eg. the first loan is x, the second loan will be (9,000 - x)
First, we need to make an equation based on the problem
first interest + second interest = 492
5% of x + 6% of (9,000 - x) = 492
This is the equation
Second, solve the equation and find out the value of x (first loan)
0.05x + 0.06(9.000 - x) = 492
0.05x + 540 - 0.06x = 492
-0.01x + 540 = 492
-0.01x = 492 - 540
-0.01x = -48
x = -48/-0.01
x = 4,800
Third, find the second loan
9,000 - x
= 9,000 - 4,800
= 4,200
SUMMARY
The first loan that has interest of 5% is $4,800
The second loan that has interest of 6% is $4,200
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
A) x – 6
B) x – 3
C) x + 1
D) x + 6
Answer:
D. x + 6
Step-by-step explanation:
In the given graph, we have 3 x-intercepts values, which are points at which the line intercepts the x-axis. They are, -6, -3 and 0.
Each of these x-intercepts can be written as a factor of a polynomial function as follows:
x = -6
x = -6 + 6
x + 6 = 0
x = -3
x = -3 + 3
x + 3 = 0
x = 0
Therefore, the factor of the polynomial function must be: x + 6
Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown. Circles X and Y are shown. Circle X has a radius of 6 units and circle Y has a radius of 2 units. Which steps would prove the circles similar? Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 4. Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 4. Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3. Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3.
The scale is 6/2 = 3
tanslate the circles to have the same center point and scale circle y by a factor of 3.
The answer is C.
Answer:
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
Step-by-step explanation:
To prove circles are similar:
Translate the circles so that they share a common center point. (The circles are now concentric as they have the same center).Dilate the smaller circle to increase its size to coincide with the larger circle. The amount that the circle needs to be dilated by is the scale factor.As the radius of circle Y is 2 and the radius of circle X is 6, determine the scale factor by dividing the larger radius by the smaller radius:
scale factor = 6 ÷ 2 = 3
Solution
Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 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.
F(x)=-14/x^2 average rate
Answer:
I am assuming that the function is f(x)=20(14)x, if it is
then f(x)=280x , The average rate of change between x =1 and x=2
is the slope of the function between the 2 and 1
Average rate of change = [f(b)-f(a)/b-a] let a and b be x and y
f(a)=f(x)=f(1)=280x1=280
f(b)=f(y)=f(2)=280x2=560
Average rate of change = [f(b)-f(a)/b-a]=[(560-280)/(2-1)]=280
There is no decimal unless the function given is wrong
Step-by-step explanation:
plss help me plss #4
Hey there!
Step 1: we multiply 5 by 1/4
=> [tex]5 ÷ \frac{1}{4} [/tex]
=> 5 ×[tex]\frac{4}{1} [/tex]
=> 20
Answer:
20 lengths
explanation:
total length of swine: 5 m
each length: [tex]\sf \frac{1}{4}[/tex] m
amount of lengths:
5 ÷ [tex]\sf \frac{1}{4}[/tex] [ division number sentence ]
5 * 4
20
20 such length can be made.
If 1 m = 100 cm, how many centimeters are in 17 meters?
If 1 m = 100 cm, how many centimeters are in 17 meters?
Answer:
It would be 1,700
Step-by-step explanation:
It's simple: just add 2 zeros onto whatever the meter amount is and change the label to cm!
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
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.
6/100+5/10+6/x+3=3.62 solve for the value of x
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)
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
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:
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
13.026 in decimal form
Answer:
Write 13.026 as
13.026
1
Multiply both numerator and denominator by 10 for every number after the decimal point
13.026 × 1000
1 × 1000
=
13026
1000
Reducing the fraction gives
6513/500
Step-by-step explanation:
. Day before today Tuesday.
Match the following.
Answer:
1. regular polygon
6. triangle
4. side of polygon
5. polygon
3. quadrilateral
2. vertex
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
1 + 16 = distance squared
Distance = √(17) Because 1 + 16 = 17
If y equals three what is the value of 5Y + 6
Answer:
21
Step-by-step explanation:
If y = 3 then multiply 5 x 3=15. Add 6 and you get 21. 21 is the correct answer.
3(2x−7)+ 1/3 (7x+2)
Please help Quick
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
Find the value of x in the triangle shown below 6 2
Answer:
B.
Step-by-step explanation:
use the pythagorean theorem
a^2+b^2=c^2
2^2+x^2=6^2
4+x^2=36
-4 -4
x^2=36
√x=√36
x=√36
The side length of one cube is 4 cm.
What is the volume of one cube?
Answer:
64 cm³
Step-by-step explanation:
Volume of cube
[tex] = \textcolor{steelblue}{\text{side}\times{\text{side} } \times\text{side}}[/tex]
[tex] = \textcolor{steelblue}{\text{side} {}^{3} }[/tex]
Given that the side is 4cm,
volume of cube
= 4³
[tex] = \textcolor{red}{64 \: \text{cm} {}^{3} }[/tex]
.please help meeeeeee
B(c) is a function
True
or
False
Answer: False :)
Step-by-step explanation:
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
This figure represents a model ramp that is being covered with nonslip material on all sides.
How much nonslip material is needed to cover the ramp?
A. 216 in²
B. 240 in²
C. 264 in²
D. 278 in²
The surface area of the given ramp is 264 in²
How to calculate the surface area of the ramp
The given ramp is a triangular based prism is calculated as;
Surface area = Area of all the faces of the prism
Surface area = 2[0.5(8*6)] + (6*9) + (9*10) + (8*9)
Surface area = 48 + 54 + 90 + 72
Surface area = 264 in²
Hence the surface area of the given ramp is 264 in²
Learn more on surface area here: https://brainly.com/question/16519513
Answer:
264
Step-by-step explanation:
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 + 19find the greatest number that exactly divide 16 and 24. ind the ornatost number that diido 20 and 20 min
Step-by-step explanation:
The greatest common factor (GCF) is the largest common factor that the numbers share. Here, 8 is the largest common factor of 16 and 24. So the GCF of 16 and 24 is 8.
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.
Learn more about Fugitive Slave Act from
https://brainly.com/question/542501