Answer:
Volume of the sphere model of earth is 321m³
Step-by-step explanation:
Parameter given:
diameter of the sphere = 8.5m
π = 3.14
Volume of a sphere is given as = 4/3 π r³
Where r is the radius of the sphere.
From given diameter, radius = 8.5/2 = 4.25m
Therefore, imputing the parameters in the formular we have:
⇒4/3 × 3.14 × 4.25³
⇒1.333 ×3.14 × 76.766
Volume of the sphere model = 321.31m³ ≅ 321m³
Is 2/10 equal to 4/5
Answer:
NO
Step-by-step explanation:
2/10 have a common term of 2. reduce both the numerator and denominator by dividing both by 2.
2/2 = 1
10/2 = 5
the reduced fraction woudl be 1/5
Answer:
No 2/10 is not the same as 4/5
Step-by-step explanation:
The reason why is because If you doubled 2/10 then it would be 4/20 not 4/5 and if you divided by 4/5 by 2 then it would be a complex fraction of 2/1/2 that is why the statement 4/5 is equal to 2/10 is false.
A rectangle is 2/5 inches long and 1/3 inches wide. WORTH 20 POINTS!!!!!
What is the area of the rectangle?
Enter your answer in the box as a fraction in simplest form.
Answer:
2/15 inches squaredStep-by-step explanation:
Area = L * W
2/5 * 1/3 =
2 * 1 = 2
5 * 3 = 15
= 2/15 inches squared
What we do is find area
Area of rectangle=(l*w)
length=2/5
width=1/3
Area=2/5*1/3
Answer=2/15
Answer=2/15
John had 84 dollars, and his brother Fred owed 12 dollars to his friend. John gave his brother some money. Fred paid his debt and now both of them has the same amount left. How much money did John give Fred? PLZZZZ HELP!!!!!
[tex]The \: money \: of \: each \: after \: Fred \: paid \: his \: debt: \frac{84 - 12}{2} = \$36 \\ John \: gave \: Fred:36 + 12 = \$48[/tex]
Answer:
36
Step-by-step explanation:
Kelly found some dimes and pennies in her dad's car . she found 5 coins in all. the coins totaled more than 20 cents, but less than 50 cents. What coins could Kelly have found?? Write the amount as a fraction of a dollar and as an equivalent decimal.
Answer:
21
Step-by-step explanation:
Tamara found the solution of x^2=64 to be x=8.
What mistake did Tamara make in finding her solution?
A. She found the incorrect square root of 64.
B. She only found the square root of one side of the equation.
C. She only found the positive square root, not the negative square root
D. She found the cube root of 64 instead of the square root.
and D is not the answer
Answer:
C
Step-by-step explanation:
given
x² = 64 ( take the square root of both sides )
x = ± [tex]\sqrt{64}[/tex] = ± 8
Tamara omitted the negative square root → C
Tamara made the mistake of only finding the positive square root, not the negative square root.
Explanation:The mistake that Tamara made in finding the solution to the equation x^2=64 is that she only found the positive square root, not the negative square root.
When solving a quadratic equation like this, you need to consider both the positive and negative square roots, because both values satisfy the equation. So the correct solution to x^2=64 is x=8 and x=-8.
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Pi is the ratio of _____ to ______
A. area to diameter
B. perimeter to area
C. radius to diameter
D. circumference to diameter
The answer is D. C ÷ d = π, where C is circumference and d is diameter.
Answer:
D. circumference to diameterStep-by-step explanation:
[tex]\text{The formula of a circumference of a circle:}\ C=d\pi\\\\d-diameter\\\\d\pi=C\qquad\text{divide both sides by}\ d\\\\\pi=\dfrac{C}{d}[/tex]
If you flip a coin 4 times, what is the best prediction possible for the number of times it will land on tails?
Answer:
2
Step-by-step explanation:
Each time you flip a coin, there is a 50% change of it landing on tails. So half the time you should get a tails.
Half of 4 is 2, so you will likely get 2 tails.
Final answer:
When you flip a coin 4 times, the best prediction for the number of tails is 2, based on the equal 50-50 chance for heads or tails on each toss. However, you may actually get any number of tails from 0 to 4 due to randomness.
Explanation:
If you flip a coin 4 times, the best prediction for the number of times it will land on tails can be determined by understanding probability. Each coin flip represents an independent event with a 50-50 chance of landing on either heads or tails. Therefore, over a small number of flips, such as 4, it is expected that you will get tails approximately half the time. However, it is possible to see any combination of heads and tails.
When considering all the possible outcomes of flipping a coin 4 times:
4 heads, 0 tails (HHHH)
3 heads, 1 tail (HHHT, HHTH, HTHH, THHH)
2 heads, 2 tails (HHTT, HTHT, HTTH, THHT, THTH, TTHH)
1 head, 3 tails (HTTT, THTT, TTHT, TTTH)
0 heads, 4 tails (TTTT)
Given that each of these outcomes is equally likely, the prediction would be 2 tails because it is the average outcome. However, it is important to recognize that while 2 tails is the most likely single outcome, any number of tails between 0 and 4 is possible due to the randomness of each flip.
The sum of four and the product of three and a number x.
Answer:
4 + 3xStep-by-step explanation:
The product of three and a number x: 3 · x = 3x
The sum of four and the product of three and a number x:
4 + 3x
A line is shown in the graph below.
What is the slope of a line that is perpendicular to the given line?
-3/2
-2/3
2/3
3/2
Answer:
3/2
Step-by-step explanation:
mm,m
Based on the calculations below, the slope of this graph is equal to: C. 2/3.
In Mathematics and Euclidean Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the given data points (0, -2), and (3, 0) into the formula for the slope of a line, we have the following;
Slope of graph = (0 - (-2))/(3 - 0)
Slope of graph = (0 + 2)/(3 - 0)
Slope of graph = 2/3
Based on the graph, the slope is the change in y-axis with respect to the x-axis, and it is equal to 2/3.
If a car travels at an average speed of x miles per hour, how far would the car travel in 90 minutes?
Answer:
1.5(x)
Step-by-step explanation:
find out how many hours are in 90 minutes
1.5
x miles
Drag the tiles to the correct boxes to complete the pairs.
Using the graph above, match each section of the graph with the situation that could describe it.
Section A_____
Section B_____
Section C_____
Section D_____
The answer's are the blue boxes with words in them.
Answer:
Section A: Sally drives from her house to her friend's house.
Section B: Sally stops to visit her friend.
Section C: Sally drives from her friend's house to the post office to drop off a card.
Section D: Sally drives back to her house.
Step-by-step explanation:
As you can see in the graph, the point (0,0) is the location of Sally's house. In that point the distance is 0 and the time is 0.
In Section A she drives 3 miles in 6 minutes from her house to her friend's house.
In Section B, the distance does not change, this means that Sally stopped at her friend's house for 4 minutes.
In Section C she drives (for 4 minutes) 1 mile from her friend's house to some place (In this case the post office).
In Section D she comes back to 0 distance, then, she drives back to home.
4x+5=2x+6 (what is x?)
Answer:
x = 1/2
Step-by-step explanation:
Subtract 2x from both sides
4x + 5x - 2x = 6
Combine 4x and -2x to get 2x.
2x + 5 = 6
Subtract 5 from both sides.
2x = 6 - 5
Subtract 5 from 6 to get 1.
2x=1
Divide both sides by 2.
x = 1/2
A rhombus has one diagonal that is 14 centimeters long and one diagonal that is 12. What is the area of the rhombus?
Answer:
168
14 times 12
in the diagram of PARALLELOGRAM ABCD, segment BE is perpendicular to segment CED, segment DF is perpendicular to BFC and segment CE is congruent to segment CF.
Prove ABCD is a rhombus.
Answer:
In parallelogram ABCD
FD is perpendicular to BC
BE is perpendicular to CD
Consider triangle BEC and triangle DFC
FC = EC (Given)
Angle BEC = Angle DFC (=90°)
Angle BCE = Angle DCF (common)
Therefore triangle BEC is congruent to triangle DFC (AAS congruency)
DF = BE (CPCT)
Since the altitudes are equal their bases will also be equal
Therefore BC = DC
Therefore BC = DC = AD = AB
Therefore ABCD is a rhombus
Hope this helps!
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Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus. Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.
To prove that parallelogram [tex]\(ABCD\)[/tex] is a rhombus, we need to show that all sides are congruent.
Given:
1. [tex]\(ABCD\)[/tex] is a parallelogram.
2. [tex]\(BE \perp CED\).[/tex]
3. [tex]\(DF \perp BFC\).[/tex]
4. [tex]\(CE \cong CF\).[/tex]
Proof:
1. Parallelogram Properties:
- In a parallelogram, opposite sides are congruent and parallel.
- Therefore, [tex]\(AB \parallel CD\)[/tex] and [tex]\(AD \parallel BC\)[/tex].
- Also, [tex]\(AB \cong CD\)[/tex] and [tex]\(AD \cong BC\)[/tex].
2. Congruent Segments:
- [tex]\(CE \cong CF\) (given).[/tex]
- Since [tex]\(BE \perp CED\)[/tex] and [tex]\(DF \perp BFC\)[/tex], [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] are heights from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] respectively to line [tex]\(CED\)[/tex].
3. Triangle Congruence:
- Consider [tex]\(\triangle CEF\)[/tex]. Since [tex]\(CE \cong CF\)[/tex] and [tex]\(BE \perp CED\)[/tex], [tex]\(DF \perp BFC\)[/tex], [tex]\(\triangle CEF\)[/tex] is isosceles with base [tex]\(EF\)[/tex].
4. Diagonals in Parallelogram:
- Diagonals of a parallelogram bisect each other.
- Since [tex]\(\triangle CEF\)[/tex] is isosceles and [tex]\(CE = CF\)[/tex], the diagonals [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] bisect each other at [tex]\(E\)[/tex] and [tex]\(F\)[/tex].
5. Symmetry and Congruence:
- Since diagonals bisect each other and the height from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] are equal, segments from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] to the diagonals are congruent.
6. Sides of Parallelogram:
- From symmetry and congruence, all sides of the parallelogram are equal.
- Therefore, [tex]\(AB \cong BC \cong CD \cong DA\)[/tex].
Conclusion:
Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus.
Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.
The population of a small town is around 4500 in 2010. The population is decreasing at a rate of 1.5% per year. After what year would the population in the town drop below 4000.
The population of a town decreasing at a rate of 1.5% per year from an initial number of 4500 will drop below 4000 in approximately 9 years, around the year 2019.
Explanation:The topic of this question concerns a decrease in population over time, which is generally described using exponential decay in mathematics. When we talk about a decrease of 1.5% per year, we're looking at an exponential decay factor of 1 - 0.015 = 0.985. We follow this process to determine the duration for the population to reduce below 4000:
Start with the initial population: 4500 Multiply that by the decay factor for each year Reiterate this until the population falls below 4000
Basically, it means:
4500 * (0.985^n) < 4000
. By solving this inequality, we find that
n ≈ 8.29
. Therefore, we can estimate the town's population will drop below 4000 in the 9th year (since we can't have a fraction of a year), which would be
2019
if we start counting from 2010.
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The population of the town would drop below 4000 in 2024.
To determine the year when the population of the town drops below 4000, we can use the formula for exponential decay:
Population = Initial population × (1 - Decay rate)^Time
where:
Population is the population at a given time
Initial population is the initial population (in 2010, which is 4500)
Decay rate is the decrease rate per year (1.5% or 0.015)
Time is the number of years since 2010
We want to find the Time when the Population is less than 4000. So, we can set up an inequality:
4000 > 4500 × (1 - 0.015)^Time
Dividing both sides by 4500, we get:
0.889 > (1 - 0.015)^Time
Taking the natural logarithm of both sides, we get:
ln(0.889) > Time × ln(1 - 0.015)
Dividing both sides by ln(1 - 0.015), we get:
Time ≈ 13.92
Since we're looking for the year when the population drops below 4000, we round up to the nearest whole year. Therefore, the population of the town would drop below 4000 in 2024.
When making a telephone call using a calling card, a call lasting 5 minutes cost $0.95. A call lasting 13 minutes cost $1.75. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that models the cost of making a call lasting x minutes.
A. y = 10x - 981/20
B. y = -0.1x + 1.45
C. y = 0.1x + 0.45
The linear equation that models the cost of making a call lasting x minutes using a calling card is y = -0.1x + 1.45.
Explanation:To write a linear equation that models the cost of making a call lasting x minutes using a calling card, we can use the given information about two calls. If a 5-minute call costs $0.95 and a 13-minute call costs $1.75, we can set up two equations:
0.95 = 5m + b
1.75 = 13m + b
Solving these equations, we find that m = -0.1 and b = 1.45. Therefore, the linear equation that models the cost of making a call lasting x minutes is y = -0.1x + 1.45.
Point O is the center of the circle. What is the value of X?
Answer options: 24, 15, 27, 20
Answer: FIRST OPTION
Step-by-step explanation:
To solve this problem you must apply the Intersecting Secant-Tangent Theorem. By definition, when a secant line and a tangent lline and a secant segment are drawn to a circle from an exterior point:
[tex](Tangent\ line)^2=(Secant\ line)(External\ Secant\ line)[/tex]
The total measure of the secant shown is:
[tex]18+Diameter[/tex]
If the radius is 7, then the diameter is:
[tex]D=7*2=14[/tex]
Therefore:
[tex]Secant\ line=18+14=32[/tex]
You also know that:
[tex]External\ Secant\ line=18\\Tangent\ line=x[/tex]
Keeping the above on mind, you can substitute values and solve for x:
[tex]x^{2}=32*18[/tex]
[tex]x=\sqrt{576}\\x=24[/tex]
The measure of the side length of the tangent line PQ to the circle O is 25 units
What is the measure of side length x?From the image, Line segment PQ is a tangent line because it touches the curve at point Q.
Therefore, triangle PQO forms a right triangle.
Leg 1 of the right triangle = OQ = 7
Leg 2 of the right triangle = PQ = x
Hypotenuse = PO = 18 + 7 = 25
Now, to solve for the measure of side length x, we use the Pythagoras theorem:
PQ = √( PO² - OQ² )
Plug in the values:
x = √( 25² - 7² )
x = √( 625 - 49 )
x = √576
x = 24
Therefore, the value of x is 24.
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Which expression is equivalent to
Answer:
[tex]\dfrac{7.7.7.7.7}{7.7}[/tex]
Step-by-step explanation:
Finding the expression of the value [tex]\dfrac{7^{5} }{7^{2}}[/tex] is just like taking the spread out value of the two variables raised to their exponents.
[tex]\dfrac{7^{5}}{7^{}}=\dfrac{7.7.7.7.7}{7.7}[/tex]
So if we multiply all the values together we get:
=[tex]\dfrac{16807}{49}[/tex]
=343
This method is just one of the methods that can be used to finding the quotient of a variable raised to an exponent.
the volume of a gold bar is 100cm cubed, the density of gold is 19.3g/cm cubed so what is the mass of the gold bar
➷ Use this formula:
density = mass / volume
Rearrange it for mass:
mass = density x volume
Substitute the values in:
mass = 100 x 19.3
Solve:
mass = 1930g
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➶ Have A Great Day ^-^
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find the area of equilateral triangle of side 4 cm.
Answer:6.928
Step-by-step explanation: formula A=√ 3*(side^2/4)
The area would be 7 cm
Step-by-step explanation:See the image
1. Does the data in the table below represent exponential growth or exponential decay?
Hint: Are the values in the bottom row increasing or decreasing?
A
exponential growth
B
exponential decay
Exponential decay because it is decreasing
a pyramid has a height of 10 inches and a base with an area of 21 square inches. Find the volume of the pyramid
a.)35in^3
b.)210in^3
c.)105in^3
d.)70in^3
Answer:
70 in³ (answer d)
Step-by-step explanation:
The volume of a pyramid with base area A and height h is
V = (1/3)(A)(h).
Here, V = (1/3)(21 in²)(10 in) = 70 in³
there are 5 teen age boys in the slack family. the boys drink 1 and 2 thirds of milk each day. at this rate, how many gallons of milk will the boys drink in a week?
A. 4 and 1 thirds
B. 11 and 2 thirds
C. 5 twentieth
D. 4 and 1 5th
What is the volume of a square pyramid that has a base length of 5 inches and a height of 9 inches?
Answer:
75
Step-by-step explanation:
To find the volume of a squared pyramid use the formula:
Volume of a squared pyramid = × base area × height
Base area = Side× side
( A square has the same length and breadth)
= 5 × 5 = 25 in
Volume of a squared pyramid = [tex]\frac{1}{3}[/tex] × 25 × 9
= 75 [tex]in^{3}[/tex]
In a rhombus VENU, diagonals VN and EU intersect at S. If VN= 12 and EU=16, what is the perimeter of the rhombus?
Answer:
40 un.
Step-by-step explanation:
The diagonals of the rhombus bisect each other at right angle. This gives us that
[tex]VS=\dfrac{1}{2}VN=6\ un.;[/tex][tex]ES=\dfrac{1}{2}EU=8\ un. ;[/tex][tex]\angle VSE=90^{\circ}.[/tex]By the Pythagorean theorem,
[tex]VE^2=VS^2+ES^2,\\ \\VE^2=6^2+8^2,\\ \\ VE^2=36+64,\\ \\VE^2=100,\\ \\VE=10\ un.[/tex]
The sides of the rhombus are all of the same length, then the perimeter of the rhombus is
[tex]P_{VENU}=4\cdot 10=40\ un.[/tex]
Which unit would you use to measure the amount of milk in a half-gallon carton?
mL
g
cm
L
Answer would be D which is L
Answer:
L
Step-by-step explanation:
Most people prefer to use a unit of measurement that gives a number they can easily visualize, usually between 0.1 and 1000.
You wouldn't use centimetres, because that is a unit of length, and grams are a unit of mass.
The amount of milk in a half-gallon carton is about 2 L or 2000 mL, so you would measure the milk in litres (L).
Louis found two bakeries to provide bagels for his sub shop. The first bakery offers 350 bagels for $168.00 and the second bakery offers 475 bagels for $209. How much will Louis pay for 800 bagels if he buys from the bakery with the lower price?
Answer:
$352Step-by-step explanation:
Find out the price of one bagel by dividing the price by the number of bagels:
350 Bagels = $168
1 Bagel = $0.48
475 Bagels = $209
1 Bagel = $0.44
0.48 > 0.44
This means the second bakery has the lower price.
Louis wants 800 bagels, so multiply the price by 800.
0.44 * 800 = $352
You can check it's lower by comparing it with the first bakery.
0.48 * 800 = $384
384 > 352
How many cubes are needed to fill the rectangular prism PLZ HUUURRRRRYYYYYY
Problem #7 PLEASE HELP ;(
Is 6(x+0.4) equivalent to 3(2x+0.8)? YES or NO???????
Show your work!
6(x+0.4) 3(2x+0.8)
Answer:
Yes
6(x+0.4) is equivalent to 3(2x+0.8)
Step-by-step explanation:
Given in the questions two expressions
6(x + 0.4)
3(2x + 0.8)
We will apply distributive law
It is a law relating the operations of multiplication and addition, stated symbolically
a(b + c) = ab + ac6(x + 0.4)
= 6(x) + 6(0.4)
= 6x + 2.4
3(2x + 0.8)
= 3(2x) + 3(0.8)
= 6x + 2.4
Since both equations when expanded have same answers, hence they are equivalent
to solve a system using the additional method, you would need to multiply the first equation by what number in order for the x’s to add out? 3x-y=3, -2x+2y=6
Answer:
2
Step-by-step explanation:
In order to solve a system using the additional method, we would need to multiply the first equation by '2' in order for the x’s to add out.
We have the following equations:
[tex] 3 x - y = 3 [/tex] --- (1)
[tex] -2x + 2y = 6 [/tex] --- (2)
We will multiply equation (1) by 2 and equation (2) by 3 to cancel the x's.
[tex] 2 ( 3x - y = 3 ) = [/tex] [tex] 6x - 2 y = 6 [/tex]
[tex] 3 ( -2x + 2 y = 6 ) = -6x + 6y = 36 [/tex]