Answer:
Hose A fills at a rate of 10 gal per min
Hose B fills at a rate of 8 gal per min
Hose B fills at a faster rate
Step-by-step explanation:
Answer:
Hose A=10 gal per min
Hose B=8 gal per min
Hose A is faster
Step-by-step explanation:
A) 160 gallon/16 minutes=10 gallons per minute
B) 240 gallon/30 minutes=8 gallons per minute
ordenada al origen 6 = paralela a la recta 2x+3y+4=0
La ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
¿Cómo determinar la ecuación de una recta?
En esta pregunta tenemos que derivar una ecuación de la recta a partir de una recta y un punto. Dos rectas bajo forma implícita son paralelas si y solo si comparten los mismos coeficientes dependientes, entonces tenemos que el coeficiente independiente de la recta es:
2 · 0 + 3 · 6 + k = 0
18 + k = 0
k = - 18
Por tanto, la ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
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Billy is hiking in Colorado. He walks eastward four miles, then turns $60$ degrees northward and walks six miles. How far is he from his starting point
He is 2√19 miles far way from starting point.
Suppose Billy starts at point A, turns at point B, and ends at point D, as shown below.
If Billy turns 60◦ northward and walks six miles, then we can draw a 30 − 60 − 90 triangle whose hypotenuse is 6 miles
It follows that Billy traveled 6/2 = 3 miles eastward during these 6 miles, and that he traveled 3√3 miles northward during these 6 miles. In total, Billy traveled 4 + 3 = 7 miles eastward and 3√ 3 miles northward.
By the Pythagorean Theorem, the distance from his starting point is q:
(7)2 + (3√3)2
=√49 + 27
= √76
= 2√19 .
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As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when _____
As a rule of thumb, when each component is selected independently from the same population, the sampling distribution of the sample percentage may be estimated by a regular probability distribution.
Why is it crucial to use the thumb rule?One of our primary, simple-to-learn ways to handle complexity is the rule of thumb. Real thumb rules take into account operating, security, and financial constraints. They inform us of the likely location of a practical solution. Additionally, they reveal which tactics are most prone to failure.What is sampling distribution?A statistic that is obtained by sampled data from a bigger population is known as a sampling distribution. It depicts an array of potential results that may result from a statistic, such as the mean or mode of a certain parameter because there is really a population.Therefore the main solution is- from the identical group, each component is individually chosen.
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prove that 3+2√5 is irrational
Step-by-step explanation:
To prove that 3 + 2√5 is an irrational number, we will use the contradiction method.
Let us assume that 3 + 2√5 is a rational number with p and q as co-prime integers and q ≠ 0
⇒ 3 + 2√5 = p/ q
⇒ 2√5 = p/ q - 3
⇒ √5 = (p - 3q ) / 2q
⇒ (p - 3q ) / 2 q is a rational number.
However, √5 is an irrational number
This leads to a contradiction that 3 + 2√5 is a rational number.
Find the smallest number by which 1008 must be multiplied to get a perfect square. also, find the square root of the perfect square so obtained
Answer:
7
Step-by-step explanation:
we have 1008=2×2××2×3×3×3
The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.
Now 1008×7=2×2×2×2×3×3×7×7
7056=2×2×3×7
=84
Answer : 7
Answer:
1. 7
2. square root is 84.
Step-by-step explanation:
First find the prime factors:
1008 =2*2*2*2*3*3*7
There's an even number of 2's and 3's but only one 7, so we multiply by 7
Smallest number = 7.
The square number is 1008 * 7
= 7056.
Its square root is 2*2*3*7 = 84.
What equation shows that 9 is a factor of 72?
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
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Solution
We can start with the pythagorean theorem:
(leg 1)2 + (leg 2)² = (hypotenuse)²
Solve for x.
Substitute the values we know.
18² + x² = 27²
x=0√O
Step-by-step explanation:
324+x²=729
x²=405===> x=√405===> 9√5
The pythagorean theorem (leg 1)2 + (leg 2)² = (hypotenuse)² the values is about 8.5, -8.5.
The Pythagorean theorem is used to find the length of the sides of a right triangle, not for solving equations like x² = 72.
To solve the equation x² = 72, to take the square root of both sides to find the value of x:
√(x²) = √(72)
Since the square root of x² is x (the absolute value of x), the equation simplifies to:
x = √(72)
Now, let's find the approximate value of √(72):
√(72) ≈ 8.49
So, the equation becomes:
x≈ 8.49
Now, remember that the absolute value of x is a positive value, so the equation gives two possible solutions for x:
x= 8.49 → x = 8.49
x = -8.49 → x = -8.49
Rounded to the nearest tenth, the solutions are:
x ≈ 8.5 and x ≈ -8.5
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Which polynomial is a quintic trinomial?
A. -x^4-5x^2
B. x^3+2x^2−8x+16
C. x² + 4
D. 3x^5+7x^2−9x^4
Answer:
D
Step-by-step explanation:
a quintic polynomial is a polynomial of degree 5
A is a polynomial of degree 4 (- [tex]x^{4}[/tex] term )
B is a polynomial of degree 3 (x³ term )
C is a polynomial of degree 2 ( x² term )
D is a polynomial of degree 5 ( 3[tex]x^{5}[/tex] term )
If the value of the sample standard deviation increases, what happens to the confidence interval?
If the value of the sample standard deviation increases, the confidence interval becomes wider and is denoted as option A.
What is Confidence interval?This term is used in statistics and refers to the probability that a population parameter will fall between two set values.
it has a direct relationship with standard deviation in which its increase will also lead to the set of values being wider thereby making it the most appropriate choice.
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The options are :
a. It becomes wider
b. It becomes more precise
c. It does not change
d. It narrows
help please a.-5 b.-1/5 c1/5 d.5
Answer:
-5
Step-by-step explanation:
Slope is rise over run. The graph decreases by 5 units every 1 unit to the right, so the slope is -5.
A hypothesis test is conducted at the 0.05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, what conclusion should be drawn
3.60
t = r√n − 2/1 − √r2
= 0.6√25 − 2/√1 − 0.62
= 3.5969 t or about 3.60 rounded to two decimal places.
Hypothesis Testing:
Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H0.
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What is the minimum point on the graph of the equation y=f(x)+5 ?
Answer:
Step-by-step explanation:
This function will have a minimum point only if f(x) has one.
Examples:
y = x + 5: straight line with no minimum
y = x^2 + 5: parabola that opens up and has vertex at (0, 5); thus, the minimum is (0, 5)
What f(x) did you have in mind? Please share it.
A rectangle's area is given by the expression 6–² -- − n +9. The width of the rectangle is 3n². w = 3n² A = 6n² − n +9
The length of the rectangle = 2 - (1/3n) +(3/n²).
How to estimate the length of a rectangle?
The formula for the area (taking this exists as a rectangle)
Area = length ⋅ width
where A exists the area of the rectangle
l exists the length of the rectangle and w exists the width of the rectangle.
If Area of the rectangle = length ⋅ width
then length of the rectangle = area/ width
Area = 6n² − n +9
width = 3n²
Area = length [tex]*[/tex] width
length = area/ width
= (6n² − n +9)/3n²
= 2 - (1/3n) +(3/n²).
The length of the rectangle = 2 - (1/3n) +(3/n²).
Therefore, the correct answer is option A. 2 - (1/3n) +(3/n²).
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The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y = startfraction 3 x 10 superscript 8 baseline over x endfraction what is the wavelength for radio waves with frequency 3 × 109?
The wavelength for radio waves with frequency 3 × 10⁹ Hz is 0.1 m.
What's the relation between frequency and wavelength of electromagnetic waves?For electromagnetic waves travelling in vaccum, the product of frequency and wavelength is the speed of light in vaccum.Mathematically, frequency × wavelength = 3×10⁸ m/s (which is speed of light)So, wavelength= 3×10⁸/ frequencyWhat's the wavelength of radio wave with frequency 3×10⁹ Hz ?Wavelength of the radio wave= 3×10⁸/3×10⁹ = 0.1 m
Thus, we can conclude that the wavelength of the radio wave with frequency of 3 × 10⁹ Hz is 0.1 m.
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What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%?
a. z = 0.52
b. z = 0.84
c. z = -0.84
d. z = -0.52
Using the normal distribution, the value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is:
z = -0.52.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is is the 30th percentile, which is Z with a p-value of -0.3, hence z = -0.52.
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How many different 4 digit numbers can be formed using only digits 1,2,3 and 4 given that they contain each of these digits as many times as you want?
Answer: 4
Step-by-step explanation:
yeh
y square plus 5y equals to 0
Answer:
y^2 + 5y = 0
y(y + 5) = 0
y = 0, -5
The answer is y = 0 and y = -5.
The given question :
y² + 5y = 0y (y + 5) = 0y = 0, y = -5Find the midpoint of points A(-9, -3) and B(1, 7) graphically.
Plot the line segment AB
Answer: (-4,2)
Step-by-step explanation:
To find the midpoint of AB, we have to find the mean of the x coordinates for the x coordinate of the midpoint and the mean of the y coordinates for the y coordinate of the midpoint
So the midpoint is ((-9+1)/2,(-3+7)/2) = (-4,2)
To plot the line AB, just find the points A and B on the graph and draw a straight line from A to B
Help me:-
Distribute to create an equivalent expression with the fewest symbols possible.
4(5+y) =
Answer:
20 + 4y
Step-by-step explanation:
The 4 multiplies the 5 and the y, i.e., it distributes over the terms of the expression in ( ).
Determine the value of x and y, show calculations
The value for x and y are 140° and 70° respectively.
How to solve Polygon QuestionThere are two ways to solve polygon question. Formula for the sum of interior angle and sum of the exterior angle of regular polygon.
Sum of the interior = (n - 2)180
Sum of the exterior = 360/n
Where n = number of sides of a polygon.
The regular polygon in which x is one of its angle is called decagon
Sum of the interior = (n - 2)180
n = 10
Substitute n into the formula
Sum of the interior angle = (10 - 2)180
Sum of the interior angle = (8)180
Sum of the interior angle = 1440
Each angle = 1400/10
x = 140°
For y, the three angles are similar.
sum of angle in a triangle = 180
Since the each triangle is an isoceles triangle, angle at each base will be y
40 + y + y = 180
2y = 180 - 40
2y = 140
y = 70°
Therefore, the value for x and y are 140° and 70° respectively.
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The diameter of the earth
at the equator is about
8.000 mi.
Based on this figure, how
far is it around the earth?
Answer:
25,132.74 miles
Step-by-step explanation:
Hello!
We are basically asked to find the circumference of the Earth's cross-section.
Circumference: [tex]C = 2\pi r[/tex]
We can replace 2r with the diameter, because the diameter is 2 times the radius.
Multiply the Diameter by pi:
[tex]C = \pi D[/tex][tex]C = 8000\pi[/tex][tex]C = 25,132.7412287183 \approx 25,132.74[/tex]It is around 25,132.74 miles around.
In a survey of 456 residents, 279 were opposed to the use of the photo-cop for issuing traffic tickets. What is the best point estimate for the proportion () of all residents opposed to the photo-cop use
The best point estimate for the proportion of all the residents opposed to the photo cop use is 60% which is the fourth option.
Given that in a survey of 456 residents , 279 were opposed to the use of the photo cop for issuing traffic tickets.
We have to find the best point estimate for the proportion of all residents opposed to the photo cop use.
Total residents=456
Residents who opposed to the use of the photo cop for issuing traffic tickets=279
Proportion=number of residents who opposed/ total residents
=279/456
=0.611
=61.1%
The nearest option is fourth which is 60%.
Hence the best point estimate for the proportion for the proportion of all the residents opposed to the photo cop use is 60% which is option 4.
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Question is incomplete as it should include options which are :
1) 500
2)50%
3)300
4)60%
5)40%
Lola has collected 935 buttons. what is the number of buttons rounded to the nearest ten?
Answer:
940
Step-by-step explanation:
Since there is a 5 in the ones spot we round the number is the tens spot up by 1: 935 --> 940
if three pies require 2 dozen apples, then four bird require ? dozen apples?
The graphs below have the same shape. What is the equation of the red
graph?
Answer:
[tex]G(x) = x^{3} -1[/tex]
Step-by-step explanation:
The red graph is the blue graph translated 1 unit down, so the answer is A.
Write the standard equation of a circle that passes through(-4,0) with center (-1,-4)
The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).
According to the question,
The circle with center at (-1,-4) that passes through the point (-4,0).
To find the radius of the circle:
Radius r = √[(-4 - (-1))² + (0- (-4))²]
=√(-4+1)² + (4)²
=√9+16
=√25
=5.
In order to find the standard equation of the circle is
(x - (-4))² + (y - (0))² = (5)²
(x + 4)² + (y )² = 25
x² + 8x + 16 + y² = 25
x² + y² + 8x + 16 = 25
x² + y² + 8x = 25 - 16
x² + y² + 8x = 9
x² + y² + 8x - 9 = 0
Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.
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what is the domain of f(x)=√11-x?
The domain of the function f(x) is:
11 ≥ x
What is the domain of the function f(x)?
Here we have the function:
[tex]f(x) = \sqrt{11 - x}[/tex]
Now, remember that the argument of a square root can only be a number equal to or larger than zero, so the domain of our function is defined by:
11 - x ≥ 0
Then, solving this for x, we get:
11 ≥ x
Concluding, the domain of the function f(x) is:
11 ≥ x
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Find the present value of a loan with a maturity value of $15,000 for 9 months at 6%.
Present value of the loan amount is $[tex]27[/tex] with a maturity value of $[tex]15000[/tex] for [tex]9[/tex] months at [tex]6[/tex]%
How to find the present value of loan amount ?
We know that
Maturity value of loan amount [tex]= 15000[/tex]
Time period is [tex]=9[/tex] months
Rate (r)[tex]=6[/tex] %
Present value of loan amount=?
So we can use the formula of maturity level
[tex]MV=PV*(1+r*t)[/tex]
Substitute the values
[tex]15000=PV *(1+6*9)\\15000=PV(55)\\\frac{15000}{55} =PV\\27.27=PV[/tex]
So present value of the loan amount is $[tex]27[/tex] in round figure.
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Consider the polynomial function of g(x)= -2x^8 +5x^6 -3x^5+50
Answer:
C) as x –> ∞, q(x) –> –∞, and as x –> -∞, q(x) –> –∞
Step-by-step explanation:
use the end behavior chart to figure out the end directions of the graph. remember these
E O
+|↑↑|↓↑
–|↓↓|↑↓
all you need to do is look at the first number of the equation and ask yourself:
1. Is the first number even or odd?
2. is the first number positive or negative?
find where the answers to both meet on the chart.
so, in this question, the first number is even and negative. when using the chart we see that they meet at the ↓↓ which means that the end behavior on both sides is going towards negative infinity.
Two ways to measure the relationship between the returns of two securities are ______ and blank______.
a. standard deviation
b. variance
c. covariance
d. correlation
Two ways to measure the relationship between the returns of two securities are correlation and covariance. That is options C and D.
What is Correlation?Correlation can be defined as the measure of the difference between two variables in a statistical analysis.
Covariance can be defined as the measure of the relationship between two variables in statistical analysis.
Therefore, Two ways to measure the relationship between the returns of two securities are correlation and covariance.
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