The amount he invested in the account that yields 4.5% interest is $7,500.
The amount he invested in the account that yields 2.5% interest is $12,500.
What is the system of equations that represent the question?a + b = $20,000 equation 1
0.045a + 0.025b = $750 equation 2
Where:
a = amount he invested in the account that yields 4.5% interest
b = amount he invested in the account that yields 2.5% interest
How much was invested in the account that yields 4.5% interest?Multiply equation 1 by 0.025
0.025a + 0.025b = 500 equation 3
Subtract equation 3 from 2
250 = 0.02a
a = 12,500
How much was invested in the account that yields 4.5% interest?Subtract 12,500 from 20,000
20,000 - 12,500 = $7,500
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2. Peter drew two rays, AC and AP with A as a common endpoint. Which of the following statements
might describe Peter's drawing?
1.
II.
AC and AP are parallel.
PAC is an angle
AC and AP are perpendicular
III.
A. I and 11
B. II and I
C. I and 111
D. I, II, and III
Complete question is;
Peter drew two rays, AC and AP with A as a common endpoint. Which of the following statements
might describe Peter's drawing?
I. AC and AP are parallel.
II. PAC is an angle
III. AC and AP are perpendicular
A. I and II
B. II and III
C. I and 111
D. I, II, and III
Answer:
Option B: II & III
Step-by-step explanation:
We are told that Peter drew two rays which are AC and AP.
We are told that A is a common endpoint.
If A is a common endpoint, it means the 2 rays interaction point at A is at an angle.
The angle could also be 90° which means it's possible that the rays AC and AP are perpendicular.
Thus, the correct statements that describe his drawing are: II & III
L need help with this pls
Answer:
answer is 150
Step-by-step explanation:
answer is 150
6/100+5/10+6/x+3=3.62 solve for the value of x
Find the product.
A.
3x2 − 11x − 20
B.
3x2 − 20x
C.
3x2 − x − 20
D.
3x2 − 3x − 60
Answer:
A. -1. (27)
B. 0.3
C. -14
D. -18
Step-by-step explanation:
I just use the calculator
helpppppp ur girl out!!!
Answer:
139.25 m²
Step-by-step explanation:
Area of the square = 10 * 10 = 100 m²
Radius of the semicircle = 5 m
Area of the semicircle = π(5)²/2 = 39.25 m²
Total area = 100 + 39.25 = 139.25 m²
Help help help help math math
Answer:
-2x+y=-3
Step-by-step explanation:
mr clean
2x+y=-3
on algebra, to move something to the other side of the equal sign you must make the variable cancel out.
so, in this case, we will add 2x to cancel out the -2x. after that rules of algebra state whatever we do to one side of the equal sign, we must do to the other. so we get 2x on the left side, resulting in 2x+y=-3
Blood GroupO A B ABEthnic Group 1)0.082 0.101 0.005 0.0042)0.140 0.141 0.018 0.0093)0.215 0.195 0.070 0.020Explain in context what each of these probabilities represents. (Select all that apply.)If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(A | C).If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(C | A).If a person has type B blood, the probability that he is from ethnic group 3 is given by P(C | A).If a person has type A blood, the probability that he is from ethnic group 3 is given by P(C | A).If a person has type A blood, the probability that he is from ethnic group 3 is given by P(A | C).If a person has type B blood, the probability that he is from ethnic group 3 is given by P(A | C).
Answer:
P (A|C) = 0.39
P (C|A) = 0.446
Step-by-step explanation:
The data provided is as follows:
Blood Group
O A B AB Total
1) 0.082 0.101 0.005 0.004 0.192
Ethnic Group 2) 0.140 0.141 0.018 0.009 0.578
3) 0.215 0.195 0.070 0.020 0.500
Total 0.437 0.437 0.093 0.033
The event C = {Ethnic group 3 is selected}
Compute the value of P (A|C) as follows:
[tex]P(A|C)=\frac{P(A\cap C)}{P(C)}=\frac{0.195}{0.5}=0.39[/tex]
If we know that the individual came from ethnic group 3, the probability that he has type A is given by P(A | C) = 0.39.
Compute the value of P (C|A) as follows:
[tex]P(C|A)=\frac{P(A\cap C)}{P(A)}=\frac{0.195}{0.437}=0.446[/tex]
If we know that the individual has type A blood group, the probability that he came from ethnic group 3 is given by P(C | A) = 0.446.
Hi I really need help please help me
Answer:
B
Step-by-step explanation:
Y-intercept is where a graph crosses the y-axis at x=0
f(x) = 6x^2 + 18x + 3
f(0) = 6(0)^2 + 18(0) + 3 = 3
From the plot, g(x) at x=0 is 6.
So the answer is B. g has a greater y-intercept than f.
For f(x)
[tex]\\ \rm\rightarrowtail y=6x^2+18x+3[/tex]
Put x =0[tex]\\ \rm\rightarrowtail y=6(0)^2+18(0)+3=3[/tex]
Y intercept at 3From the graph
y intercept of g(x)=6
So option B is correct
Twelve large bottles of water cost $9. How many bottles can you buy for $3?
Answer:
4
Step-by-step explanation:
12/3= 4
Answer:
4 bottles
Step-by-step explanation:
Use a proportion.
12 bottles are to $9 as x bottles are to $3.
12/9 = x/3
4/3 = x/3
x = 4
Answer: 4 bottles
A town had a population of 10,000 people. the population decreased 3% each year. what was the population 5 years later?
Answer:
8,588 people
Step-by-step explanation:
We can represent this exponential decay as [tex]P=10000(0.97)^n[/tex] where [tex]n[/tex] is the number of years later:
[tex]P=10000(0.97)^n\\\\P=10000(0.97)^5\\\\P=10000(0.8587340257)\\\\P=8587.340257\\\\P\approx8588[/tex]
Therefore, the population 5 years later will be 8,588 people
Step-by-step explanation:
Ok so after the first year we expect the population to reach 97% of it's initial population.
So 97% of 10 000 can be written as:
97/100 ×10 000=0.97×10 000=9 700
After the second year we expect the population to drop to 97% of the first year's population
So, it can be said that:
0.97×9700= 9409
Similarly after year 3,
0.97× 9409= 9126.73
Year 4,
0.97× 9126.72= 8852.9281
Year 5,
0.97× 8852.9281=8587 rounded to the nearest number
The new population would be 8587
What are the steps of solving 5r + 16r - 6
Answer:
Step-by-step explanation:
Combine like terms:
21r - 6
micheal is knitting a blanket. she can knit 6 rows per minute. which rate is equivalent to the rate at which micheal is knitting?
Answer:6 rows per minute
Step-by-step explanation:
find 3 consecutive integers if three times the first integer is two times the third.
Answer:
4, 5, and 6
Step-by-step explanation:
Three Consecutive integers are x, x+1, x+2
We are given 3 times the first integer is 2 times the third
So
3x = 2(x+2)
Solve for x
3x = 2x+4
x = 4 (first integer)
so the 3 integers are 4, 5, and 6
You pull out the plug from the bathtub. After 40 seconds, there are 13 gallons of water left in the tub. One minute after you pull the plug, there are 10 gallons left.
Assume that the number of gallons varies linearly with the time since the plug was pulled.
Write the particular equation expressing the number of gallons (g) left in the tub in terms of the number of seconds (s) since you pulled the plug.
Answer:
g = -3/20s + 19Step-by-step explanation:
Let's assume this is a function
The points are
(40, 13) and (60, 10)Since it is linear relation, we'll get the slope intercept form
g = ms + b, where g- number of gallons, s- time in seconds, b- y interceptUsing the points, let's calculate the formula
m = (10 - 13)/(60 - 40) = -3/2010 = -3/20*60 + b10 = - 9 + bb = 19So the formula is:
g = -3/20s + 19Enter the mixed number as an improper fraction.
2 1/4
Answer:
9/4
Step-by-step explanation:
1.If +20 represents 20 m above sea level, then –20 represents?
1.If +90 represents a movement of 90 m to the north then _90 represents?
Answer:
-20 represents 20m below sea level.
-90 represents a movement of 90m to the South.
Luigi's Pizzeria is having a Pi Day lunch special where you can choose either one 18" pizza or two 12" pizzas. The cost of each option is the same, $14.00. Which option gets you more pizza? Note: Pizza is measured by the diameter so a 10" pizza is 10" in diameter.
The option which gets you more pizza is two 12" pizzas.
What is a Diameter?It can be defined as the longest chord of the circle and it is twice the size of a radius.
We were told that one 18" pizza or two 12" pizzas costs the same and the one with the largest size is two 12" pizzas which was why it was chosen as the most appropriate choice.
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solve the inequality −23s ≥6 s=−9
Answer:
Given:
s = -9
We exchange this value into our inequality;
-23s ≥ 6
-23(-9) ≥ 6
207 ≥ 6
Please please please help!!!!
I will start off by defining the angle
[tex] \alpha = 90 - \beta [/tex]
as being the angle between altitude and the hypotenuse of the triangle.
[tex] \alpha = 90 - 30.1 = 59.9[/tex]
Using trigonometry, and the definition of the tan function defined by
[tex] \tan( \alpha ) = \frac{opp}{adj} = \frac{x}{1836.3} [/tex]
[tex] \tan( 59.9 ) = \frac{x}{1836.3} [/tex]
[tex]x = 1836.3 \times \tan(59.9) [/tex]
[tex]x = 3167.78[/tex]
Rounding to the nearest tenth
[tex]x = 3170[/tex]
What is 50/45 simplified
Answer:
10/9 is the simplified fraction for 50/45.
Step-by-step explanation:
The girls varsity basketball team had 850 fans attend their first game of the season. For the second game they had 1037 fans attendance. What was the percentage increase in attendance?
Answer:
22%
Step-by-step explanation:
It's 22% because if we want to find the percent change in something, the formula for that is new number - (minus) old number, than divide by old number, and lastly multiply by 100. So,
1. 1037 - 850 = 187
2. 187 / 850 = 0.22
3. 0.22 x 100 = 22 --> 22%
How did the Fugitive Slave Act of 1850 affect enslavement?
It stopped enslavers from looking for people who had run away.
It give citizenship to any enslaved person who ran away to a free state.
It punished people who helped enslaved people escape.
It allowed enslaved persons the right to trial by jury.
The Fugitive Slave Act of 1850 affect enslavement is one that stopped enslavers from looking for people who had run away.
What was the impact of the Fugitive Slave Act of 1850?This Act was said to have hinder enslavers from searching for people who had run away.
It was said to have given citizenship to any kind of enslaved person that has ran away to a free state. It also punished individuals that helped enslaved people escape. This law was passed on September 18, 1850.
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Simplest form of 6 3/8 + 7 5/6 =
Step-by-step explanation:
first, add the whole numbers
6 + 7 = 13
then the fractions
3/8 + 5/6
we need to get common denominators
do you know how to do that
Which of these is a counterexample to the conditional statement, "If a number ends in the digit 5, then it is divisible by 3"
Answer:
5 times 3 is 15 and if you divide 3 by 15 you answer will be 5
Step-by-step explanation:
a rectangle has a length 12 meters and a width of 400 centimeters. what is the perimeter, in cm of the rectangle
Answer:
P= 3200 cm
Step-by-step explanation:
Perimeter = 2(l+w)
In this case since the perimeter has to be in centimeters, we have to change the length of the rectangle to centimeter.
12 meter to centimer = 12 x 100 = 1200 cm
2( 1200 +400)
2 (1600)
= 3200 cm
And equation for loudness in decibels is L equals 10logR where R is the relative intensity of a sound. Sounds that reach levels of 120 decibels , what is the density?
Answer:
10 log(R) = 120 log(R) = 12 R = 1012 ---- From the definition of a logarithm: 10log(x) = x
Explanation :
A = log10[1000(1 + 0.04)5]
an unknown or changeable quantity is called
The term varies or changes, and often there are restrictions set on the variable (eg: x is positive). Think of a variable as a placeholder for a number.
1)
Which of the following is an example of mistaking correlation for causation?
A. Running more frequently causes you to buy more running shoes.
B. Living in a Spanish-speaking country causes you to do poorly on the AP
English exam
C. Not going to school causes you to do poorly on the AP English exam.
D. Running more frequently causes you to buy more running outfits.
ОА
OB
Ос
OD
HINT
SUBMIT
2)
B(c) is a function
True
or
False
Answer: False :)
Step-by-step explanation:
(3x+8) + (2x+4)= 32
Answer
4
Answer:
[tex]\huge\boxed{x=4}[/tex]
Step-by-step explanation:
[tex](3x+8)+(2x+4)=32\\\\3x+8+2x+4=32\qquad|\text{combine like terms}\\\\(3x+2x)+(8+4)=32\\\\5x+12=32\qquad|\text{subtract 12 from both sides}\\\\5x+12-12=32-12\\\\5x=20\qquad|\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{20}{5}\\\\x=4[/tex]