The surface area of a sphere is given by
[tex]S_s=4\pi r^2[/tex]in our case r=10 units ( the radius). By substituting this value into the last formula, we have
[tex]S_s=4(3.1416)(10^2)[/tex]which gives
[tex]S_s=1256.64u^2[/tex]On the other hand, the surface area of a cube is given by
[tex]S_c=6L^2[/tex]where L is the length of one side, that is, L=10. Then, we have
[tex]\begin{gathered} S_c=6\cdot(10^2) \\ S_c=6\cdot100=600u^2 \\ S_c=600u^2 \end{gathered}[/tex]By comparing both results, we can see that the surface area of our sphere is larger than the surface area of the given cube. So the answer is TRUE.
In 2000, the population of a town was 46.020. By 2002 wpulation had increased to52,070. Assuming that the towns population is increasing linearly answer the followingquestions.a.What is the population of the town by 2006?
We know that the population increased linearly, so an adequate model for the population P in year t is:
[tex]P(t)=m\cdot t+b[/tex]We know that in 2000 the population is 46,020.
In 2002 the population is 52,070.
This are two points of the line that can be written as (2000, 46020) and (2002, 52070).
Then, we can calculate the slope m as:
[tex]m=\frac{P_2-P_1}{t_2-t_1}=\frac{52070-46020}{2002-2000}=\frac{6050}{2}=3025[/tex]With the slope value we can write the equation in slope-point form:
[tex]\begin{gathered} P-P_0=m(t-t_0) \\ P-46020=3025(t-2000) \\ P=3025(t-2000)+46020 \end{gathered}[/tex]With the linear equation defined like this (we don't need to calculate the y-intercept), we can calculate the population expected for 2006:
[tex]\begin{gathered} P(2006)=3025(2006-2000)+46020 \\ P(2006)=3025\cdot6+46020 \\ P(2006)=18150+46020 \\ P(20060)=64170 \end{gathered}[/tex]Answer: the population in 2006 is expected to be 64,170.
Graph the line that passes through the points (9,4) and (9,1) and determine the equation of the line.
Both points of the given points have the same x-coordinate. This is only possible if we have a vertical line. The vertical line have the format
[tex]x=k[/tex]Where k represents the x-coordinate of all points of the line. The x-coordinate of our points is 9, therefore, the equation of the line is
[tex]x=9[/tex]And its graph is
What is the probability that a meal will include a hamburger
ANSWER:
The probability that a meal will include a hamburger is 25%
SOLUTION:
The total combination of one entree and one drink is 4* 2 = 8
The total combination of one hamburger meal is 1*2 = 2
The probability is 2/8 or 1/4 or 25%
Match each expression on the left to its equivalent value on the right. Some answer options on the right will not be used.
Let us write out our expressions:
[tex]\begin{gathered} -29+(-7) \\ -34+(-94) \\ -8+(-14) \\ -12+(-48) \end{gathered}[/tex]The trick here is to get rid of the minus, then solve the sum as usual, and add a minus to the result. Let us do that for each of them:
-29+(-7)] Step one gives us:
[tex]29+7[/tex]Step two gives us:
[tex]36[/tex]Step three gives us:
[tex]-36[/tex]Then, -29+(-7) should be linked to -36.
-34+(-94)] Step one gives us:
[tex]34+94[/tex]Step two gives us:
[tex]128[/tex]Step three gives us:
[tex]-128[/tex]Thus, -34+(-94) should be linked to -128.
-8+(-14)] Step one gives us:
[tex]8+14[/tex]Step two gives us:
[tex]22[/tex]And step three gives us:
[tex]-22[/tex]This implies that -2+(-14) should be linked to -22.
-12+(-48)] Step one gives us:
[tex]12+48[/tex]Step two gives us:
[tex]60[/tex]And step three gives us:
[tex]-60[/tex]Then, -12+(-48) should be linked to -60.
Need help finding the volume and rounding to nearest whole number.
For a cylinder, the volume can be calculated using the formula:
[tex]V=\pi r^2h[/tex]Where r is the radius of the base and h is the height. From the problem, we identify:
[tex]\begin{gathered} r=\frac{16}{2}=8\text{ yd} \\ \\ h=10\text{ yd} \end{gathered}[/tex]Then, using these values to calculate the volume of the cylinder:
[tex]\begin{gathered} V=\pi(8)^2(10)=\pi(64)(10)=640\pi \\ \\ \therefore V=2011\text{ yd}^3 \end{gathered}[/tex]Hi can you help me find the correct match to each question?
GIVEN:
We are given a set of 4 statements as indicated in the attached image.
Required;
Determine whether each statement is TRUE or FALSE.
Solution;
(1) Look at the digit to the right of the digit to which you are rounding to tell whether to round up or leave it the same.
This statement is TRUE
(2) If the digit to the right of the digit to which you are rounding is four or less, you keep the digit the same.
This statement is TRUE.
(3) If the digit to the right of the digit to which you are rounding is five or more, you keep the digit the same.
This statement is FALSE.
(4) Look at the digit to the left of the digit to which you are rounding to tell whether to round down or leave it the same.
This statement is FALSE.
There are 10 males and 18 females in the Data Management class. How many different committees of 5 students can be formed if there must be 3 males and 2 femalesA: 18360B: 2600C: 98280D: 15630
Answer:
A: 18360
Explanation:
The number of ways of combinations to select x people from a group of n people is calculated as
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]Since we need to form committees with 3 males and 2 females, we need to select 3 people from the 10 males and 2 people from the 18 females, so
[tex]10C3\times18C2=\frac{10!}{3!(10-3)!}\times\frac{18!}{2!(18-2)!}=120\times153=18360[/tex]Therefore, there are 18360 ways to form a committee.
So, the answer is
A: 18360
Your cousin is building a Sandbox for his daughter how much sand will he need to fill the Box? Explain. How much paint will he need to paint all six surface of the sandbox? Explain. 1ft 4ft 6ft not answer choices
Since the image is a rectangular prism
The volume of the box can be obtained by using the formula:
Volume = l x b x h
The box has a dimension of 1ft x 4ft x 6ft
The volume of the box = 1 x 4 x 6 = 24 cubic feet
Therefore, the volume of sand needed to fill the box will be = 24 cubic feet of sand
The surface area of the box can be obtained using the formula:
2(lb + lh + bh)
= 2(1x4 + 1x6 + 4x6)
=2(4 + 6 + 24)
=2 (34)
= 68 square feet
Therefore a total surface area of 68 square feet needs to be painted
8) Remus earns $.15 per unit for the work he does. For all units heproduces in a week, over 1,000, he receives $.20. What were his weeklyearnings if he produced 1,420 units?
You have the following information:
- Remus earns $.15 per unit
- For units he produced over 1,000 he receives $.20
- He produced 1,420 units
In order to determine what were the weekly earnings, you first take into account the earnings for the first 1,000 units:
0.15 x 1,000 = 150
Next, you calculate the earnings for the units over 1,000, which are 420:
0.20 x 420 = 84
Next, you sum both contributions:
150 + 84 = 234
Hence, the weekly earning os Ramus were of $234
The radius, R, of a sphere is 5.7 cm. Calculate the sphere's volume, V.Use the value 3.14 for r, and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The volume formula of a sphere is :
[tex]V=\frac{4}{3}\pi r^3[/tex]From the problem, the radius of the sphere is r = 5.7 cm
Using the formula above :
[tex]\begin{gathered} V=\frac{4}{3}(3.14)(5.7)^3 \\ V=775.3 \end{gathered}[/tex]ANSWER :
775.3 cm^3
show the prime factorisation of 49 :-;
thankyou.
Answer:
The prime Factorization of 49 is 7.7
Step-by-step explanation:
Hope this helps! :))
Answer:
7
Step-by-step explanation:
The factors of 49 are 1, 7, and 49
Find the equation of the tangent line to the curve y = x^3- 4x - 5 at the point (2, -5).Tangent Line Equation:
Let's find the derivative of y:
[tex]\begin{gathered} y=x^3-4x-5 \\ \frac{dy}{dx}=3x^2-4 \end{gathered}[/tex]Evaluate the derivative for x = 2:
[tex]\frac{dy}{dx}\begin{cases} \\ x=2\end{cases}=3(2)^2-4=12-4=8[/tex]Now, we have the slope, let's use the point-slope formula to find the equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ _{\text{ }}where\colon \\ (x1,y1)=(2,-5) \\ m=8 \\ y+5=8(x-2) \\ y+5=8x-16 \\ y=8x-21 \end{gathered}[/tex]Answer:
y = 8x - 21
The volume of a rectangular prism is 2 x cubed + 9 x squared minus 8 x minus 36 with height x + 2. Using synthetic division, what is the area of the base?
2 x cubed + 13 x squared + 18 x
2 x cubed + 5 x squared minus 18 x
2 x squared + 13 x + 18
2 x squared + 5 x minus 18
Answer:
2 x squared + 5 x minus 18
Step-by-step explanation:
Hope this helps sorry if not right
Answer: D
Step-by-step explanation: EDGE
Given a function described as the equation y= 4x - 4, what is y when x is 1, 2, and 3?A 2, 8, 16B 4,8, 12C 0,4,8D 0, 6, 12
Answer
C. 0, 4, 8
Explanation
Given function:
y = 4x - 4
What to find:
To find y when x = 1, 2, and 3
Step-by-step solution:
When x = 1
y = 4(1) - 4
y = 4 - 4
y = 0
When x = 2
y = 4(2) - 4
y = 8 - 4
y = 4
When x = 3
y = 4(3) - 4
y = 12 - 4
y = 8
The diagram has a hollow cylindrical tube, of internal radius 4cm and external radius 6cm. How can I determine the area of an external curved surface, how can I get the area of the inner curved surface and how can I get the total surface area of the tube?
Given:
internal radius = 4cm
External radius = 6cm
Height = 20cm
Curved surface area of the external surface
The formula for the curved surface is:
[tex]\begin{gathered} =2\pi rh \\ \text{Where r is a radius} \\ \text{and h is the height of the cylinder} \end{gathered}[/tex]Hence, the curved surface area:
[tex]\begin{gathered} C\mathrm{}S\mathrm{}A\text{ of external surface = 2}\times\pi\times6\times20 \\ =753.982cm^2 \end{gathered}[/tex]Curved surface area of the inner surface:
[tex]\begin{gathered} C\mathrm{}S\mathrm{}A\text{ of inner surface = 2 }\times\pi\times4\times\text{ 20} \\ =502.654cm^2 \end{gathered}[/tex]The total surface area of the tube :
The total surface area can be found using the formula:
[tex]\text{Total Surface area = }2\pi(R^2-r^2)\text{ + }2\pi h(R\text{ + r)}[/tex]Where R is the radius of the external surface and r is the radius of the inner surface
Hence:
[tex]\begin{gathered} \text{Total Surface area = 2}\times\pi\times(6^2-4^2)\text{ + 2}\times\pi\times20\times(6\text{ + 4)} \\ =\text{ }1382.3cm^2 \end{gathered}[/tex]What is the value of x if x + 15 = 38 ? Enter answer below
x=23
1) Evaluating x +15=38
x +15=38 Subtract 15 from both sides
x+15-15 = 38 -15
x=23
2) So the quantity of x = 23
x=23
1) Evaluating x +15=38
x +15=38 Subtract 15 from both sides
x+15-15 = 38 -15
x=23
2) So the quantity of x = 23
find the value of tan A in simplest radical form
In the given right angle triangle BCA : BC = 5, CA = 3 and BA = root 34
From the trignometric ratio of right angle triangle :
The tangent of angle is the ratio of the Adjacent side to the opposite side
[tex]\tan \theta=\frac{Opposite\text{ side}}{Adjacent\text{Side}}[/tex]In the given triangle, the side opposite to angle A = BC and adjacent side CB
Substitute the value :
[tex]\begin{gathered} \tan \theta=\frac{Opposite\text{ side}}{Adjacent\text{Side}} \\ \tan A=\frac{BC}{CB} \\ \tan A=\frac{5}{3} \\ \tan A=1.66 \\ \\ ^{} \end{gathered}[/tex]The value of tanA = 5/3 or 1.66
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
The transformation of the map is given as; translation of 1 unit to the right and rotated 180 degree counterclockwise about origin.
What is termed as the translation?In geometry, translation refers to a function which moves an object a specified distance. The element is not otherwise altered. It is not rotated, mirrored, or resized.Each point of the element must be relocated within the same direction and at the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, and the element after the translation is referred to as the image.For the given question;
The graph of the triangle is given,
The triangle is first translated to the 1 unit to its right such that vertex of the triangles lies on the y -axis.
Now, the triangle is rotated about origin in counter clock wise direction about 180 degrees.
Thus, the final image is shown by red triangle.
To know more about the translation, here
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which of the relationships below represents a function with the same rate of change of the function y= -4x + 2
Given data:
The given equation of the line is y= -4x + 2.
Substitute 0 for x in the given equation.
[tex]\begin{gathered} y=-4(0)+2 \\ =2 \end{gathered}[/tex]Substitute 1 for x in the given equation.
[tex]\begin{gathered} y=-4(1)+2 \\ =-2 \end{gathered}[/tex]Thus, option (D) is correct.
8. A certain virus infects one in every 700 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. (a) Find the probability that a person has the virus given that they have tested positive. (b) Find the probability that a person does not have the virus given that they have tested negative.
Part a
Find the probability that a person has the virus given that they have tested positive
Probability in fraction form
p=(1/700)*(90/100)=90/70,000
simplify
P=9/7,000Part b
Find the probability that a person does not have the virus given that they have tested negative
Probability in fraction form
P=(699/700)*(10/100)
P=6,990/70,000
simplify
P=699/7,000the coldest temperature ever recorded on earth is 135.8 Fahrenheit below zero recording in Antarctica on July 21st 1983 the hottest temperature ever recorded on earth is 134 Fahrenheit recorded in Death Valley California on July 10th 1913 what is the difference between those two temperature
Let's begin by listing out the information given to us:
The coldest temperature ever recorded on earth (T1) = -135.8 Fahrenheit
The hottest temperature ever recorded on earth (T2) = 134 Fahrenheit
The difference between the two temperature = Hottest - Coldest temperature
[tex]undefined[/tex]Find the area of this parallelogram. Be sure to include the correct unit in your answer.19 yd12 yd11 yd
Given a parallelogram as shown below:
The formula to calculate the area of the parallelogram is given to be:
[tex]A=b\times h[/tex]From the question provided, we have the following parameters:
[tex]\begin{gathered} a=12\text{ yd} \\ b=11\text{ yd} \\ h=9\text{ yd} \end{gathered}[/tex]Therefore, we can use the formula to calculate the area as shown below:
[tex]\begin{gathered} A=b\times h \\ A=11\times9 \\ A=99yd^2 \end{gathered}[/tex]The area of the parallelogram is 99 squared yards (99 yd²).
Please help me
I give brainliest
worth 15 points
The amount of money in a bank account is given by the function y = 200(1+0.05), where y is in dollars and t is measured in months since the account was opened.
What is the percent rate of growth of the bank account?
Enter your answer in the box.
Answer:
60% annual rate
Step-by-step explanation:
Your equation is incorrect
It should be Y = 200 (1+.05)^t
T is the number of compounding periods per year (12 to a year)
.05 is the periodic interest rate ( 1/12 th of the annual)
.05 * 12 = .6 Which is 60% <=====REALLY high annual rate!
Solve the missing angles by using trig function Answer Choices: A. 57.4B. 53.1
We can relate an angle x to its opposite leg and its adjacent leg, by means of the trigonometric function tangent of x, like this:
[tex]\tan (x)=\frac{\text{opposite}}{\text{adjacent}}[/tex]Then we can find the value of the angle by applying the inverse function of tangent, like this:
[tex]x=\tan ^{-1}(\frac{opposite}{adjacent})[/tex]Let's replace the values from the figure into this equation to find x, like this:
[tex]\begin{gathered} x=\tan ^{-1}(\frac{25}{16}) \\ x\approx57.4 \end{gathered}[/tex]Then, x equals 57.4°
find the slope of a line that is PARALLEL to y=3/5x-2
Parallel lines have the same slope.
In this case, the slope of the line is 3/5.
Then, any line that satisfies y=3/5*x+C, being C any constant, is parallel to our line.
Then, when C=0 for example, we have the line y=3/5*x that is parallel and goes through the center of coordinates (0,0).
Graphically, we can see that they a re parallel:
Answer: y = 3/5*x + C, with C=constant. There are infinte solutions if no other restriction is made, so for example y=3/5*x is parallel to y=3/5*x-2.
there are about 6*10^24 molecules in a litre of water. it is estimated that a person drinks about 2.2 *10^3 litres of water a year. how many molecules of water does a person drink in a year?
As per the concept of multiplication, the amount of molecules of water does a person drink in a year is 13.2 x ²⁷ or 1.32 x 10²⁸.
Molecules:
Molecules are referred as the smallest particle of a substance that has all of the physical and chemical properties of that substance. It is made up of one or more atoms.
Given,
There are about 6 x 10²⁴ molecules in a liter of water. it is estimated that a person drinks about 2.2 x 10³ liters of water a year.
Here we need to find the amount of molecules of water does a person drink in a year.
To calculate the total amount of molecules consumption for the year we have to use the following formula,
That is,
Total molecules per year = amount of water per year x molecules in water.
Here we know that,
the amount of water consumption per year = 2.2 x 10³ liters
And the amount of molecules of one liter water = 6 x 10²⁴
When we apply the values on the formula, then we get,
=> total amount of molecules consumption = (2.2 x 10³) x (6 x 10²⁴)
=> (2.2 x 6) x (10³ x 10²⁴)
=> 13.2 x 10³⁺²⁴
=> 13.2 x ²⁷
Therefore, the amount of molecules of water does a person drink in a year is 13.2 x ²⁷ or 1.32 x 10²⁸.
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How many liters of paint must you buy to paint the walls of a rectangular prism-shaped room that is 20 m by 10 m with a ceiling height of 8 m if 1 L of paint covers40 m2? (Assume there are no doors or windows and paint comes in 1-L cans.)
17 Liters
Explanation
Step 1
find the total area to paint
we need to assume the floor wont be painted, so the total are to paint is
the are of a rectangle is gieven by:
[tex]Area=length*width[/tex]so, the total area will be
[tex]\begin{gathered} total\text{ surface area=\lparen20*10\rparen+2\lparen20*8\rparen+2\lparen10*8\rparen} \\ total\text{ surface area=200+2\lparen160\rparen+2\lparen80\rparen} \\ total\text{ surface area=200+320+160} \\ total\text{ surface area=680 m}^2 \end{gathered}[/tex]so , the area to paint is 680 square meters
Step 2
finally, to know the number of Liters need , divide the amount ( total area) by the rate of the paitn, so
[tex]\begin{gathered} paint\text{ needed=}\frac{total\text{ area}}{rate\text{ paint}} \\ paint\text{ needed=}\frac{680m^2}{40\frac{m^2}{L}}=17Liters \end{gathered}[/tex]so, the total paint needes is 17 Liters, and paint comes in 1-L cans, so
[tex]\begin{gathered} 17\text{ Liters} \\ 17\text{L}\imaginaryI\text{ters\lparen}\frac{1\text{ Can}}{1\text{ L}})=17cans \end{gathered}[/tex]therefore, the answer is
17 Liters
I hope this helps you
Haley spent 1/2 oven hour playing on her phone that used up 1/9 of her battery how long would she have to play on her phone to use the entire battery
1/2 hour playing -- 1/9 battery
1 hour playing -- 2/9 battery
1 1/2 hours playing --- 3/9 battery
2 hours playing ------ 4/9 battery
2 1/2 hours playing ---- 5/9 battery
3 hours playing ----- 6/9 battery
3 1/2 hours playing --- 7/9 battery
4 hours playing -----8/9 battery
4 1/2 hours playing ---- 9/9 battery
9/9 represent the entire battery so che can play 4.5 hours on her phone
it can be represented into a fraction as
[tex]4.5=4\frac{1}{2}=\frac{9}{2}[/tex]Comparing Two Linear Functions (Context - Graphically)
start identifying the slope and y-intercept for each high school.
The slope represents the growth for each year, in this case for high school A is 25 and for high school B is 50.
The y-intercept is the number of students that are enrolled currently, in this case for A is 400 and for B is 250.
The complete equations in the slope-intercept form are
[tex]\begin{gathered} A=25x+400 \\ B=50x+250 \end{gathered}[/tex]Continue to graph the equations
High school B is projected to have more students in 8 years.
I have the answers for 1 and 2 3. Use your answers from # 1 and # 2 to find the length of each arc between gondola cars . Use 3.14 for and round to the nearest hundredth . You must write out all the numbers you are multiplying together meaning show your work for full credit . ( 5 points ) Central angle = 8°Radius = 95 ft
The length of an arc = 13.26 ft
Explanation:The length of an arc is given by the formula:
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ \end{gathered}[/tex]Substitute θ = 8°, r = 95 ft, and π = 3.14 into the formula
[tex]\begin{gathered} l=\frac{8}{360}\times2\times3.14\times95 \\ \\ l=13.26\text{ ft} \end{gathered}[/tex]The length of an arc = 13.26 ft
