Volume of a cone =
[tex]v=\frac{1}{3}\pi r^2h[/tex]From the question;
r= 4 h=7
π is a constant and it is equal to 22/7
substitute the values into the formula;
[tex]V=\frac{1}{3}\times\frac{22}{7}\times4^2\times7[/tex][tex]V=\text{ }\frac{2464}{21}[/tex][tex]V=117.33inch^3[/tex]find the surface area of the figure in square inches.
The surface area of a cone is given by the sum of the areas of the lateral surface and the area of the circular base.
The area of the circular base is given by:
[tex]\pi\cdot r^2[/tex]Where r is the radius of the base.
The area of the lateral surface is given by:
[tex]\pi rs[/tex]Where s is the length of the slant.
Since s=17 in and the radius is half the diameter, r=8 in, the area of the cone is:
[tex]\begin{gathered} A=\pi rs+\pi r^2 \\ =\pi(8)(17)+\pi(8)^2 \\ =136\pi+64\pi \\ =200\pi \\ =628.3185307\ldots \end{gathered}[/tex]To the nearest hundredth, the area of the cone in square inches, is:
[tex]628.32[/tex]What is the logarithm of
6.5
The logarithm of the number 6.5 is log(6.5) = 0.8129
What is the logarithm of numbers?This is the number that represents the power by which a fixed number known as the base must be raised to result in another number.
How to evaluate the logarithm of the number?The number is given as
6.5
The logarithm of the number is then represented as
log(6.5)
There are several ways to calculate the logarithm of the number
Some of which are:
By logarithm tableBy calculatorIn this case, the only way is by using a calculator
Using a calculator, we have
log(6.5) = 0.8129
Hence, the logarithm of 6.5 is 0.8129
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1. Which statement is true? (1 point)
29 20
35
18
34
14
A
A
30
16
32
17
>
21 24
20 28
15
23
Fraction - A,C,D is the incorrect option that means 18 >17 is the correct option B
What does compare mean in fractions?Equivalent fractions with the same denominator should be used to compare fractions with different denominators. Comparing fractions: If the denominators are the same, the numerators can be compared. The greater fraction is the one with a larger numerator.
Now, comparing the fraction,
first of all write the fraction in simplest form then cross multiplication.
1. [tex]\frac{29}{35} < \frac{20}{30}[/tex]
[tex]\frac{29}{35} < \frac{2}{3}[/tex]
87 < 70
This option is wrong.
2. [tex]\frac{18}{34} > \frac{16}{32}[/tex]
[tex]\frac{9}{17} > \frac{1}{2}[/tex]
18 >17
This option is correct.
3. [tex]\frac{14}{21} > \frac{17}{24}[/tex]
[tex]\frac{2}{3} > \frac{17}{24}[/tex]
48 > 51
This option is wrong.
4. [tex]\frac{20}{15} < \frac{28}{23}[/tex]
[tex]\frac{4}{3} < \frac{28}{23}[/tex]
92 < 84
This option is wrong.
Hence, option b is correct.
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The table represents an absolute value function f(x). x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6 3 7 What are the vertex and range of the function? Vertex (0, 4), Range: {y | 0 ≤ y < ∞} Vertex (0, 4), Range: {y | 4 ≤ y < ∞} Vertex (−4, 0), Range: {y | 0 ≤ y < ∞} Vertex (−4, 0), Range: {y | −4 ≤ y < ∞}
The vertex and range of this absolute value function is: Vertex (0, 4), Range: {y | 0 ≤ y < ∞}.
What is an absolute value function?An absolute value function can be defined as a type of function that consist of an algebraic expression, which is placed within absolute value symbols.
Mathematically, the standard form of the equation for an absolute value function is given by:
y = a|x - h| +k.
Where:
h and k are the vertex of the graph.
Furthermore, an absolute value function is defined by this piecewise rule, especially based on its input:
|x| = -x, x < 0.|x| = x, x ≥ 0.In conclusion, the vertex or turning point of this absolute value function in the table above is at (0, 4).
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Answer:
Vertex (0, 4), Range: {y | 0 ≤ y < ∞}.
Step-by-step explanation:
HELP ME OUT PLEASE!!!!!!!
What is the solution to the system?
Answer:
(-7, 5) is correct.
Step-by-step explanation:
[tex]2x + 3y = 1[/tex]
[tex] - 2x - y = 9[/tex]
Add these two equations, and then solve for y.
[tex]2y = 10[/tex]
[tex]y = 5[/tex]
Substitute this value of y into 2x + 3y = 1, and solve for x.
[tex]2x + 3(5) = 1[/tex]
[tex]2x + 15 = 1[/tex]
[tex]2x = - 14[/tex]
[tex]x = - 7[/tex]
So (-7, 5) is the correct solution.
Which did you include in your response? Check all that apply? Use ten StartFraction 1 Over 12 EndFraction bars. Circle groups of StartFraction 4 Over 6 EndFraction. There is one group of StartFraction 4 Over 6 EndFraction, with StartFraction 1 Over 6 EndFraction remaining. The quotient is 11 and one-fourth.
The simplified expression of the fraction expression is (b) One group of 4/6, with 1/6 remaining.
How to evaluate the fraction?
The fraction expression is given as
ten StartFraction 1 Over 12 EndFraction bars.
Rewrite the fraction properly
So, we have
Ten 1/12 bars
This can be represented as
10 * 1/12
Rewrite 10 as 10/1
So, we have the following equation
10 * 1/12 = 10/1 * 1/12
Evaluate the products of the numerator
So, we have the following equation
10 * 1/12 = 1/1 * 10/12
Evaluate the products of the denominator
So, we have the following equation
10 * 1/12 = 10/12
Simplify the fraction
10 * 1/12 = 5/6
Split the fraction
10 * 1/12 = 4/6 + 1/6
This means that, the result is
Quotient = 4/6 and remainder = 1/6
Hence, the true statement about the fraction is (b)
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Complete question
Which did you include in your response? Check all that apply?
Use ten 1/12 bars.
4/6One group of 4/6, with 1/6 remaining. The quotient is 11 and one-fourthAn inground sprinkler nozzle sprays water onto the grass in the shape of a circle, with the nozzle at the center of the circle. On the coordinate plane, the nozzle is located at (20, 0) and the points (35, 0) and (5, 0) lie on the circle. Which equation represents the boundary that the sprinkler covers?
In order to determine which equation represents the boundary, replace the values of the coordinates of the given points, into the choices for the equations, and then verify if the left hand side matches with the right hand side.
For points (35,0) and (5,0) you have:
x = 35
y = 0
x = 5
y = 0
Then, for the first answer choice we have:
[tex]\begin{gathered} (x-20)^2+y^2=225 \\ (35-20)^2+0^2= \\ 15^2=225 \\ (5-20)^2+0^2= \\ 15^2=225 \end{gathered}[/tex]As you can notice, the equation matches for values of x and y.
Then, there is no necessary to verify for the other choices.
Hence, the equation (x - 20)^2 + y^2 = 225 represents the boundary that the sprinkler covers.
please help me solve part 3!
Step-by-step explanation:
probabilities are always
desired cases / totally possible cases
24 cans in total, 4 of them are diet, therefore 20 of them are regular.
2 cans are picked.
for the first can
the probability to pick a diet can is
4/24 = 1/6
the probability to pick a regular is
20/24 = 5/6
a)
to pick 2 diets, the first one has to be diet.
that leaves 23 cans with 3 being diet.
so, the probability for the second can being diet too is
3/23.
as combined event the probability to pull 2 diet cans is
1/6 × 3/23 = 1/2 × 1/23 = 1/46 = 0.02173913...
≈ 0.0217
b)
now the same for picking 2 regular cans.
the first one has to be regular :
5/6
that leaves for the second one 23 cans and 19 of them regular
19/23
combined this gives the probability
5/6 × 19/23 = 95/138 = 0.688405797...
≈ 0.6884
this is not unusual.
what would be considered "usual" or "unusual" ?
c)
one of them is diet, and one of them is regular.
the simple answer ?
it is the only other option, when the cans are not of the same type. it is the opposite of the sum of a) and b).
so, it is
1 - 0.688405797... - 0.02173913 = 0.289855072...
≈ 0.2899
but what to do, if we want to calculate it directly ?
it is the case that either
1. the first can is diet and the second can is regular,
or
2. the first can is regular and the second can is diet.
case 1.
the first can is diet = 1/6
leaving 23 cans with 20 being regular
the second can being regular = 20/23
together
1/6 × 20/23 = 1/3 × 10/23 = 10/69 = 0.144927536...
case 2.
the first can is regular = 5/6
leaving 23 cans with 4 diets.
the second can being diet = 4/23
together
5/6 × 4/23 = 5/3 × 2/23 = 10/69 = 0.144927536...
in an "exclusive or" situation we can add the probabilities.
so, the probability of having exactly one can diet and exactly one can regular is
0.144927536... + 0.144927536... = 0.289855072...
≈ 0.2899
we were correct in the first place !
Find the midpoint M of the line segment joining the points
Given,
The coordinates of the points is,
[tex](-4,5)\text{ and \lparen2,-1\rparen}[/tex]The coordinates of the mid point is:
[tex]\begin{gathered} Consider,\text{ x and y are the coordinates of the midpoint} \\ x=\frac{-4+2}{2}=-\frac{2}{2}=-1 \\ y=\frac{5-1}{2}=\frac{4}{2}=2 \\ \end{gathered}[/tex]Hence, the mid point of the line segment is (-1,2).
what is (9.74c-250.50)+(-5.48p+185.70)
Here, we want to solve find the value of the expression
We start by opening up the brackets and then, we bring together like terms
We have this as;
[tex]\begin{gathered} (9.74c-250.5)+(-5.48p+185.70) \\ =\text{ 9.74c - 250.5 -5.48p+185.7} \\ =\text{ 9.74c-5.48p-250.5+185.7} \\ =\text{ 9.74c-5.48p-64.80} \end{gathered}[/tex]at what point does the like given by the following equation cross the y axis? y=(-5/7)x+5A.(0,-5/7)B.(5,0)C.(0,5)D.(0.-25/7)
Given:
Given the equation
[tex]y=-\frac{5}{7}x+5[/tex]Required: Point at which the equation crosses the y axis.
Explanation:
At y -axis, the value of x is zero. Substitute 0 for x in the equation of y.
[tex]\begin{gathered} y=-\frac{5}{7}\cdot0+5 \\ =0+5 \\ =5 \end{gathered}[/tex]So, the point at which the equation cross the y-axis is (0, 5).
Final Answer: The point at which the equation cross the y-axis is (0, 5).
pls answer the pic below
The value of the missing angles are; m∠ABC = 36° and m∠DBC = 41°
How to find the missing angles?We are given that;
m∠ABD = 77°
Addition angle postulate states that the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together.
Now, by addition angle postulate, we can say that;
m∠ABC + m∠DBC = 77°
Now, we are given that;
m∠ABC = (5x - 4)°
m∠DBC = (5x + 1)°
Thus, by substitution property, we have;
(5x - 4)° + (5x + 1)° = 77
10x - 3 = 77
10x = 77 + 3
10x = 80
x = 8
Thus;
m∠ABC = (5(8) - 4)°
m∠ABC = 36°
m∠DBC = (5(8) + 1)°
m∠DBC = 41°
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500/675x9876=? what is the answer ???????????
Answer:
7315.55
Step-by-step explanation:
just dont be lazy solve it.
Which of the following inequalities would be graphed with an open circle? Select all that apply.
SOLUTION
Note that for an inequality to be graphed with an open circle the inequality sign must be either less than or greater than
Therefore the inequalities are:
[tex]\begin{gathered} 3(x-2)<18 \\ h+6>-3h+12 \end{gathered}[/tex]Find f(4) if f(x) =5x-4
To find f(4) you substitute the x in the given equation for 4:
[tex]\begin{gathered} f(4)=5(4)-4 \\ f(4)=20-4 \\ f(4)=16 \end{gathered}[/tex]Then, f(4) is 16how many meters are in 11.75 millimeters
ANSWER
0.01175 metres
EXPLANATION
We want to find how many metres are in 11.75 millimetres.
There are 1000 millimeters in 1 meter:
We will simply divide 11.75 milimetres by 1000
1000 millimetres = 1 metre
[tex]11.75\text{ millimetres = }\frac{11.75}{1000}\text{ = 0.01175 metres}[/tex]write from largest to smallest these numbers 5/4,.2,60%,.75,.5
The following are the reasons why sampling is used except for a. Sampling is used if taking a census of the entire population is impractical. b. Sampling is less time-consuming and less costly than census. c. Sampling is so easy. d. The data from the sampling can be used to estimate corresponding population measures.
The following are the reasons for sampling:
1. To bring the population to a manageable number
2. To reduce cost
3. To help in minimizing error from the despondence due to large number in the population
4. Sampling helps the researcher to meetup with the challenge of time.
Therefore, the answer is:
c. Sampling is so easy.
Caleb is going to see a movie and is taking his 3 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $3.50 each. How much total money would Caleb have to pay for his family if he were to buy 5 snacks for everybody to share? How much would Caleb have to pay if he bought xx snacks for everybody to share?
The total money would Caleb have to pay for his family if he were to buy 5 snacks for everybody to share is;
How to Solve Algebra Word Problems?
We are told that the cost of each movie ticket is $13. Now, if he buys one movie ticket for his 3 kids, then total he would pay for the 3 kids and himself is;
13 * 4 = $52
Now, an assortment of snacks available to purchase for $3.50 each. Thus, if Caleb buys 5 snacks, then it means that;
Cost of the 5 snacks = 3.5 * 15 = $16.5
Total paid = $52 + $16.5
= $67.5
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Write a function that models the population of 400 birds decreased at an annual rate of 6%
A function that models the population of 400 birds decreasing at an annual rate of 6% is [tex]f(x) = 400(1 - 0.06)^{t}[/tex] where t is the time period.
What is the Exponential decay formula?The Exponential decay formula aids in determining the quick decrease over time, i.e. the exponential decrease. The exponential decay formula is used to calculate population decay, half-life, radioactivity decay, and so on.
Its general form is f(x) = a (1 - r)ⁿ.
Where a = the initial amount
1 - r = decay factor and n = time period.
Given:
The initial population of birds, P = 400
Rate of decay, r = 6% = 0.06
Time = t years
By using the exponential decay formula,we get
[tex]f(x) = P (1 - r)^{t}[/tex]
[tex]f(x) = 400(1 - 0.06)^{t}[/tex]
Therefore, the function that models the population of 400 birds decreased at an annual rate of 6% is [tex]f(x) = 400(1 - 0.06)^{t}[/tex].
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14 pound in 1 stone and 2.2 pound in 1 kilogram. a certain person weight 9 stone.
Given that 1kg=2.2 pound, also there is 14 pounds in 1 stone
There are 9 stones totally,so totally 9 stones will have 405 pounds
To convert into kilogram to should divide pounds by 2.2
[tex]\frac{405}{2}=183.705[/tex]Thus 183.705 is the required answer.
Find the surface area of the net.Enter the correct answer in the box.
We can divide the given figure into different rectangular faces:
Faces 1 and 3 have the same measure, also 2 and 4, and faces 5 and 6.
Faces 1 and 3 have the following dimensions: L=100cm W=50cm.
Faces 2 and 4 have the following dimensions: L=100cm W=35cm.
Faces 5 and 6 have the following dimensions: L=50cm W=35cm.
The surface area of a rectangular face is given by:
[tex]SA=L*W[/tex]Thus, the surface areas of the given faces are:
[tex]\begin{gathered} SA_1=100cm*50cm=5000cm^2 \\ SA_3=100cm*50cm=5000cm^2 \\ SA_2=100cm*35cm=3500cm^2 \\ SA_4=100cm*35cm=3500cm^2 \\ SA_5=50cm*35cm=1750cm^2 \\ SA_6=50cm*35cm=1750cm^2 \end{gathered}[/tex]The surface area of the net is the addition of all of these surface areas:
[tex]\begin{gathered} SA_{net}=(5000+5000+3500+3500+1750+1750)cm^2 \\ SA_{net}=20500cm^2 \end{gathered}[/tex]Abigail wants to find three consecutive even integers whose sum is four times the smallest of those integers. She lets n represent the smallest integer, then writes this equation: n + (n + 2) + (n + 4) = 4n. What are the three integers?
The three consecutive integers according to the expression will be 6, 8, 10
In the given question, there is an expression stated that tells the condition for a sequence in which a number is represented by 'n'. The expression is the sum of three even integers whose sum is equal to four times the smallest of numbers.
The expression is n + (n + 2) + (n + 4) = 4n. We have to find out the values for each of the numbers.
Here, First Number = n
Second number = (n + 2)
Third Number = (n + 4)
Now, We will calculate the given expression to find out the value of n.
=> n + (n + 2) + (n + 4) = 4n
=> 3n + 6 = 4n
=> n = 6
We get the smallest number n = 6 which is the first number, the second number is 8, and the third number is 10.
Hence, the numbers are 6, 8, and 10.
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65% of the workers at Costco have a pet dog. If thereare about 162 workers who have a dog, how manyCostco employees are there in total? .
To find how many Costco employees are, we can use the formula of
Atoms can’t ever be _ or _ in a chemical reaction. the atoms must always be _ each side of the equation
In a chemical reaction, atoms are neither CREATED nor DESTRUCTED. According to science, each side of the equation must contain the SAME amount of atoms.
You must place COEFFICIENTS in front of the chemical formulas in the equation in order to make it equal.
What does a chemical reaction always involve?
Only atoms from the reactants can end up in the products of a chemical reaction. No atoms are destroyed or made into new ones. When reactants come into touch with one another, the bonds between their atoms are broken, and the atoms then reorganize and form new bonds to create the products.
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Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 318 with 57% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.
A population proportion's 95% confidence interval is 0.45416 ≤ P ≤ 0.66584.
Given sample size n is 318, the probability of success,
p = x ÷ n = 181 ÷ 318 = 0.56
A population proportion's 95% confidence interval is calculated as follows:
(p - [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n) , p + [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n)
(0.56 - 1.96 √ ((0.56(1 - 0.56) ÷ 318) , 0.56 + 1.96 √ ((0.56(1 - 0.56) ÷ 318))
(0.56 - 1.96 × 0.054) , (0.56 + 1.96 × 0.054)
(0.45416 , 0.66584)
95% confidence interval for a population proportion of 0.45416 ≤ P ≤ 0.66584.
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Question 22 of 25Which list is ordered from least to greatest?L) 52.932M) 583.31N) 52.930) 8.39P) 89.223A. N, L, M, P, OOB. M, P, L, N, OOC. O, N, L, P, MOD. P. O, L, M, N
Solution
- The ordered list from the least to the greatest is:
[tex]8.39,52.93,52.932,89.223,583.31[/tex]- Thus, using the arrangement of the numbers, we can rearrange using the letters.
O, N, L, P, M
Final Answer
O, N, L, P, M (OPTION C)
A rectangular calendar is hanging on a wall. The diagram below shows several dimensions of the wall and the calendar.Based on the diagram, determine the distance that the top edge of the calendar is from the ceiling, and explain your reasoning.
SOLUTION
We want to find the distance that the top edge of the calendar is from the ceiling.
The diagram below will help us
From the diagram above x is the distance we want to find
We can see that the entire wall is 9 ft long,
Distance from the foot of the calender to the floor is 5 1/4 ft and
Halve of the calendar is 2/3 ft
So the whole calendar is
[tex]\begin{gathered} 2\times\frac{2}{3} \\ =\frac{4}{3}\text{ ft } \end{gathered}[/tex]So, to find x, we will add length of the calendar which is 4/3 ft to distance from the foot of the calender to the floor which is 5 1/4 ft and subtract this from height of the wall which is 9 ft
We have
[tex]\begin{gathered} 9-(\frac{4}{3}+5\frac{1}{4}) \\ 9-(\frac{4}{3}+\frac{21}{4}) \\ 9-(\frac{16+63}{12}) \\ 9-\frac{79}{12} \\ =\frac{108-79}{12} \\ =\frac{29}{12} \\ =2\frac{5}{12} \end{gathered}[/tex]Hence the answer is
[tex]2\frac{5}{12}\text{ ft}[/tex]Identify the translation of the vertices P (-4, -5), L (1, -7), and K (-9, 8), along the vector , <-6 , 3 >.
Given:
The vertices are P (-4, -5), L (1, -7), and K (-9, 8).
The vector is < -6,3 >.
Aim:
We need to find the image of the vertices when translating given vertices along the vector.
Explanation:
The translation vector <-6,3> means each point is being moved 6 units to the left and 3 units up.
For each vertex, we subtract 6 from each x value and add 3 to each y value.
[tex]P^{\prime}(-4-6,-5+3)=P^{\prime}(-10,-2)[/tex][tex]L^{\prime}(1-6,-7+3)=L^{\prime}(-5,-4)[/tex][tex]K^{\prime}(-9-6,8+3)=K^{\prime}(-15,11)[/tex]Final answer:
[tex]P^{\prime}(-10,-2)[/tex][tex]L^{\prime}(-5,-4)[/tex][tex]K^{\prime}(-15,11)[/tex]
a) The perimeter is ____. Include units.b) The area is ___. include units.Another question is: Fully Simplify the following equation: (3x + 7) (5x^2 + 4x +9)
The perimeter is 54 inches
The area is 108 square inches
Explanation:The perimeter of the triangle is:
15 in + 15 in + 24 in
= 54 in
The area is:
(1/2)(24)(9)
= 108 sq. in