The rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.
What is rate in mathematics?
A rate is the ratio of two related quantities expressed in different units. the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable. One unit of one of these quantities is used to represent the ratio's denominator, and if it can be altered consistently, then the ratio can be stated as follows: (i.e., is an independent variable).
The rate can be configured as.
Rate = [tex]\frac{1/3}{5/6}[/tex]
Rate = [tex]\frac{2}{5}[/tex]
Hence, the rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.
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a baseball diamond is a square with side 90 feet. if a batter hits the ball and runs towards first base with a speed of 25 ft/sec, at what speed is his distance from second base decreasing when he is two thirds of the way to first base?
The rate when his distance from second base changes and it is two third of the way to first base is - 13.86 feet/s.
let us consider the following values
distance between batter to Second base = d feet
distance between batter to First base
= x feet
distance between first to second base
= 90 feet
Using the Pythagorean theorem:
d² = x² + 90²
Knowing that the velocity of the bat to first base is 25 ft/s,
the distance x can be written as: x
= 90 - 25t
The equation for is,d² = 90²+(90 -25t)²--(1)
we want to find the rate of change of d.
let it be d' and from implicit differentiation:
2d.d' = 2(90-24t) × (-25)
d' = -50(90 - 25t) / (2d)
d' = -25 (90 - 24t) / d ---(*)
We can determine t and d from the fact that the batter is two third to his first base: d = √90^2 + 60^2 = √1 = 108.2 feet
putting the values of d in (1) we get,
=> 90 - 25t = 60 => 25t = 30 => t = 6/5.
Substitute d' in the formula equation (*)
d' = -25 (90 - 24t) / d = -25(90-30)/108.2
d'= - 13.86
d' = - 13.86 feet/s
negative sign means decreasing distance from second base (as it approaches the first
bases, it approaches the second base).
Hence,The required speed is 13.86 feet/s
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Fall Math Benchmark
1. For the scenario given, explain in words your process for solving the problem.
Two rectangular walls need to be painted. They are each 12 feet high and 23 feet
wide. It costs $1.50 per square foot for paint. How much will it cost to paint the
walls?
The amount that it will cost to paint the walls, given the cost per square foot and the dimensions of the rectangular walls is $828
How to find the cost?First, find the area of the rectangular walls by the formula for the area of a rectangle which is:
= Length x Width
The area of the rectangles is therefore:
= 12 x 23
= 276 feet ²
The area of the two rectangular walls is:
= 276 + 276
= 552 feet ²
The cost to paint the walls is:
= Area of walls x cost per square feet to paint
= 552 x 1.50
= $828
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What is the slope of a line perpendicular to the line whose equation is 6x + 2y = -32. Fully simplify your answer.
The slope of a line is m=−3
The slope of a line indicates its steepness. The slope is determined mathematically as "increase over run" (change in y divided by change in x).
Given that
the slope of 6x+2y=−32:
slope using the standard form:
slope m of a line of the form Ax+By=C equals –A/B
A=6, B=2
m=−6/2
simplify
m=−3
Therefore the slope of a line is m=−3
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there are 32 students in categories a and b combined; 24 are in a, and 24 are in b. how many are in both a and b?
The number of students that are in both the Categories A and B are 16 students.
In the question ,
it is given that ,
the total number of students in category A and category B is 32 students .
which is represented as A union B ,
that is n(AUB) = 32 ,
the number of students in category A = n(A) = 24
the number of students in category B = n(B) = 24
we need to find the number of students that are in both category ,
that is n(A∩B) .
we know that ,
n(AUB) = n(A) + n(B) - n(A∩B)
Substituting the values , we get
n(A∩B) = 24 + 24 - 32
= 48 - 32
= 16
Therefore , The number of students that are in both the Categories are 16 students.
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A rectangular dining room has a perimeter of 24 meters. Its area is 35 square meters. What are the dimensions of the dining room? IN NEED ASAP CLASS IS ABOUT TO END
The dimensions of the rectangle which form the dining room is 7 by 5 meters.
The perimeter of the rectangle is 24 meters.
The total length of a shape's boundaries is its perimeter. The total lengths of all other edges and sides are added to find a shape's perimeter.
Let the length be a and the width be b.
Hence 2(a + b) = 24
or, a+b = 12
Now the area of the rectangle is given as 35 square meters.
Therefore ab = 35
now we will use these two equations to find the dimension of the rectangle
a+b = 12
or, a = 12 - b
again:
ab = 35
or, (12 - b)b = 35
or, 12 b - b² = 35
or, - b² +12b -35 = 0
or, b² - 12b + 35 = 0
or, (b-7) (b-5) = 0
either b = 7 or b = 5 .
Therefore the value of a from the equations is 5 or 7.
Therefore the dimensions of the dining room are 7 by 5 meters.
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in a multiple regression model, which of the following is correct regarding the value of the adjusted r^2?
A. It can be negative
B. It has to be positive
C. It can be larger than 1
D. It has to be larger than the coefficient of multiple determination
The correct option is option (B) .
In a Multiple regression Model , the value of adjusted r-Squared is positive.
Adjusted r-Squared :
Adjusted r-squared is a modified version of r-squared adjusted for the number of predictors in the model. The fitted r-squared increases only if the new term improves the model beyond what would be expected by chance. This is reduced if the predictor happens to not improve the model more than expected.
The formula for r-squared,
Adjusted r-squared= 1 - [ ( 1 -r²)(n-1)/(n-k-1)]
where
N --> number of points in the data sample.
K --> number of independent regressors, i. number of variables in the model excluding or constant.
r²--> Indicates how well a term (data point) fits a curve or line.
r-squared values range from 0 to 1 and are commonly stated as percentages from 0% to 100%.
100% r-squared means that all movements in the security are completely explained by movements in the index.
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solve the simultaneous equations
y = 2 - x
6x + 5y = 11
x + 2y = 2
2x + y = 1
Answer:
x = 2
y = 0
Step-by-step explanation:
Here are the simultaneous equations:
[tex]y=2-x\\6x+5y=11\\x+2y=2\\2x+y=1\\[/tex]
There are only two unknown values, so only two equations are needed to find the answer. I will use these:
[tex]y=2-x\\x+2y=2[/tex]
Substitute the first equation into the y in the second equation:
[tex]x+2(2-x)=2[/tex]
Simplify
[tex]x+4-2x=2\\x=2[/tex]
Use the value of x to find y in equation 1:
[tex]y=2-x\\y=2-2\\y=0[/tex]
Drag the numbers below to put them in order from least to greatest:
6.426.42 6.536.53 6.4976.497 6.66.6 6.4536.453 6.486.48
The numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.
What is number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that the numbers are,6.42,6.53,6.497,6.66,6.453,6.486.
Ascending order refers to a list of numbers that are arranged from least to greatest. The numbers are arranged in ascending order in this form. The first figure must be less than the second figure. It is referred to in descending order when the numbers are listed from greatest to least.
Thus, the numbers below to put them in order from least to greatest will be 6.42, 6.453, 6.486, 6.497, 6.53, and 6.66.
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PLEASE HELP ME I FEEL LIKE THIS SHOULD BE SUPER EASY BUT MY BRAIN CAN NOT RN
Answer:
x = 62
y = 41
Step-by-step explanation:
y + 21 = x
x + y + 77 = 180
2y+77 = 180
2y = 82
y = 41
x = 62
What is the rectangular form of Θ = 3π/4?
x − y = 0
x − y = 1
x + y = 0
x + y = 1
The rectangular form of Θ = 3π/4 will be; y + x = 0.
What are Complex value?Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
On converting the rectangluar to polar form of the complex number;
x = rcosθ and y = rsinθ
z = r(cosθ+isinθ)
r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Given the Θ = 3π/4
Therefore, θ = tan⁻¹y/x = 3π/4
y/x = tan (3π/4)
Now multiply both side by x
yx/x = tan (3π/4) x
y = tan (3π/4) x
Thus, y = -x
in rectangular form y + x = 0
Hence, the rectangular form of Θ = 3π/4 will be; y + x = 0.
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Evaluate 1/2x^4 – 3/4x² for x = 2.
Answer:
[tex]-\frac{5}{32}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2(2)^4}-\frac{3}{4(2)^2} \\\frac{1}{32} - \frac{3}{16} = -\frac{5}{32}[/tex]
What is the measure of ZD in the parallelogram below?
Check the picture below.
What is one over four to the fifth power?
one over one thousand twenty-four
one over six hundred twenty-five
five over twenty
six over nine
Elaine roll 2 fair dice . What i the probability of both dice howing a prime number
The probability of both the dice showing prime numbers is 1/4.
Prime numbers:
The numbers which have only two factors, one and itself are known as prime numbers.
A dice has 6 faces numbering from 1 to 6.
Prime numbers from 1 to 6 are 2, 3, and 5.
Probability of one dice showing a prime number
= (number of favorable outcomes) / (total number of outcomes)
= 3/6
= 1/2
Probability of two dice showing a prime number = (1/2) x (1/2)
= 1/4
Therefore, the probability of both the dice showing a prime number is 1/4.
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aaliyah went into a grocery store and bought 5 peaches and 6 mangos, costing a total of $17.75. tristan went into the same grocery store and bought 2 peaches and 3 mangos, costing a total of $8. write a system of equations that could be used to determine the price of each peach and the price of each mango. define the variables that you use to write the system.
Answer:
Step-by-step explanation:
Define Variables:
Let p= the price of each peach
Let m=the price of each mango
One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangos cost 6m. The total cost 5p+6m equals $17.75:
5p+6m=17.75
Likewise, if 2 peaches and 3 mangos cost $8, then:
2p+3m=8
Write System of Equations:
5p+6m=17.75
2p+3m=8
System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.
Let p= the price of each peach
Let m=the price of each mango
One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangoes cost 6m. The total cost 5p+6m equals $17.75:
5p+6m=17.75
Likewise, if 2 peaches and 3 mangoes cost $8, then:
2p+3m=8
System of Equations:
5p+6m=17.75
2p+3m=8
Therefore System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.
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13) You have $80 and your sister has $160. You are saving
$7 per week and your sister is saving $5 per week. In
how many weeks you and your sister will have the same
amount of money? Write an equation and solve.
Answer: 30 weeks
Step-by-step explanation:
let w = number of weeks
you have = 60 + 7w
she has = 120 + 5w
60+7w = 120 + 5w
7w-5w = 120-60
2w = 60
w = 30 weeks
a pole that is 3m tall casts a shadow that is 1.4m long. at the same time, a nearby tower casts a shadow that is 39.5m long. how tall is the tower? round your answer to the nearest meter.
The nearby tower that casts a shadow that is 39.5 m long is 85 m tall.
Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.
The ratio of the shadow of a pole to its length is 1.4 m : 3 m.
At the same time, the ratio of the shadow of a tower to its length should also be equal to the ratio of the shadow of a pole to its length, which is 1.4 : 3.
Let x = length of the tower
Using proportion, determine the length of the tower by solving for x.
1.4 : 3 = 39.5 m : x
x = 39.5(3)/1.4
x = 84.64
Round off to the nearest meter.
length of the tower = 85 meters
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the average starting salary of graduates of a large university (lu) is $20,000 with a standard deviation of $8,000. furthermore, it is known that the starting salaries are normally distributed. if 189 of the graduates have salaries of at least $32,240, how many students graduated from this university?
Total students who graduated this year from this university is 3000.
This is a normal distribution problem with
Mean , μ = $20,000
Standard deviation, σ = $8,000
If 189 of the recent graduates have salaries of at least $32240.
Then, We first find the percentage of LU graduates with salaries more than $32240.
Required probability = P(x ≥ 32240)
We first normalize or standardize $32,240, then as we know,
z = (x - μ)/σ
= (32240 - 20000)/8000 = 1.53
The required probability:
P(x ≥ 32240) = P(z ≥ 1.53)
We'll use data from the normal probability table for these probabilities
P(x ≥ 32240) = P(z ≥ 1.53) = 1 - P(z < 1.53)
= 1 - 0.93699
= 0.06301
= 6.301%
So, 6.301% of the graduates this year = 189
Total Number of graduates this year = (189/0.06301) = 2999.5 = 3000 graduates this year.
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if the point D (8. -5) is reflected over the y axis, the coordinates of D would be
If the point D (8. -5) is reflected over the y-axis, the coordinates of D' would be: (-8, -5).
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to point D, the coordinates of the vertices of point D' include the following:
(x, y) → (-x, y)
Point D = (8, -5) → Point D' = (-8, -5)
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Henry drinks 1/2 of a bottle of soda. Sasha then drinks 1/3 of the soda that is left in the bottle. There is now 6 ounces of soda in the bottle. How many ounces of soda were there in the full bottle?
Answer: There were 18 oz. in the full bottle.
Step-by-step explanation:
If there are 6 oz. left, and Sasha drank 1/3 of half the bottle, then that means she drank 3 oz, since 6 is 2/3 of 9, which means that half of the bottle was 9 oz. 9 oz. is half of 18 oz, which means that there were 18 ounces in the full bottle.
In the function y = |x² - 4|, for
how many values of x does y = 3?
Answer:
4 answers
Step-by-step explanation:
y = |x² - 4|
3 = |x² - 4|
3 = x² - 4 and -3 = x² - 4
3+4=x² - 4 + 4 and -3+4=x² - 4 + 4
7=x² and 1=x²
x=[tex]\sqrt{7}[/tex] and x=-[tex]\sqrt{7}[/tex] since x²=7
x=-1 and x=1 since x²=1
x= -[tex]\sqrt{7}[/tex], [tex]\sqrt{7}[/tex], -1, 1 ==> 4 answers
Finding Angle Measures When Parallel Lines Are Cut By a Transversal
which of the following is not true of a chi squared test?(a) a chi-squared test can be used if one of the sample cells has a value of less than five
(b) the Chi-square test can be used to test how likely it is that an observed distribution is due to chance.
(c) a chi-square test can be used to analyze nominal data
(d) a chi-squared test can be used to test the probability of independence of a distribution of data
A) Chi-square test can be used if one of the samples has a value of less than five is the correct option.
Chi-square distribution and Chi-square test for independence:
A Chi-square distribution is the sum of squares of the standard normal deviates. The Chi-square test can be used for checking the association between categorical variables.The test can be used to decide whether the effect of one categorical data is dependent on the other variable or not on the basis of the critical value and p-value. The expected frequency of each categorical variable is calculated to compute the test statistic.The assumptions for the chi-square test are:
The frequency of each cell should be at least or more than 5.The variables should be categorical in nature and the observations should be independent of each other.Chi-square test can be used to analyze the nominal or categorical data. It can be used to test whether the observed data fits well with the expected frequency or not. It is used to test the independence of the data distribution by calculating probability.Hence, options (b), (c), and (d) are the assumptions that are true for chi-square test. Therefore, the options (b), (c), and (d) are considered incorrect.
The Chi-square test of independence can be used only if none of the frequencies of the sample cell is less than five.Hence, option (a), that is, “a Chi-square test can be used if one of the samples has a value of less than five” is the correct option.
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Every complex number can be written in the form a+bi. For the complex numbers 8-4i, identify the values of a and b
Answer:
C
Step-by-step explanation:
Mrs. Singh is making snack packs for her class to eat on their field trip. She estimates that she will need 35 snack packs. The day of the field trip 4 students are absent and Mrs. Singh actually only needs 31 snack packs. What is Mrs. Singh's percent error?
Singh percent error is approximately 13%.
What is percent error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.
Mrs. Singh is making snack packs for her class to eat on their field trip. She estimates that she will need 35 snack packs. The day of the field trip 4 students are absent and Mrs. Singh actually only needs 31 snack packs.
Therefore, Singh's percent error can be calculated as follows:
percent error = 35 - 31 / 31 × 100
percent error = 4 / 31 ×100
percent error = 400 / 31
percent error = 12.9032258065
percent error ≈ 13%
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Please help me!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
-24
Step-by-step explanation:
-3[-4(3-10)-12]/-2(-1)
-3[-4(-7)-12]/2
-3[28-12]/2
-3[16]/2
-48/2
-24
Hopes this helps
On a straight road, Jorge is 7 kilometers east of Peter, Jason is
10 kilometers west of Juan, and Juan is 13 east of Peter. how
many miles is Jorge from Jason?
Answer:
7x10x13=910=910 kilograms
Step-by-step explanation:
If f (x) = 2x2 + 4x − 3, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
The difference quotient for the given quadratic equation is:
d = (2h + 4x + 4)
How to get the difference quotient for f(x)?Here we have the quadratic function:
f(x)= 2x² + 4x - 3
And we want to get the difference quotient that is defined as:
d = ( f(x + h) - f(x))/(h)
Replacing our function there, we get:
d = ( 2(x + h)² + 4*(x + h) - 3 - (2x² + 4x - 3)/h
d = (2x² + 2h² + 4xh + 4x + 4h - 3 - 2x² - 4x + 3)/h
d = (2h² + 4xh + 4h)/h
d = (2h + 4x + 4)
That is the difference quotient.
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What is the value of (−13)4?
52
−52
28,561
−28,561
Solve each equation.
9^(x+2)=2^(5x-4)
Value of x is 1.411
Given Eq.
[tex]9^{x+2} = 2^{5x-4} \\\\[/tex]
Applying exponent rules
[tex](x+2)ln(9) = (5x-4)ln(2)\\[/tex]
Solving for x
[tex]x = \frac{4ln(6)}{5ln(2)-2ln(3)}[/tex]
[tex]x = \frac{1.791}{5(0.693)-2(1.098)}[/tex]
[tex]x = \frac{1.791}{3.465-2.196} \\[/tex]
[tex]x = \frac{1.791}{1.269}[/tex]
[tex]x = 1.411[/tex]
Value of x is 1.411
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