rectangle is represented by y
If the area of the rectangle is represented by A now.
So by the formula,
A = x*y
When A is constant then,
x = A/y
[tex]\therefore x \propto \frac{1}{y}[/tex]
So from the above calculation we can conclude that about relation between length and width that,
"When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle."
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