We can find the volume of a cone using the formula
[tex]V=\frac{\pi r^2h}{3}[/tex]Where
h = height
r = radius
Remember that
[tex]d=2r\Rightarrow r=\frac{d}{2}[/tex]Therefore, let's find out the radius first, the problem says that the diameter is 6cm, then
[tex]r=\frac{6}{2}=3\text{ cm}[/tex]The radius is 3cm and the height is 10cm, let's use it in our formula:
[tex]\begin{gathered} V=\frac{\pi\cdot(3)^2\cdot10}{3} \\ \\ V=30\pi \end{gathered}[/tex]The problem also say to use = 3.14, then the volume is
[tex]\begin{gathered} V=30\cdot3.14 \\ V=94.2 \end{gathered}[/tex]Therefore, the volume is
[tex]V=94.2\text{ cm}^3[/tex]
what is 1 5/8 + 2 1/3=
1 5/8 + 2 1/3
= 3 23/24
Explanation:1 5/8 + 2 1/3
= 1 + 2 + 5/8 + 1/3
= 3 + 23/24
= 3 23/24
? QuestionWhat is the equation of the quadratic function represented by this table?х5678910f(x)-4585-4-19HolaType the correct answer in each box. Use numerals instead of words.f(x) =(x -12 +
To determine the equation of the quadratic equation, which is a parabola, we substitute the coordinates of the vertex of the parabola (h,k) into the general equation.
[tex]y=a(x-h)^2+k[/tex]From the given, notice that the only value of f(x) that does not repeat is 8. This means that the vertex is at (7,8).
[tex](h,k)=(7,8)[/tex]Thus, we only need to obtain the value of a.
Substitute the coordinate of a point (x,y) into the equation and the vertex as well. In this case, let us use the first given point, (5,-4).
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ (5,-4)\rightarrow-4=a(5-7)^2+8 \end{gathered}[/tex]Simplify the obtained equation.
[tex]\begin{gathered} (5,-4) \\ -4=a\mleft(5-7\mright)^2+8 \\ -4=a\mleft(-2\mright)^2+8 \\ -4=a(4)+8 \\ -4-8=4a \\ -12=4a \\ a=\frac{-12}{4} \\ a=-3 \end{gathered}[/tex]Now that we have the value of a, substitute the coordinates of the obtained vertex and the value of a into the equation of the quadratic equation.
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=-3(x-7)^2+8 \end{gathered}[/tex]To check, the graph of the given function is as follows:
Therefore, the equation of the quadratic equation is y=-3(x-7)²+8.
What is an equation of the line that passes through the points (-3,-5) and (-5, -3)? Put your answer in fully reduced form.
Express the general equation of a line passing through two points (x1,y1) and (x2,y2).
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Put (-3,-5) for (x1,y1) and (-5,-3) for (x2,y2) implies,
[tex]\begin{gathered} y+5=\frac{-3+5}{-5+3}(x+3) \\ y+5=\frac{2}{-2}(x+3) \\ y+5=-x-3 \end{gathered}[/tex]Further simplifying gives,
[tex]y=-x-8[/tex]Therefore, the equation of the line is y=-x-8.
west high schools population is 250 students fewer than twice the population of east high school. the two schools have a total of 2858 students. how many students attend east high school?
From properties of linear equation, 1036 students attend east high school.
What is linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Let east high school have x students
West high school have 2x - 250
Total count of students from both the schools are 2858 students.
Then we get
x + 2x-250 = 2858
=> 3x - 250 = 2858
=> 3x = 2858 + 250
=> 3x = 3108
=> x = 3108/3
=> x = 1036
Therefore, 1036 students attend east high school.
To learn more about linear equation from the given link
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In a school, 10% of the students have green eyes. Findthe experimental probability that in a group of 4students, at least one of them has green eyes.The problem has been simulated by generating randomnumbers. The digits 0-9 were used. Let the number "9"represent the 10% of students with green eyes. A sampleof 20 random numbers is shown.
Given that in a group of 4 students at least one has green eyes.
Also, the number 9 represents the 10% of the students with green eyes.
From the 20 random experimental numbers given, the number 9 appeared in only nine of them.
The experimental probability in percentage will be:
[tex]\frac{9}{20}\ast100\text{ = }45\text{ percent}[/tex]ANSWER;
45%
you are standing 200 feet from a tall building . The angle from your feet to the top of the building is 51°.
the sum of angles in a triangle is 180
missing angle + 90 + 51 = 180
missing angle = 180 - 141
missing angle = 39 degrees.
in the triangle,
[tex]\frac{x}{200}=\tan 51[/tex]x = 200 tan51
x = 200 * 1.234
x = 246.97 ft apporx 247 ft
'so the length x = 247 ft
that is greater than 200
so the answer is
x > 200 ft
Type the correct answer in each box.1020PX1150Parallel lines pand gare cut by two non-parallel lines, mand n, as shown in the figure.►gmnThe value of xisdegrees, and the value of y isdegrees.ResetNext
EXPLANATION
Given the parallel lines that are cutted by two non-parallel lines, m and n, the supplementary angle to 102 degrees is by the supplementary angles theorem 180-102= 78 degrees.
By the alternate interior angles theorem, the value of x is 78 degrees.
Also, by the corresponding angles theorem, the value of y is 115 degrees.
Describe in words where the square root of 60 minus 11 would be plotted on a number line.
Answer:
it would be on 7 since 60-11=49 and the square root of 49 is 7
What is the product of V3 and 7V30 in simplest radical form?
Determine the product of two expressions.
[tex]\begin{gathered} \sqrt[]{3}\times7\sqrt[]{30}=7\sqrt[]{30\cdot3} \\ =7\sqrt[]{3\cdot3\cdot10} \\ =7\cdot3\sqrt[]{10} \\ =21\sqrt[]{10} \end{gathered}[/tex]So answer is,
[tex]21\sqrt[]{10}[/tex]I’ve been stuck for a while and it logged me out:(
Solution
A polynomial is a function in the form of ; where n is non- negative integers which is known as the degree of polynomial. from this definition, it is clear that only option (2) √2 x -1 , is polynomial. because coefficient of variables ; √2, -1 are real number and also power of variable is non-negative integer.
I have selected the options , the ones I have ticked are polynomials, while the one cancelled are none polynomials:
A resort rented 62 cabins during its first season in operation. Based on the data for a similar resort, management estimated the equation of the line of best fit for the number cabins rented as y= 4x + 62, where x is the number of seasons since the first season of operation, and y is the number of cabins rented during that season. In reality, unusually bad weather for several years beginning in the first season led to the number of rentals for each season decreasing at the rate they were expected to increase. Which is the best choice for the equation for the line of best fit for the cabin rentals?A) y = 1/4 + 62B) y = - 4x + 62C) y = - 1/4x + 62D) y = 4x - 62
In the equation y = 4x + 62, the increasing rate is 4
If the actual rate decreases at the rate they were expected to increase, then it is -4 instead of 4.
Then, the equation of the line is:
B) y = - 4x + 62
Make a scatter plot of the data. Scale the x-axis by ones and the y-axis by twos.
Answer
Age of Car in years is represented as x
Avg. Miles per Gallon is represented as y
y = 0.97x + 1.214
Correlation Coefficient = 0.673
Explanation
Age of Car in years is represented as x
Avg. Miles per Gallon is represented as y
The datapoints are fed into a calculator and plotted with the datapoints also processed according to some formulas that'll be provided here
The first figure contains the data points and the regression data processed to be used to calaculate the required parameters.
The second attached image shows the plotted data and the line of best fit and the equation that best represents the relationship between the two parameters.
Then the last image shows the parameters used to calculate the equation of correlation and the correlation coefficient.
Hope this Helps!!!
33Select the correct answer from each drop-down menu.A75°B40°AoIn the figure, line segment AB is parallel to line segment CD.СDdegreesThe measure of angle Cisdegrees, and the measure of angles Dis>254075ResetNext
Answer:
Angle C = 40 degrees
angle D = 75 degrees
Explanation:
From the information given,
Angle A = 75 degrees
Angle B = 40 degrees
AB is parallel to CD. This means that AD and BC are transversals.
Angles A and D have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
angle D = 75 degrees
Angles B and C have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
Angle C = 40 degrees
I need help with this question please. Just do question 1 please. Also this is just apart of a homework practice
Answer:
P(x) = 1.3x² + 0.1x + 2.8
Explanation:
We need to find an equation that satisfies the relationship shown in the table. So, let's replace x by 2 and then compare whether the value of p(x) is 8.2 or not
P(x) = 1.3x³ + 0.1x² + 2.8x
P(2) = 1.3(2)³ + 0.1(2)² + 2.8(2)
P(2) = 16.4
Since P(2) is 16.4 instead of 8.2, this is not a correct option
P(x) = 1.3x² + 0.2x - 2.8
P(2) = 1.3(2)² + 0.2(2) - 2.8
P(2) = 2.8
Since 2.8 and 8.2 are distinct, this is not the correct option
P(x) = 2.3x² + 0.2x + 1.8
P(x) = 2.3(2)² + 0.2(2) + 1.8
P(x) = 11.4
Since 11.4 and 8.2 are distinct, this is not the correct option
P(x) = 1.3x² + 0.1x + 2.8
P(2) = 1.3(2)² + 0.1(2) + 2.8
P(2) = 8.2
Therefore, this is the polynomial function for the data in the table.
So, the answer is P(x) = 1.3x² + 0.1x + 2.8
61 less than twice vidy's score
We are given the following word problem
"61 less than twice Vidy's score"
Let us translate the word problem into an algebraic expression
Let v represents Vidy's score
twice Vidy's score means 2 times v
61 less than means to subtract 61 from 2 times v
So, the algebraic expression becomes
[tex]2v-61[/tex]When a projectile is launched at an initial height of H feet above the ground at an angle of theta with the horizontal and initial velocity is Vo feet per second. the path of the projectile...
Given,
The initial height of H feet.
The initial velocity of the object is Vo.
The equation of the path of projectile is,
[tex]y=h+x\text{ tan }\theta-\frac{x^2}{2V_0\cos ^2\theta}_{}\text{ }[/tex]This is the expression of the projectle path.
Hence, the path of the projectile object is y = h + xtan(theta) - x²/2V₀²cos²(theta)
You have to multiple the whole number and the fraction if you don’t know how to do it
We need to find how much spare represents the given space for vegetables.
The total are is 24 square feet and she will use 3/4 of the space for vegetables.
Then, you need to multuply the result by 3 and then, we need to divide 24 by 4.
Therefore:
24*(3/4) =72/4 = 18
Hence, she will use 18 square feet for vegetables.
How to put 7^3/4 in radical form
Given:
[tex]7^{\frac{3}{4}}[/tex]Resolving it to its radical form can be gotten based on the general laws of indices.
We have:
[tex]A^{\frac{x}{y}}=\sqrt[y]{A^x}[/tex]I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.
Thus:
[tex]\begin{gathered} 7^{\frac{3}{4}}=\sqrt[4]{7^3}=\sqrt[4]{343} \\ \sqrt[4]{343}=343^{\frac{1}{4}}=343^{(\frac{1}{2}\times\frac{1}{2})} \\ =343^{(\frac{1}{2}\times\frac{1}{2})}=\sqrt[]{343^{\frac{1}{2}}} \end{gathered}[/tex]Now, we have our value in the square root form as:
[tex]\sqrt[]{343^{\frac{1}{2}}}=\sqrt[]{7^{\frac{3}{2}}}[/tex]The perimeter of a rectangular field is 360 m.If the width of the field is 85 m, what is its length?
In order to calculate the length of the rectangular field, you use the following formula for the calculation of the perimeter:
P = 2l + 2w
w: width = 85 m
l: length = ?
P: area = 360m
You know the value of P and w, so, you can solve for l in the formula for the perimeter of the field, just as follow:
P = 2l + 2w
2l = P - 2w
l = (P - 2w)/2
Next, you replace the values of P and w:
l = (360m - 2(85m))/2 = 95 m
Hence, the length of the rectangular field is 95m
solve the equation and check the solution:7x - 7 = 13 + 12x
we have the equation
7x - 7 = 13 + 12x
solve for x
Group terms
12x-7x=-7-13
Combine like terms
5x=-20
x=-20/5
x=-4Verify
substitute the value of x=-4 in the original expression
7(-4)-7=13+12(-4)
-28-7=13-48
-35=-35 -------> is ok
Which expression is equivalent to 8 - (-5) ?O 8+50 -8 +(-5)O 8+-5O -5 +8
Answer:
The first option is correct
[tex]8+5[/tex]Explanation:
[tex]\begin{gathered} 8--5 \\ \\ 8+5 \\ \end{gathered}[/tex]Two negatives makes a positive.
find the slope and y intercept, then write out the linear equation (y=mx+b) below
Answer:
y = 2x + 3
Step-by-step explanation:
You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.
Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.
The slope is 2. Fill in 2 in place of m in
y = mx + b
y = 2x + b
Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.
y = 2x + 3
Explain why (-1)^n = 1 for any even number n.How is this possible? I thought it would equal -1. Does that mean the answer is "not possible"?
The expression (-1)^n means the number -1 multiplies itself n times.
So for example if n = 2, we have that:
[tex](-1)^2=(-1)\cdot(-1)=1[/tex]For n = 3, we have:
[tex](-1)^3=(-1)\cdot(-1)\cdot(-1)=1\cdot(-1)=-1[/tex]For n = 4:
[tex](-1)^4=(-1)^2\cdot(-1)^2=1\cdot1=1[/tex]We can see that the result alternates from -1 and 1, and when n is odd, the result is -1, and when n is even, the result is 1.
So for any even number n, the result will be 1.
It takes 2000 bees 1 year to make 7 jars of honey. How long will it take 5000 bees to make 70 jars of honey?
If the bees are working at the same rate, the number of years taken to make 70 jars is 4 years.
What is the rate of jar making by a bee?
The rate at which a bee makes a jar is calculated as follows;
rate = 2000 bees / 7 Jars
rate = 285.71 b/J
The later of rate of the bees is calculated as follows;
rate = 5000 bees / 70 jars
rate = 71.42 b/J
If the bees were to maintain the first rate, the number of years taken to make 70 jars is calculated as follows;
number of years = (285.71) / (71.42) = 4 years
Learn more about rate of work here: https://brainly.com/question/1144815
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Laura, a sandwich maker, produces 80 sandwiches on average per day. How many sandwiches will she produce in pdays?Number of sandwiches =
Number of sandwiches = 80p
Explanation:Given:
Laura produces 80 sandwiches per day
To find:
The number of sandwiches that will be produced in p days
1 day = 80 sandwiches
p days = 80 × p
p days = 80p
This means that she will produce 80p number of sandwiches in p days
if the radius of the circle is 5 units, find the arc length of RQ
The radius of the circle is r = 5 units.
The formula for the arc length of RQ is,
[tex]RQ=2\pi r\times(\frac{\theta}{360})[/tex]Substitute the values in the formula to obatin the arc length RQ.
[tex]\begin{gathered} RQ=2\pi\cdot5\cdot(\frac{142}{360}) \\ =12.391 \\ \approx12.39 \end{gathered}[/tex]So arc length of RQ is 12.39 units.
I’m struggling on this math question and could use some help on it
Let's determine the values of f(-4) and g(6).
For f(-4),
[tex]\text{ f\lparen x\rparen= -2x}^3\text{ - 5}[/tex][tex]\text{ f\lparen-4\rparen= -2\lparen-4\rparen}^3-5\text{ = -2\lparen-64\rparen- 5}[/tex][tex]\text{ f\lparen-4\rparen = 128 - 5}[/tex][tex]\text{ f\lparen-4\rparen = 123}[/tex]Therefore, f(-4) = 123
For g(6),
[tex]\text{ g\lparen x\rparen = -3x - 3}[/tex][tex]\text{ g\lparen6\rparen = -3\lparen6\rparen - 3 = -18 - 3}[/tex][tex]\text{ g\lparen6\rparen = -21}[/tex]Therefore, g(6) = -21
Puppets made by each puppeteer43ASCNumber of puppetsAsMYCol?0AlexKalinBruceMarcoMYPuppeteerProIf the mean of the data set is 3 puppets, find the number of puppets Marco made.ProTeapuppets
Remember that we can get the mean of a dataset by adding up each datum and dividing such sum by the number of data.
Now, let's call the number of puppets Marco made M
This way, we would have that:
[tex]\frac{1+4+3+M}{4}=3[/tex]Solving for M :
[tex]\begin{gathered} \frac{1+4+3+M}{4}=3 \\ \\ \rightarrow\frac{8+M}{4}=3 \\ \\ \rightarrow8+M=12\rightarrow M=12-8 \\ \Rightarrow M=4 \end{gathered}[/tex]Therefore, we can conclude that Marco made 4 puppets.
PLEASE HELP I WILL MARK BRAINLIEST!!Which of the following equations is a linear function?A) 2x + 3y = 6B) y = x^2 + 1C) y=x^3D) x^2 + y^2 = 9
Given data:
The given sets of equations.
The polynomial in which degree of the variable is 1 is said to be linear expression.
The first option 2x+3y=6 is only linear function.
Thus, the option (A) is correct.
Carl Heinrich had lateral filing cabinets that need to be placed along one wall of a storage closet. The filing cabinets are each 2 1/2 feet wide and the wall is 15 feet long. Decide how many cabinets can be placed along the wall
In this case we have to divide the length of the wall by the width of a cabinet. Doing so, we have:
[tex]\begin{gathered} 2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2}\text{ (Converting the mixed number to an improper fraction)} \\ \frac{15}{1}\div\frac{5}{2}=\frac{15\cdot2}{5}(\text{Dividing fractions)} \\ \frac{15\cdot2}{5}=\frac{30}{5}=6\text{ (Simplifying the result)} \\ \text{The answer is 6 cabinets.} \end{gathered}[/tex]