Answer:
[tex]S = (2,5)[/tex]
Step-by-step explanation:
Given
[tex]T = (0,3)[/tex]
[tex]Midpoint (M) =(1,4)[/tex]
Required
Determine the other end point (S)
Midpoint is calculated as thus:
[tex]M(x,y) = (\frac{S_x + T_x}{2},\frac{S_y + T_y}{2})[/tex]
This gives:
[tex](1,4) = (\frac{S_x + 0}{2},\frac{S_y + 3}{2})[/tex]
[tex](1,4) = (\frac{S_x}{2},\frac{S_y + 3}{2})[/tex]
Multiply through by 2
[tex]2 * (1,4) = (\frac{S_x}{2},\frac{S_y + 3}{2}) * 2[/tex]
[tex](2,8) = (S_x,S_y + 3)[/tex]
By comparison:
[tex]S_x = 2[/tex]
[tex]S_y + 3 = 8[/tex]
[tex]S_y = 8 - 3[/tex]
[tex]S_y = 5[/tex]
Hence:
The coordinates of S is
[tex]S = (2,5)[/tex]
The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years.
Required:
a, What was the initial population P0?
b. How fast is the population growing at t = 10?
Step-by-step explanation:
Let the initial population of a community be P0 and the population after time t is P(t).
If the population of a community is known to increase at a rate proportional to the number of people present at time t, this is expressed as:
[tex]P(t) = P_0e^{kt}[/tex]
at t = 5 years, P(t) = 2P0
substitute:
[tex]2P_0 = P_0e^{5k}\\2 = e^{5k}\\ln2 = lne^{5k}\\ln2 = 5k\\k = \frac{ln2}{5}\\k = 0.1386[/tex]
If the population is 9,000 after 3 years
at t = 3, P(t) = 9000
a) Substitute into the formula to get P0
[tex]9000 = P_0e^{0.1386\times 3}\\9000 = P_0e^{0.4158}\\9000 = 1.5156P_0\\P_0 = \frac{9000}{1.5156}\\ P_0 = 5938.24[/tex]
Hence the initial population is approximately 5938.
b) In order to know how fast the population growing at t = 10, we will substitute t = 10 into the formula as shown:
[tex]P(10) = 5938.24e^{0.1386(10)}\\P(10) = 5938.24e^{1.386}\\P(10) = 5938.24(3.9988)\\P(10) = 23,745.97[/tex]
Hence the population of the community after 10 years is approximately 23,746
2x + 7 = 13
Please help
Answer:
x=3
Step-by-step explanation:
Hope this helps u..
how many times can 130 go into 22? DIVIDE
130 cannot go into 22.
22 can go into 130 5 times
130 can not go into 22 idk if u meant 22 into 130
If a polygon is a pentagon, then it has 5 sides hypothesis conclusion
Answer:
Hypothesis
Step-by-step explanation:
a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon.
hope this helps
A math class consists of 26 students, 14 women, 10 men, and 2 non-binary. Two students are selected at random to participate in a probability experiment. Compute the probability that:
Answer:
there's a higher probability for females
ANSWER ONE PLS :(
Beyonce’s fish tank holds 180 gallons of water and is leaking at a rate of 8 gallons per day. Jay Z’s fish tank holds 160 gallons of water and is leaking at a rate of 6 gallons per day. At how many days will the two fish tanks have the same amount of water in them?
Justin Bieber’s sand castle is 180cm tall but the wind is blowing away sand at a rate of 8cm per minute. Taylor Swift’s sand castle is 160cm tall and she it adding sand to it at a rate of 6cm per minute. After how many minutes will their sand castles be the same height?
Answers:
1) 160 + 8x = 180 + 6x
2) 160 + 6x = 180 - 8x
The fish tank problem:
x = # of days
180 - 8x = 160 - 6x
Add 8x to both sides and subtract 160 from both sides.
20 = 2x
Divide both sides by 2
10 = x
It will take 10 days for the fish tanks to have the same amount of water in them.
The sand castle problem:
x = # of minutes.
180 - 8x = 160 + 6x
Add 8x to both sides and subtract 160 from both sides.
20 = 14x
Divide both sides by 14
x = 10/7 mins
After 10/7 mins their sand castles will be the same height
Find the exponential function that satisfies the given conditions: initial value = 70, decreasing at a rate of 0.43% per week
Answer choices:
A) f(t) = 70 x 0.9957^t
B) f(t) = 70 x 1.43^t
C) f(t) = 0.43 x 0.3^t
D) f(t) = 70 x 1.0043^t
(x-3) (x2+2x+1)
Foil method
Step-by-step explanation:
(x-3)(x^2+2x+1)
=x^3-3x^2+2x^2-6x+x-3
=x^3+2x^2-3x^2-6x+x-3
=x^3-x^2-5x-3
___________
Vanessa and Tia buy a printer. Vanessa pays $90 for her printer and each replacement ink cartage cost $25. The equation T=80+20c can be used to find the total cost, T, Tia pays for her printer plus C number of ink cartridges. Who buys the less expensive printer
Answer:
Vanessa, she only needs to buy one ink cartridge according to the question
where Tia has to buy more? I need more info on the question
Step-by-step explanation:
Tia bought less expensive printer.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Vanessa and Tia buy a printer. Vanessa pays $90 for her printer and each replacement ink cartage cost $25. The equation T = 80 + 20c can be used to find the total cost, T, Tia pays for her printer plus C number of ink cartridges.
Equation that represents the cost for Vanessa's printer is -
V = 90 + 25c
Equation that represents the cost Tia's printer is -
T = 80 + 20c
For {c} = 1, the cost for Vanessa's printer is -
V(1) = $115
For {c} = 1, the cost for Tia's printer is -
T(1) = 80 + 20 = $100
Therefore, Tia bought less expensive printer.
To solve more questions on algebraic expressions, visit the link below -
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3. Determine if the graph below is a function.
Explain your reasoning.
Answer:
A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on. A causal relationship is often implied (i.e. "x causes y"), but does not *necessarily* exist.
Step-by-step explanation:
Consider the following probability distribution function of the random variable X which represents the number of people in a group (party) at a restaurant: X P(X) 1 0.10 2 0.25 3 0.20 4 0.20 5 0.10 6 7 0.05 8 0.05 a. Find the population mean of X. b. Find the population variance and standard deviation of X. c. Find the probability that the next party will be over 4 people. d. Find the probability that the next three parties (assuming independence) will each be over 4 people.
Answer:
(a) 3.55
(b) 3.45 and 1.86
(c) 0.25
(d) 0.016
Step-by-step explanation:
The random variable X denotes the number of people in a group (party) at a restaurant.
(a)
The formula to compute the mean is:
[tex]\mu=\sum {x\cdot P(X=x)}[/tex]
Consider the Excel sheet attached.
The mean is, 3.55.
(b)
The formula to compute the variance is:
[tex]\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}[/tex]
Consider the Excel sheet attached.
Compute the variance as follows:
[tex]\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}\\\\=16.05-(3.55)^{2}\\\\=3.4475\\\\\approx 3.45[/tex]
The variance is, 3.45.
Compute the standard deviation as follows:
[tex]\sigma=\sqrt{\sigma^{2}}\\\\=\sqrt{3.45}\\\\=1.85742\\\\\approx 1.86[/tex]
The standard deviation is, 1.86.
(c)
Compute the probability that the next party will be over 4 people as follows:
[tex]P(X>4)=P(X=5)+P(X=6)+P(X=7)+P(X=8)\\\\=0.10+0.05+0.05+0.05\\\\=0.25[/tex]
Thus, the probability that the next party will be over 4 people is 0.25.
(d)
Compute the probability that the next three parties will each be over 4 people as follows:
It is provided that the three parties are independent.
P (Next 3 parties will be each over 4) = [P (X > 4)]³
[tex]=(0.25)^{3}\\=0.015625\\\approx 0.016[/tex]
Thus, the probability that the next three parties will each be over 4 people is 0.016.
Which coordinate pair is a solution of the linear
equation below?
-X + 3y = 21
Click on the correct answer.
(3,-8)
(-3,8)
(3,8)
Answer:
slope is 4/3 and y intercept is -7
Step-by-step explanation:
3y+21=4x.........now subtract 21 from each side
3y=4x-21......now divide all terms by 3
y=%284%2F3%29x-7......there ya go ...slope is 4/3 and y intercept is -7
Answer:
B (-3,8)
Step-by-step explanation:
awnser A is incorrect because if you switch out the x for 3 and the y for -8. The equation would look like -3+3×(-8)=21. and after multiplying 3×-8 which equals -24. The equation turns into -3+(-24)=21 . And after adding -3 and -24 you get -27=21
awnser B is correct because if you switch out the x for -3 and the y for 8. The equation would look like -3+3×8=21. After multiplying 3×8 which equals 24. The equation turns into -3+24=21. And after adding -3and 24 which is pretty much subtracting you get 21=21.
Best apologies if incorrect
the measure of an angle is 79.7 what is the measure of its complementary angle
Answer:
10.3
Step-by-step explanation:
Answer:
10.3°
Step-by-step explanation:
complementary angles are angles that sum up to 90°.
Therefore the complement of 79.7
= 90-79.7
=10.3°
Which of the following is equal to the opposite of −45?
−|45|
−|−45|
−(−45)
−45
Which of the following statements does not represent the same value as the others?
the absolute value of 9
the absolute value of negative 9
the opposite of 9
the distance between 0 and −9
All of the following are true statements except _____.
|−93| = −93
|−93| = 93
−|93| = −93
|93| = 93
If you move from zero to 15 on the number line, you are representing all of the following except _____.
the absolute value of 15
the distance between zero and 15
the opposite of −15
the opposite of 15
All of the following expressions are equal to N except _____.
−(− N )
− N
| N |
|− N |
Answer:
The first one
Step-by-step explanation:
HELP ME PLEASE I ALREADY GRAPHED IT BUT PLEASE ANSWER THE QUESTION BELOW
Answer:
32ed
Step-by-step explanation:
How many pounds are in 80 kilograms? Round your answer to the nearest whole number. Note: There are approximately 2.2lbs in a kg.
Answer:
176.37 orrrr 176
Step-by-step explanation:
Answer:
176 pounds
Step-by-step explanation:
7) Order the numbers from least to greatest.
A. 6.66
B. 6.07
C. 7
D. 6.32
the Answear is B,D,A,C
The mean of the standard normal distribution is 1 and the standard deviation is 0. Group of answer choices False True
Answer:
True
Step-by-step explanation:
The standard normal distribution is special case of normal distribution which centers at 0 thus the mean μ of standard normal distribution is zero and the dispersion from mean value is unity measured by standard deviation σ.
Thus, the mean of standard normal distribution is zero and standard deviation is unity.
a pizzeria had 4 cans of tomato sauce how many pizzas could they make with the cans if each pizza took one fourth of a can
Answer:
16 pizzas.
Step-by-step explanation:
That is 4 divided by 1/4
= 4 * 4/1
= 16.
Answer:
16
Step-by-step explanation:
There are 4 pizzas per can and you have 4 cans.
4 x 4 = 16
Kumar is opening a lemonade stand. He spent $4.50 to build the stand and $2.50 for lemons and sugar. He has enough ingredients to make 20 glasses of lemonade. How much should he charge for one glass of lemonade to cover his expenses and make $10 in profit?
Round to the nearest cent.
Timed test
Answer:
profit = revenue - cost
10 = 20x - (4.5 + 2.5)
10 = 20x - 7
10 + 7 = 20x
17 = 20x
17/20 = x
0.85 = x
check...
profit = revenue - cost
10 = 20(0.85) - 7
10 = 17 - 7
10 = 10 (correct)
so he would have to sell each cup at 0.85 ccents to make a profit of $ 10
Step-by-step explanation:
Answer:
I cant find the next one hehrh
I need help with this ASAP !! I’m failing !!!
Answer:
c=130,b=50
Step-by-step explanation:
[tex]c = 180 - 50 = 130[/tex]
[tex]b = 180 - 130 = 50[/tex]
i think this is the answer
Intro:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
<b and 50° are vertical angles so that means they are congruent. So that means <b is 50.
<c and 50° are supplementary angles which means when you add them you should get 180. So if do 180 - 50 we will get 130. So that means <c is 130°.
Ellie the elephant has some peanuts. She eats up 49 peanuts. Now Ellie the elephant has 31 peanuts. How many peanuts did she have before?
Answer:
80
Step-by-step explanation:
do: 49+31=Your answer
Ellie had 80 peanuts before she ate 49 of them.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of peanuts Ellie had before she ate 49 of them.
After eating 49 peanuts, Ellie has 31 peanuts left, so we can write an equation:
x - 49 = 31
To solve for x, we add 49 to both sides of the equation:
x - 49 + 49 = 31 + 49
Simplifying, we get:
x = 80
Therefore, Ellie had 80 peanuts before she ate 49 of them.
To learn more on Equation:
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If the points P(5,2),Q(0,7) and R(-5,2) are drawn on coordinate plane,where must point S be located so that figure PQRS is square.
Answer:
(0, -7) i think
hope this helps :3
sorry if im wrong
Simplify this expression
(6 x 2) + 8 - (40 - 4 x 5)
8 Simplify this expression:
30
12
Answer:
the first one, if you solved it using the calculator, the answer will be 0
point Q was rotated about the origin (0,0) by 180
Answer:B
Step-by-step explanation:
The coordinates of the image of the rotation of the point Q is:
Q' = (4, 2)
What is the image of the rotation?
We can see that the original coordinates of point Q are (-4, 0).
If we apply a rotation of 180° about the point (0, 0), it is equivalent to a reflection around the y-axis.
It only changes the sign of the x-component.
Then the image of the rotation is:
Q' = (4, 0)
If you want to learn more about rotations:
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Consider matrix A.
A=[−385−123]
What matrix results from the elementary row operations represented by −3R2+4R1?
Enter your answer by filling in the boxes.
Answer:
[tex]\left[\begin{array}{ccc}-3&8&5\\-9&26&11\end{array}\right][/tex]
Step-by-step explanation:
Given the matrix A
[tex]\left[\begin{array}{ccc}-3&8&5\\-1&2&3\end{array}\right][/tex]
We are to find the matrix that results from the elementary row operations represented by −3R2+4R1
R2 means row 2
R1 means row 1
Applying the elementary row operation will change the second row of the matrices.
For the first column, second row (a₂₁)
If R1 = -3, R2 = -1
a₂₁ = -3R2+4R1
a₂₁ = -3(-1)+4(-3)
a₂₁ = 3-12
a₂₁ = -9
For a₂₂
If R1 = 8, R2 = 2
a₂₂ = -3R2+4R1
a₂₂ = -3(2)+4(8)
a₂₂ = -6+32
a₂₂ = 26
For a₂₃
If R1 = 5, R2 = 3
a₂₃ = -3R2+4R1
a₂₃ = -3(3)+4(5)
a₂₃ = -9+20
a₂₃ = 11
Hence the resulting matrix will be:
[tex]\left[\begin{array}{ccc}-3&8&5\\-9&26&11\end{array}\right][/tex]-3R2+4R1
Answer:
[-3 5 2]
[-36 23 -1]
Step-by-step explanation:
Note abidemiokin did the steps right just has the "given" wrong.
Given the matrix A
[-3 5 2]
[ 8 -1 3]
We are to find the matrix that results from the elementary row operations represented by −3R2+4R1
R2 means row 2
R1 means row 1
Applying the elementary row operation will change the second row of the matrices.
For the first column, second row (a₂₁)
If R1 = -3, R2 = 8
a₂₁ = -3R2+4R1
a₂₁ = -3(8)+4(-3)
a₂₁ = -24-12
a₂₁ = -36
For a₂₂
If R1 = 5, R2 = -1
a₂₂ = -3R2+4R1
a₂₂ = -3(-1)+4(5)
a₂₂ = 3+20
a₂₂ = 23
For a₂₃
If R1 = 2, R2 = 3
a₂₃ = -3R2+4R1
a₂₃ = -3(3)+4(2)
a₂₃ = -9+8
a₂₃ = -1
Hence the resulting matrix will be:
[-3 5 2]
[-36 23 -1] -3R2+4R1
The 5 members of the
Jackson family went
to a hockey game.
They paid $20 for
snacks. In all, the
tickets cost 4 times
the cost of the snacks.
How much did a
single ticket cost?
Answer:
16
Step-by-step explanation:
80 divide by 5 is 16
Round 24.9652 to
1 decimal Place
Answer:
2.5 one decimal rounding off means to make it to one decimal place.the no is 24.9652 if you want to round of then you have to put decimal after 2 only then it will be one decimal place .this is because when we see a number after the point greater than 5 then we add 1 to the right side .now if we add 1 to the right side of 24.9652 by rounding off and making it to one decimal place then it will be 2.5.
Please need help thank you
Answer:
31825 is your answer. Hope that helps.
Answer:
Lydia´s address is 8 Cypress street.
Step-by-step explanation:
5 digit.
6 less than 7.
3 and 1 are the product.
Simplify them.
6 - 7 + 3 + 1 = 5
Simplify.
6 - 7 = -1.
Then Simplify.
-1 + 3 = 2.
Simplify.
2 + 1 = 3.
3 + 5 = 8.
Hope this helps.
Have a good night ma´ám/sir.
Be safe!
A 168-inch board is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
Answer:
42
Step-by-step explanation:
168 Inches. One is three times the length of the other so, the bigger piece is 3/4 while the shorter is 1/4. Simply multiply 1/4 by 168. You get 42.