Answer:
If a polygon has 3 sides, then the polygon is a triangle.
Step-by-step explanation:
Bold = hypothesis
Italic = conclusion
Statement:
If p, then q.
Converse: If q, then p.
To find the converse, switch the hypothesis and conclusion.
Statement:
If a polygon is a triangle, then it has 3 sides.
Now we switch the hypothesis and the conclusion to write the converse of the statement.
If it has 3 sides, then a polygon is a triangle.
We fix a little the wording:
If a polygon has 3 sides, then it is a triangle.
Answer: If a polygon has 3 sides, then the polygon is a triangle.
The converse statement will be;
⇒ If a polygon has 3 sides, then the polygon is a triangle.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The statement is,
''If a polygon is a triangle, then it has 3 sides. ''
Now,
Since, The statement is,
''If a polygon is a triangle, then it has 3 sides. ''
We know that;
The converse of statement for p → q will be q → p.
Thus, The converse statement is find as;
⇒ If a polygon has 3 sides, then the polygon is a triangle.
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A population of bacteria P is changing at a rate of dP/dt = 3000/1+0.25t where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t. Then find the population when t = 3 days.
Answer:
- At any time t, the population is:
P = 375t² + 3000t + 1000
- At time t = 3 days, the population is:
P = 13,375
Step-by-step explanation:
Given the rate of change of the population of bacteria as:
dP/dt = 3000/(1 + 0.25t)
we need to rewrite the given differential equation, and solve.
Rewriting, we have:
dP/3000 = (1 + 0.25t)dt
Integrating both sides, we have
P/3000 = t + (0.25/2)t² + C
P/3000 = t + 0.125t² + C
When t = 0, P = 1000
So,
1000/3000 = C
C = 1/3
Therefore, at any time t, the population is:
P/3000 = 0.125t² + t + 1/3
P = 375t² + 3000t + 1000
At time t = 3 days, the population is :
P = 375(3²) + 3000(3) + 1000
= 3375 + 9000 + 1000
P = 13,375
Find the area of the following figure. Explain how you found your answer.
HELP ASAP WILL GIVE BRIANLYEST
Answer:
Below
Step-by-step explanation:
Let's say that each square on the grid represents 1 cm
First find the area of the two triangles
For the larger one: A = bh/2
A = 3 x 3 / 2
= 4.5 cm^2
For the smaller one : A = bh/2
A = 2 x 2 / 2
= 2 cm^2
For the rectangle : A = lw
A = 4 x 5
= 20 cm^2
Add them all up to get the area
4.5 + 2 + 20 = 26.5 cm^2
Hope this helps!
Answer:
26 1/2 units
Step-by-step explanation:
First find the area of the rectangle at the bottom
A = l*w
A = 5 *4 = 20
Then find the area of the left triangle
A =1/2 bh = 1/2 (3 * 3) = 9/2
Then find the area of the right triangle
A = 1/2 bh = 1/2 ( 2*2) = 4/2 =2
Add the areas together
20 + 9/2+2 = 22 +9/2 = 22+4 1/2= 26 1/2
Three guests check into a hotel room. The manager says the bill is $30, so each guest pays $10. Later the manager realizes the bill should only have been $25. To rectify this, he gives the bellhop $5 as five one-dollar bills to return to the guests.
On the way to the guests' room to refund the money, the bellhop realizes that he cannot equally divide the five one-dollar bills among the three guests. As the guests aren't aware of the total of the revised bill, the bellhop decides to just give each guest $1 back and keep $2 as a tip for himself, and proceeds to do so.
As each guest got $1 back, each guest only paid $9, bringing the total paid to $27. The bellhop kept $2, which when added to the $27, comes to $29. So if the guests originally handed over $30, what happened to the remaining $1?
Answer:
the manager has it
Step-by-step explanation:
this sounds more like a riddle than a math question
Answer:
This was so confusing and I had to use like 3 sheets of paper
Step-by-step explanation:
$25 + $2 + $1 + $1 + $1 = $30.
So the manager has it, the point is to change the numbers so your brain gets confused.
An opinion poll asked a random sample of adults whether they believe flu shots are ineffective in the United States. A commentator believes less than 35% of all adults believe they are ineffective. Which null and alternative hypotheses should be used to test this claim? H0: p ≠ 0.35, Ha: p 0.35
Complete Question
The complete question is shown on the first uploaded image
Answer:
The second option is the correct option
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.35[/tex]
The Null Hypothesis is [tex]H_o : \r p = 0.35[/tex]
The reason for this is that the this original claim when represented mathematically does not contain an equality sign ([tex]i.e \ it \ is \ mathematically \ represented \ as \ \r p < 0.35[/tex]) so the null hypothesis is the compliment of it ( i.e [tex]\r p = 0.35[/tex])
The Alternative hypothesis is [tex]H_a : \r p < 0.35[/tex]
Need help with this problem ASAP, don’t need an explanation, just an answer
Answer:
x^3-10x^2+1/9
Step-by-step explanation:
For standard form you need to put the exponents in order. So x^3 is first, followed by -10x^2, and finally 1/9. Hope this helps!
what is the answer of
445+584-85
Answer:
944 is the correct answer
Answer:
the answer it's 944
445+558=1,029
1,029-85=. [944]✓
Identify the vertex of the graph. Tell whether it is a minimum or maximum.
(-2,-2); maximum
(-2,-2); minimum
(-2, -1); minimum
(-2, -1); maximum
Answer:
(-2,-2); minimum
Step-by-step explanation:
From the graph, the vertex is (-2, -2) and since there are no y values that go less than the y value of the vertex, it is a minimum.
Black Diamond Ski Resort charges $50 for ski rental and $15 an hour to ski. Bunny Hill Ski Resort charges $75 for ski rental and $10 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same. 15x − 75 = 10x − 50 15x − 50 = 10x − 75 15x + 50 = 10x + 75 15x + 75 = 10x + 50
Answer:
The cost of 5 hours of skiing would be the same ($125) after 5 hours.
Step-by-step explanation:
Black Diamond: ChargeBD(h) = $50 + ($15/hr)h, where h is the number of hours spent skiing.
Bunny Hill: ChargeBH(h) = $75 + ($10/hr)h
We equate these two formulas to determine when the cost of using the ski slopes is the same:
ChargeBD(h) = $50 + ($15/hr)h = ChargeBH(h) = $75 + ($10/hr)h
We must now solve for h, the number of hours spent skiing:
50 + 15h = 75 + 10h
Grouping like terms, we obtain:
5h = 25, and so h = 5 hours.
The cost of 5 hours of skiing would be the same ($125) after 5 hours.
How many solutions does the system of equations below have y=3x+2 y-2x=4
Answer:
Only one solution.
Step-by-step explanation:
y = 3x +2
y -2x =4
y - 2x = 4
=> y = 2x +4
y = 3x + 2
y = 2x + 4
Since both equations are not the same, so the answer cannot be "infinitely many solutions".
They both intersect each other 1 point, so it cannot be "no solutions".
So the answer is "Only 1 solution".
solve for y then find the slope and y intercept and graph
y=4x+3
y=
b=
m=
Answer:
y = 4x+3
m =4
b =3
Step-by-step explanation:
y=4x+3
This is already solved for y
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 4x+3
m =4
b =3
The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. A paper described a study in which the left atrial size was measured for a large number of children ages 5 to 15 years. Based on this data, the authors conclude that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.5 mm and a standard deviation of 4.8 mm.
Required:
a. Approximately what proportion of healthy children has left atrial diameters less than 24 mm?
b. Approximately what proportion of healthy children has left atrial diameters greater than 32 mm?
c. Approximately what proportion of healthy children has left atrial diameters between 25 and 30 mm?
d. For healthy children, what is the value for which only about 20% have a larger left atrial diameter?
Answer:
a) P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b) P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) z(s) = 0,84
Step-by-step explanation:
Normal Distribution N ( μ₀ ; σ ) is N ( 26,5 ; 4,8 )
a) P [ X < 24 mm ] = ( X - μ₀ ) / σ
P [ X < 24 mm ] = (24 - 26,5)/ 4,8 = - 0,5208 ≈ - 0,52
P [ X < 24 mm ] = - 0,52
And from z-table we find area for z score
P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b)P [ X > 32 mm ] = 1 - P [ X < 32 mm ]
P [ X < 32 mm ] = ( 32 - 26,5 ) / 4,8
P [ X < 32 mm ] = 5,5/4,8 = 1,1458 ≈ 1,15
P [ X < 32 mm ] = 1,15
And from z-table we get
P [ X < 32 mm ] = 0,8749
Then:
P [ X > 32 mm ] = 1 - 0,8749
P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = P [ X < 30 ] - P [ X < 25 ]
P [ X < 30 ] = 30 - 26,5 / 4,8 = 0,73
From z-table P [ X < 30 ] = 0,7673
P [ X < 25 ] = 25 - 26,5 / 4,8 = - 0,3125 ≈ - 0,31
From z-table P [ X < 25 ] = 0,2709
Then
P [ 25 < X < 30 ] = 0,7673 - 0,2709
P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) If 20 %
z- score for 20% is from z-table
z(s) = 0,84
Which represents a measure of volume?
O 5 cm
O 5 square cm
05 cm
05 cm
Answer:
5 cm³
Step-by-step explanation:
The correct options to the given question will be:
5 cm³ 5 square cm 5 cm 5 cm²The volume of a solid is referred to as the space that the figure occupies. The three dimensions are covered and recorded to measure the volume. It is measured by multiplying the length, breadth, and the height of the solid. Since three units are multiplies, therefore the unit of the volume becomes a cubic unit. Usually, the volume is measured in cubic meter or cubic centimetre.
Find the particular solution of the differential equation that satisfies the initial condition. f '(x) = −8x, f(1) = −3
Step-by-step explanation:
f(x) = integral (-8x) dx = -4x^2 + C
f(1) = -3 = -4 + C
C = 1
f(x) = -4x^2 + 1
The particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is: f(x) = -4x² + 1.
Here, we have,
To find the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3,
we can integrate the equation and use the initial condition to determine the constant of integration.
First, integrate both sides of the equation with respect to x:
∫ f'(x) dx = ∫ -8x dx
Integrating, we get:
f(x) = -4x² + C
Now, we can use the initial condition f(1) = -3 to find the value of the constant C.
Substituting x = 1 and f(x) = -3 into the equation, we have:
-3 = -4(1)² + C
-3 = -4 + C
C = -3 + 4
C = 1
Therefore, the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is:
f(x) = -4x² + 1
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0.25÷3=x÷1 1/2 That fraction is one and a half.
Answer:
x = 1/8Step-by-step explanation:
Given the expression 0.25÷3=x÷1 1/2, we are to look for the value of x from the given equation. Rewriting the equation we will have;
[tex]\dfrac{0.25}{3} = \dfrac{x}{1\frac{1}{2} }[/tex]
On simplification;
[tex]0.25 * \frac{1}{3} = x * \frac{2}{3} \\ \\ \frac{25}{100}*\frac{1}{3} =\frac{2x}{3}\\\\ \frac{1}{4} * \frac{1}{3} = \frac{2x}{3}\\\\ \frac{1}{12} = \frac{2x}{3}\\\\cross \ multiply\\\\2x * 12 = 3\\\\24x = 3\\\\Divide \ both \ sides \ by \ 24\\\\24x/24 = 3/24\\\\x = 1/8[/tex]
Hence the value of x in the expression is 1/8
Question 7
2 pts
Find the value of x and the length of segment AC if point B is between A and C.
AB = 5x, BC = 9x-2, AC = 11x + 7.6
Value of x=
Length of AC is
Answer: x=3.2 AC= 42.8
Step-by-step explanation:
As point B lies at segment AC AC=AB+BC
Otherwise we can write the equation
5x+9x-2=11x+7.6
14x-2=11x+7.6
14x-2+2=11x+7.6+2
14x=11x+9.6
14x-11x=11x-11x+9.6
3x=9.6
x=9.6:3
x=3.2
AC= 11*x+7.6= 11*3.2+7.6=35.2+7.6=42.8
Part III- Percentage Problems
1. You currently have $4,500 saved in your bank account. You have decided to use $2700.
What percentage of your savings did you use? Show all your work to justify your answer.
2. An organization raises money for students who attend Berkeley College every year.
Currently, they have raised $11,250 which represents 45% of the money they raise.
Determine the amount of money the organization will raise in total. Show all your work
to justify your answer.
The percentage of your savings that I use is 60%
This shows that the amount of money the organization will raise in total is $25,000.
1) Given
Total amount saved = $4500
Amount used = $2,700
Percentage of money used = Amount used/Total amount saved × 100%
[tex]Percentage \ of \ money \ used = \frac{2700}{4500} \times 100\\Percentage \ of \ money = \frac{27}{45} \times 100\\Percentage \ of \ money \ used = \frac{2700}{45} \\Percentage \ of \ money \ used = 60 \%[/tex]
Hence the percentage of your savings that I use is 60%
2) Let the amount of money the organization will raise in total be x
Since the 45% of the money they raise represents $11,250, hence:
[tex]45\% \ of \ x = \$11,250\\0.45x = 11,250\\x = \frac{11250}{0.45}\\ x = 25,000[/tex]
This shows that the amount of money the organization will raise in total is $25,000
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Write the degree of the following polynomials.
a⁴+a³b²+a²b²+b⁵
Answer:
downloadable content of the year and I have a nice day ahead of
Answer:
5Step-by-step explanation:
The highest cumulative degree of variables is the degree of the polynomial.
a⁴+a³b²+a²b²+b⁵4, 5, 4, 5As we see the highest degree is 5
Please help. I’ll mark you as brainliest if correct
Answer:
bonds: $65,000
cd's: $30,000
stocks: $20,000
Step-by-step explanation:
b + c + s = 115000
0.045b + 0.0325c + 0.082s = 5540
b = c + 35000
b = 65,000
c = 30,000
s = 20,000
HaLP a beggar in need
Answer:
C) 2
Step-by-step explanation:
From the point (2,0), the next point on the graph is up 2, right 1, meaning that the slope is a positive 2.
The products of (2,3) and (-2,-3) is
Answer:
(-4,-9)
Step-by-step explanation:
multiply (a,b)
the area of an equilateral triangle of side 8cm is
pls i need answer ASAP
I'll mark brainliest for anyone who can help me
[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}a^2[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}(8)^2[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{64\sqrt{3}}{4}[/tex]
[tex]\\ \sf\longmapsto Area=16\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto Area=16\times 1.732[/tex]
[tex]\\ \sf\longmapsto Area=27.7cm^2[/tex]
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = - 1/2x
B.
y = 1/2x
C.
y = 2x
D.
y = -6x
E.
y = 6x
F.
y = 3x
Answer:
y=-6x
Step-by-step explanation:
using sets what is the intersection of a=(-2-1,0,1,7) I=(-2,-1,1,2,8)
Erik drew the diagram below of his irregularly shaped garden.
What is the area of Erik's garden? Show all work.
answer:
238 ft
explanation:
area of rhombus base×hight (14×12) = 168
find area of triangle 1/2(10)(14)=70
total area 168+70=238 ft.
A group of pirates captures Kevin, Lisa, Matt and Neal, and forces them to play a game. They each roll a fair 6-sided-die once. If the product of their roll is a multiple of 3, they all have to walk the plank, but otherwise they are safe. What is the probability that they survive? A)2/3 B)16/81 C)145/1296 D)65/81 E)625/1296 PLZ answer been waiting. I'll give 30 points
Answer: Option B, 16/81
Step-by-step explanation:
So we have 4 prisoners, they will roll a fair six side die and the product of the four rolls must NOT be a multiple of 3.
We know that every integer number can be "decomposed" into a product of prime numbers.
Then a number N, that is divisible by 3, can be written as:
N = 3*k
Where k is another integer.
Here we will have a product of 4 numbers, each of them are in between 1 and 6.
Now, if only one of the prisoners rolls a 3, then the product of the rolls will always be a multiple of 3. And if one of the rolls is 6 the same will happen, because 6 = 3.2
Then the probability of surviving is when in none of the four rolls we have a 3 or a 6.
Then we must have a 1, 2, 4 or 5.
The probability of 4 outcomes out of 6, is:
P = 4/6.
But we have 4 rolls, so we have that probability four times, and the joint probability will be equal to the product of the probabiliities for each roll, then the probability of surviving is:
P = (4/6)^4 = (2/3)^4 = 16/81
Answer:
16
Step-by-step explanation:
5 pencils for 15 dollers how much for each pencil
5 pencils = 15 dollors
1 pencil = 15/5 dollors
therefore 1 pencil = 3 dollors...
Answer:
Each pencil would cost $3.00
Step-by-step explanation:
If 5 costs $15, to find the cost of one you divide 15 by 5
15 ÷ 5 = 3
look at the image below
Answer:
4.2 mi²
Step-by-step explanation:
Volume of a cone = (1/3)πr²h, where r = radius and h = height
(1/3)πr²h
= (1/3)×π×1²×4
= 4π/3
= 4.2 mi² (rounded to the nearest tenth)
The volume of a rectangular prism is the products it’s dimensions. If the dimensions of a rectangle prism are approximately 1.08 feet,5.25 feet, and 3.3 feet ,what is the approximate volume of the cube?Express your answer using an approximate level of accuracy.
Answer:
18.711
Step-by-step explanation:
Volume = L * W * H
V = 1.08 * 5.25 * 3.3
1.08 * 5.25 = 5.67
5.67 * 3.3 =
V = 18.711
Which of the following is the correct factorization of 64x³ + 8? (2x + 4)(4x² - 8x + 16) (4x + 2)(16x² - 8x + 4) (4x - 2)(16x² + 8x + 4) (2x - 4)(4x² + 8x + 16)
Answer:
work is pictured and shown
9.3.2 Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d overbar and s Subscript d. In general, what does mu Subscript d represent? Temperature (degrees Upper F )at 8 AM 98.1 98.8 97.3 97.5 97.9 Temperature (degrees Upper F )at 12 AM 98.7 99.4 97.7 97.1 98.0 Let the temperature at 8 AM be the first sample, and the temperature at 12 AM be the second sample. Find the values of d overbar and s Subscript d.
Answer:
[tex]\frac{}{d}[/tex] = −0.26
[tex]s_{d}[/tex] = 0.4219
Step-by-step explanation:
Given:
Sample1: 98.1 98.8 97.3 97.5 97.9
Sample2: 98.7 99.4 97.7 97.1 98.0
Sample 1 Sample 2 Difference d
98.1 98.7 -0.6
98.8 99.4 -0.6
97.3 97.7 -0.4
97.5 97.1 0.4
97.9 98.0 -0.1
To find:
Find the values of [tex]\frac{}{d}[/tex] and [tex]s_{d}[/tex]
d overbar ( [tex]\frac{}{d}[/tex]) is the sample mean of the differences which is calculated by dividing the sum of all the values of difference d with the number of values i.e. n = 5
[tex]\frac{}{d}[/tex] = ∑d/n
= (−0.6 −0.6 −0.4 +0.4 −0.1) / 5
= −1.3 / 5
[tex]\frac{}{d}[/tex] = −0.26
s Subscript d is the sample standard deviation of the difference which is calculated as following:
[tex]s_{d}[/tex] = √∑([tex]d_{i}[/tex] - [tex]\frac{}{d}[/tex])²/ n-1
[tex]s_{d}[/tex] =
√ [tex](-0.6 - (-0.26))^{2} + (-0.6 - (-0.26))^{2} + (-0.4 - (-0.26))^{2} + (0.4-(-0.26))^{2} + (-0.1 - (-0.26))^{2} / 5-1[/tex]
= √ (−0.6 − (−0.26 ))² + (−0.6 − (−0.26))² + (−0.4 − (−0.26))² + (0.4 −
(−0.26))² + (−0.1 − (−0.26))² / 5−1
= [tex]\sqrt{\frac{0.1156 + 0.1156 + 0.0196 + 0.4356 + 0.0256}{4} }[/tex]
= [tex]\sqrt{\frac{0.712}{4} }[/tex]
= [tex]\sqrt{0.178}[/tex]
= 0.4219
[tex]s_{d}[/tex] = 0.4219
Subscript d represent
μ[tex]_{d}[/tex] represents the mean of differences in body temperatures measured at 8 AM and at 12 AM of population.