Answer:
Step-by-step explanation:
volume of a sphere = ⁴/3 π r³. r = D/2. V = 4/3 × π × (D/2)³. V = 4/3 × π × D³/8. V = ⅓ × π × D³/2. V = ⅓× π × (24mm)³/2.
Solve this equation:
11x^2=-8
Answer:
See below
Step-by-step explanation:
11x^2 = - 8
x^2 = - 8/11
x = + - i sqrt (8/11) or - .727 i or .727 i
One gallon of paint usually covers about 350 square feet. How many square feet will 2.5 gallons cover? Show your work, including labeling your answer with the appropriate units of measure.
someone please help!!!
Answer:
875 square feet.
Step-by-step explanation:
Multiply 350 square feet by 2.5 gallons.
consider the matrix
what is the value of |C|
If the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12
The given matrix is
C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]
The matrix is defined as the set of numbers that arranged in rows and columns to form a rectangular array. The numbers in the matrix are called the elements of the matrix.
Here we have to find the determinant of the matrix C
The determinant of the matrix is defined as the scalar value calculated for a given square matrix.
The determinant of C is represented by |C|
Then,
C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]
|C| = -6×4 - 6×-2
= -24 -(-12)
= -24 + 12
= -12
Hence, if the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12
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When parallel lines are cut by a transversal, then
Answer:
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
Find the slope of a line crossing through the following points: (4, -3) and (10,-7). (Answer in a simplified fraction if necessary... Example: 4/5)
A jewel case contains 7 white gems, 5 green gems, and 3 blue gems. Gems are selected at random. Explain why
the events picking a green gem and then another green gem without replacement are dependent. Then, identify
the probability.
A.) P(green) is the same when it is known that a green gem has been picked already.
P(green and green) = 4/45
B.) Pgreen) is different when it is known that a green gem has been picked already.
P(green and green) = 2/21
C.) P(green) is different when it is known that a green gem has been picked already.
P(green and green) = 5/42
D.) Pgreen) is the same when it is known that a green gem has been picked already.
P(green and green) = 1/9
The second probability is affected by the first probability. So, we can say that this is a dependent probability.
Probability of choosing the first gem green = 1/3Probability of choosing the second gem green = 2/7Given,
Number of white gems = 7
Number of green gems = 5
Number of blue gems = 3
Total number of gems = 7 + 5 + 3 = 15
We have to find the probability when picking a green gem and then another green with out replacement are dependent.
Here,
Probability of choosing the first gem green = Number of green gems / total number of gems
Probability = 5/15 = 1/3
Now,
Number of green gems = 4
Total number of gems = 14
Probability of choosing the second gem green = Number of green gems / Total number of gems
Probability = 4/14 = 2/7
Here,
The second probability is affected by the first probability. So, we can say that this is a dependent probability.
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represent the following expressions as a power of the number a (a≠0) (a^-1xa^-2)^-3
The solution of the exponential expression will be a⁹.
What is an exponential expression?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied.
Given exponential expression is (a⁻¹ x a⁻²)⁻³. The expression will be solved as below,
E = (a⁻¹ x a⁻²)⁻³
The base is the same and the variables are in multiplication with powers then the powers will be added,
E = (a⁻³)⁻³
E = a⁹
Therefore, the solution of the exponential expression will be a⁹.
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The area of a rectangle is 3/5 square meter. The width is 2/5 meter. a. What is the length of the rectangle? Write your answer as a fraction in simplest form. The length of the rectangle is _ meters. b. How many times greater is the length than the width? Write your answer in simplest form. The length is _ times greater than the width.
Answer:
a. 3/2 meters
b. 15/4 times as great
Step-by-step explanation:
You want the width of a rectangle that is 3/5 m² in area and 2/5 m long. You also want to know the factor by which the length is greater than the width.
a. WidthThe formula for the area of a rectangle is ...
A = LW
Filling in the known values, we can solve for the length:
3/5 m² = (2/5 m)·L
L = (3/5)/(2/5) m = 3/2 m . . . . . . divide by the coefficient of L
The length of the rectangle is 3/2 meters.
b. Aspect ratioThe ratio of length to width is ...
length/width = (3/2 m)/(2/5 m) = (15/10)/(4/10) = 15/4
The length is 15/4 times greater than the width.
Please help!!
Solve this system of equations by graphing. First graph the equations, and then type the solution.
x+2y=2
y=–x+4
(you'll need to graph this).
By graphing, the solution of the system of equations is: (6, -2).
How to Solve a System of Equations by Graphing?To solve the system of equations by graphing, plot each of the line of the equations, then find the coordinates of the point where both lines intersect. Where they intersect is the solution to the systems of equations.
Given the following equations:
x + 2y = 2
y = -x + 4
x + 2y = 2 can be rewritten as y = -1/2x + 1. The graph for x + 2y = 2 will intercept the y-axis at 1 and also has a slope of -1/2. (It is the red line in the image below).
The graph of y = -x + 4 will also have a slope of -1 and intercept the y-axis at 4. (It is the blue line in the image below).
The graph of the equations are shown below, and they intersect at (6, -2), which is the solution to the system of equations.
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8. If a population doubles every 5 years, how many years will it take for the population to increase by 10 times
its original amount?
First: If the population gets multiplied by 2 every 5 years, what does it get multiplied by each year? Use this
to help you answer the question.
After ≈16.61 years the population will increased by times it's original amount.
What do you mean by population?
A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.
Given: If a population doubles every 5 years.
Assume, 'A' is the starting population, and 't' is the passing time in years.
Given the fact that a population doubles every five years, our population is growing exponentially, as per the question.
Here, the equation can be written as follows: [tex]A(t) = A(2)^{\frac{t}{5} }[/tex] (1)
We now need to determine when the population will have multiplied by 10 by that time.
Let's substitute [tex]A(t) = 10A[/tex] in the above equation.
[tex]10A = A(2)^{\frac{t}{5} }[/tex]
[tex]10 = (2)^{\frac{t}{5} }[/tex]
Taking the natural log of both sides we get:
[tex]ln10 = \frac{t}{5} \times ln2[/tex] {[tex]ln(a)^n= nln(a)[/tex]}
2.3025 x 5 = t x 0.6931
[tex]t = \frac{2.3025}{0.6931}\\t = 16.6096[/tex]
Therefore, After ≈16.61 years the population will increased by times it's original amount.
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A-B =2
A+2= B
What is A and B
The given system of equations has no solution.
The given system of equations are A-B =2 and A+2= B.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Here,
A-B =2 --------(I) and A+2= B --------(II)
From equation (II) substitute B=A+2 in the equation (I), we get
A-(A+2)=2
⇒ A-A-2=2
⇒ 0-2=2
Hence, the given system of equations has no solution.
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PLEASE FIND X ALGEBRA 1
Answer:
x = 135
Step-by-step explanation:
You need to find the supplementary angle of x.
Find the angle to the left of 100°. Recognize that the vertical angle theorem can be used. It equals 35°Now, you can use the triangle sum theorem to find the needed supplementary angle. 100+35+z=180, where z is the supplementary angle. z = 45.To find x, use the supplementary angle theorem. (The angles "lie" on a straight line, so they add up to 180°, or a straight line.)
45+x = 180
x = 135
Can yall help me on this?
x-intercept is (-250, 0) and y-intercept is (0, 100)
What is x-intercept and y-intercept
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.
First, find x-intercept
For x-intercept it means y = 0
observe the graph and see the blue line cuts the x-axis when y = 0
We see, x = -250
so, the x-intercept is = (-250, 0)
Now, same thing do to find y-intercept
For y-intercept it means x = 0
observe the graph and see the blue line cuts the y-axis when x = 0
We see, y = 100
so, the y-intercept is = (0, 100)
Therefore, x-intercept is (-250, 0) and y-intercept is (0, 100).
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Factorise
(a) 4ab + 6abc + 8ac
(b) 9x2y + 6xy - 15xy²
(c) 10ab²-8ab + 2a²b
(d) 6xy - 7x²y + 3xy²
The length of the base of a triangle with
constant area varies inversely as the height.
When the base is 18 cm long, the height is 7
cm. Find the length of the base when the
height is 6 cm.
The length of the base when the height is 6 cm is 21 cm .
In the question ,
it is given that ,
the length of the base(b) of the triangle varies inversely with the height(h) ,
which is represented as
b ∝ 1/h
b = k/h
where k is the constant of variation
given that when b = 18 , h is = 7
18 = k/7
k = 18 × 7
k = 126
Substituting , the value of k = 126 in the equation b = k/h ,
we get ,
b = 126/h
So, the length of the Base When h = 6,
b = 126/6
b = 21
Therefore, the length of the base when the height is 6 cm is 21 cm .
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Which comic section is formed in the image
Answer:hyper bola
Step-by-step explanation:
All you have to do is look up all the answers on images and then pick the one that looks the most similar
[tex]\left \{ {{y=x^2+x-1} \atop {y + 2 x = 3}} \right.[/tex]
Solve the following system of equations algebraically or by graphing, and give the answer as points. Which method did you pick and why?
How could you check your answer afterwards?
Solving the system of equations using the algebraic method gives x = 1 or x = -4
How to solve the system of equations algebraically?Given: y = x²+x-1 and y+2x=3
In order to solve the system of equations algebraically
First, rewrite y+2x=3 to make y the subject:
y = 3-2x
Then, equate the two y of the equations and solve for x:
x²+x-1 = 3-2x
x²+x-1-3+2x = 0
x²+3x-4 = 0 (factorize)
x²+4x-1x-4 = 0
(x-1)(x+4) = 0
x-1 = 0 or x+4 = 0
x = 1 or x = -4
Therefore, the solution of the system of equations is x = 1 or x = -4
I pick the algebraic method because it is easier, faster and more accurate
I can check my answer by substituting the values of x into the equation
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Answer:
(-4, 11) and (1, 1)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=x^2+x-1\\y+2x=3\end{cases}[/tex]
The solutions to the given system of equations are the points of intersection of the two graphs.
To solve the given system of equations algebraically, first rearrange the second equation to make y the subject:
[tex]\implies y=3-2x[/tex]
Substitute the found expression for y into the first equation:
[tex]3-2x=x^2+x-1[/tex]
Rearrange to a quadratic equation and factor:
[tex]x^2+3x-4=0[/tex]
[tex]x^2+4x-x-4=0[/tex]
[tex]x(x+4)-1(x+4)=0[/tex]
[tex](x+4)(x-1)=0[/tex]
Apply the zero-product property to solve for x:
[tex](x+4)=0\implies x=-4[/tex]
[tex](x-1)=0\implies x=1[/tex]
To find the y-values of the solutions, substitute the found x-values into the rearranged second equation:
[tex]x=-4 \implies y=3-2(-4)=11[/tex]
[tex]x=1\implies y=3-2(1)=1[/tex]
Therefore, the solutions to the given system of equations are:
(-4, 11) and (1, 1)Estimate the measure of
Answer: 110°
Step-by-step explanation:
Looks like a bit more than 100°.
Ben bowled 151 and 183 in his first two games. What must he bowl in his third game to have an average of at least 1702
Answer:
1368
Step-by-step explanation:
let 3rd game be x
151+183+x=1702
334+x=1702
x=1702-334
x=1368
FInd the value of x in each case.
pls help i will give 100 points
Answer:
x=10
Step-by-step explanation:
4x+5x+angle g should equal 180 degrees total.
with this in mind, we can subtract angle g from 180, as it is know,. (180-90)
so 4x+5x=90. 9x=90, x=10.
hope this helps.
Check the picture below.
help again for a friend
The required equation of slope is y = x/2 + 6
Given : y = 3x + 6
this is of the form y = mx + c
thus on comparing we get
the slope or m = 3
And the y intercept = 0, 6
It is also given that we have to find the equation of the slope which passes through the point ( -2, 5 )
thus the two points are:
( -2, 5 ) and ( 0,6 )
Thus the slope or m = y2 - y1/ x2 - x1
=> m = 6 - 5 / - ( -2 )
m = 1/ 2
Thus the equation of the slope is
y - y₁ = m ( x - x₁ )
₁Substituting the value of m from above we get
y - 5 = 1/2 ( x + 2 )
this implies 2y - 10 = x + 2
x - 2y = - 12
or we can also write this as
y = x/2 + 6
Refer to the graph given below for further understanding.
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a grocery store has an average sales of $7,100 per day. the store introduced several advertising campaigns in order to increase sales. to determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 100 days of sales was selected. it was found that the average was $7,275 per day. from past information, it is known that the standard deviation of the population is $1,500. we know that the test statistic is 1.1667. find the p-value.
The P value of the question in the given condition is less than 0.05 hence it reject the null hypothesis.
What is null hypothesis?According to the null hypothesis, an independent variable and a dependent variable have no association with one another. The results might be the result of an experimental or sampling error if the hypothesis indicates a link between the two factors. There is a relationship in the measured phenomena, but, if the null hypothesis is incorrect.
First we find the value of small z
z = (x - μ) / (α / [tex]\sqrt{100}[/tex])
z = (7275 - 7100) / (1500/[tex]\sqrt{100}[/tex])
z = (175) / 150
z = 1.1667
As we have verified the test statistic value and it matched.
Then,
P value approach
Hence P value must be equal to 0.0013
As p value is less than 0.05 , Reject the null hypothesis.
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Divide.
8 3/4÷(−3 1/2)
Enter your answer as a mixed number, in simplified form, in the box.
Factor completely, than place the factors in the proper location on the grid
Y^2x -y^x-20
Answer: Cannot be factored
Step-by-step explanation:
= Factor Y^2x -y^x-20
= Cannot be factored
Factor x^2-x-72 Please
Answer:
(x+8)(x-9)
Step-by-step explanation:
1. Use the sum-product pattern
x²-x-72
x²+8x-9x-72
2. Find the common factor from the 2 pairs
x²+8x-9x-72
x(x+8)-9(x+8)
3. Rewrite in factored form
x(x+8)-9(x+8)
(x-9)(x+8)
Solution to problem: (x-9)(x+8)
What is the domain of y equals two divided by the quantity x minus three squared all minus one ?
All real numbers less than 3
All real numbers except 3
All real numbers greater than 1
All real numbers greater than 3
All real numbers
The domain of y equals two divided by the quantity x minus three squared all minus one [y = (2)/(x - 3)² - 1] is: all real numbers.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values which are located on the x-coordinate.
Translating the word problem into an algebraic equation, we have;
y = (2)/(x - 3)² - 1
When x = 3, we have:
y = (2)/(3 - 3)² - 1
y = 2/-1 = -2
When x = 1, we have:
y = (2)/(1 - 3)² - 1
y = 2/3
In conclusion, the domain of this function is all real numbers.
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Find the measurement of V.
Answer:
60°
Step-by-step explanation:
As we can conclude from the equal measured side lengths, this is an equilateral triangle so all angles have equal measurement.
Since the sum of interior angles in a triangle is equal to 180 to find the measure of angle V we need to divide 180 by 3:
180 ÷ 3 = 60
the average monthly rent for one-bedroom apartments in a particular city has been $770. because of a downturn in the real estate market, it is believed that there has been a decrease in the average rental. which is the correct hypotheses to be tested?
The set of values for Rents lesser than $700. So, rent 700 <y<0
Hypothesis.Though there is not so much information, but the fact that $700 is an average. We can work with two hypothesis at first, he first Hypothesis before the downturn the rent are over $700. And the second one, the bedroom rent are under $700.1) Graphically, the shaded area before the downturn, represents the set of values for Rents greater than $700. So, rent (y) > 7002) Graphically, the shaded area after the downturn, represents the set of values for Rents lesser than $700. So, rent 700 <y<0A hypothesis is an educated prediction regarding the solution to a scientific question that is supported by sound reasoning. It is the expected result of the experiment, however it is not proof in an experiment. Depending on the information received, it might be supported or might not be supported at all.learn more about hypothesis click here:
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Find the values of x and y that satisfy the equation.
22 + 1/5yi = 2x - 2
Answer:
[tex]x=12, y=0[/tex]
Step-by-step explanation:
[tex]22+\frac{1}{5}yi=2x-2 \\ \\ (24-2x)+\frac{1}{5}yi[/tex]=0[/tex]
Setting the real and imaginary parts of the left hand side equal to 0,
[tex]24-2x=0 \implies x=12 \\ \\ \frac{1}{5}y=0 \implies y=0[/tex]
A researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. Her data is expressed in the scatter plot and line of best fit below. What does the slope of the line represent?
Temperature (Degrees Fahrenheit)
Chirps Per Minute
How long the cricket continues to chirp.
The expected change in number of cricket chirps in one minute for each additional degree Fahrenheit.
The expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.
The expected temperature when the cricket chirps 1 time.
The slope of the line of best fit represents: the expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.
What is a line of best fit?A line of best fit simply refers to a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between data points.
What is a slope?A slope is also referred to as the rate of change and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or data points.
In this scenario, the slope for the given data is the change in temperature with respect to a unit change in the number of chirps sold.
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