Answer:
The bank loan out at $5000 at 9%
Step-by-step explanation:
A bank loaned out $20,000
Let x be the amount loaned at at the rate of 9% per year
So, 20000-x amount loaned at at the rate of 17% per year
Formula : [tex]A =P(1+r)^t[/tex]
Amount at 9% interest in 1 year
[tex]A=x(1+0.09)^1[/tex]
A=1.09x
Interest = Amount - Principal = 1.09x-x=0.09x
Amount at 17% interest in 1 year
[tex]A=(20000-x)(1+0.17)^1[/tex]
A=1.17(20000-x)
Interest = Amount - Principal = 1.17(20000-x)-(20000-x)
We are given that the interest received in one year totaled $3000
So,1.17(20000-x)-(20000-x)+0.09x=3000
x=5000
So, the bank loan out at $5000 at 9%
Which sequence shows a pattern where each term is 1.5 times the previous term?
–4, 6, –9, 13.5, …
10, 15, 25, 40, …
98, 99.5, 101, 102.5 …
–200, –300, –450, –675, …
Answer:
-200, -300, -450, -675
The geometric sequence which shows a pattern in which each term is 1.5 times the previous term is A = -200 , -300 , -450 , -675 ...
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric progression be represented as A
Now , the value of A is
A = -200 , -300 , -450 , -675 ...
The common ratio of the GP = second term / first term
On simplifying , we get
r = -300 / -200
r = 3/2
r = 1.5
Therefore , each term is 1.5 times the previous term
Hence , the GP is solved
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Find the volume of the given solid. Leave your answer in terms of pi
Answer: 465 π
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Volume of a cylinder (V): π x (diameter /2) ² x height
Replacing with the values given and solving for v (Volume)
V = π x (6/2)²x 50
V = 450π
And then for the bottom part:
Volume of a cone = 1/3 x π x (diameter/2)^2 x height
Replacing with the values given:
V = 1/3 π (6/2) ^2 (5) = 15π
Finally we add the volumes:
450π+15π = 465 π
In conclusion, the volume of the solid is 465π m3.
Feel free to ask for more if needed or if you did not understand something
Find the radius round your answer to the nearest tenth
Answer:
r = 3m
Step-by-step explanation:
Formula for the volume of a sphere: V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
We want to find the radius so we use algebra to rearrange the equation to make the radius (r) the subject of the equation
Divide both sides by [tex]\frac{4}{3}[/tex]
[tex]\frac{3V}{4}[/tex] = [tex]\pi[/tex][tex]r^{3}[/tex]
Divide both sides by [tex]\pi[/tex]
[tex]\frac{3V}{4\pi }[/tex] = [tex]r^{3}[/tex]
Take the cube root of both sides
[tex]\sqrt[3]{\frac{3V}{4\pi } }[/tex]= r
Substitute V = 36[tex]\pi[/tex] into the equation
r = [tex]\sqrt[3]{\frac{3(36\pi) }{4\pi } }[/tex]
Expand the bracket
r = [tex]\sqrt[3]{\frac{108\pi }{4\pi } }[/tex]
Divide 108[tex]\pi[/tex] by 4[tex]\pi[/tex] (For this, the two [tex]\pi[/tex] in the numerator and denominator cancel each other out, and you only need to divide 108/4)
r = [tex]\sqrt[3]{27}[/tex]
The cube root of 27 is 3, because [tex]3^{3}[/tex] = 3 x 3 x 3 = 27
r = 3
Is the sqre root of 16 + 3/4 irrational
The square root of 16 is a rational number. The square root of 16 is 4, an integer. This is because 16 is a perfect square.
An rock is thrown upward from a platform that is 202 feet above ground at 70 feet per second. Use the projectile formula
h
=
−
16
t
2
+
v
0
t
+
h
0
to determine when the rock hit the ground.
[Recall that
v
0
is the initial velocity of the object and
h
0
is the inital height of the object.]
Answer:
in 6.36004793262 seconds
Step-by-step explanation:
h(t) = –16t^2 + v*t + h
0=-16t^2 + 70*t+ 202
t=(-70 ± sqrt((70^(2)-4*(-16)*202))/(2*(-16))
t=(-70 ± sqrt(4900+64*202))/-32
t=(-70 ± sqrt(4900+12928))/-32
t=(-70 ± sqrt(17828))/-32
t=(-70 ± sqrt(2*2*4457))/-32
t=(-70 ± 2 sqrt(4457))/-32
t=(-70 + 2 sqrt(4457))/-32
t=-1.98504793262
t=(-70 - 2 sqrt(4457))/-32
t=6.36004793262
since we need the time it will fall to the ground after it was thrown and time can't be negative, answer is
in 6.36004793262 seconds
I don't know till what I am supposed to round, so I will leave it there.
Leah drives her truck 270KM in the same time Deborah drives her car 250KM. If Leah drives 4km/h faster than Deborah. What is each of their driving speeds?
Answer:
Leah: 54km/h
Deborah: 50 km/h
Step-by-step explanation:
250+4x=270
4x=20
x=5
both drove 5 hours
Deborah:
250/5=50km/h
Leah:
270/5=54km/h
Question 1(Multiple Choice Worth 1 points)
(08.01 MC)
What are the zeroes of f(x) = x2 − x − 2?
x = −2, 1
x = 2, −1
x = −2, −1
x = 2, 1
Answer:
I think its x = 2 , -1 but i don't really know how to explain things sorry
An architecture firm makes a blueprint
for a building with scale 1 in. = 8 ft. If
the building's length is 82 feet, what is
the length of the blueprint?
Answer:10.25
Step-by-step explanation:
What is the slope of the line described by the equation below?
y- 5= -3(x - 17)
O A. -3
B. 3
O c. 5
OD. -5
Hellppp
Write an equation to represent the total cost for a certain number of cans. Use “c” for cost and “n” for number of cans.
Answer:
C = 1.25n
Step-by-step explanation:
From the given table,
There is a common difference of $1.25 in every successive term to the previous term of the total cost,
Difference in the costs of 2 cans and 1 can = $2.50 - $1.25 = $1.25
Similarly, Difference in the costs of 3 cans and 2 cans = $3.75 - $2.50 = $1.25
Total cost of the cans are forming an Arithmetic sequence, explicit formula the sequence will be,
[tex]T_n=a+(n-1)d[/tex]
= 1.25 + (n -1)(1.25)
Or, C = 1.25 + 1.25n - 1.25
C = 1.25n
Viet solved a quadratic equation. His work is shown below. In which step did Viet make an error? Step 1,2,or 3?
Answer:
Step 1
Step-by-step explanation:
he added 4 to the other side instead of taking away 4
Answer:
step 1
Step-by-step explanation:
Which of the following graphs represents exponential decay?
Answer:
C
Step-by-step explanation:
C is the only viable answer, because it it the only one that decreases as x approaches infinity. Exponential decay decreases, hence the decay part.
The graph of the unknown function C represents exponential decay.
The correct option is C.
What is exponential decay?An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.
The exponential decay function:
Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.
Given:
Two graphs of the unknown functions are given.
And when the value of x approaches to positive infinity,
the value of y decrease exponentially.
And from the above definition,
the graph is C.
Therefore, the graph is C.
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The largest colored pencil drawing ever documented is 500 yards long. How many feet is that? Show or explain your reasoning.
Answer:
1500 ft
Step-by-step explanation:
1 yd=3 ft
500 yd*3 ft/yd=1500 ft
Answer:
1500 ft
Step-by-step explanation:
Multiply 500 yds by the conversion factor derived from 1 yd = 3 ft:
500 yd 3 ft
----------- * ----------- = 1500 ft
1 1 yd
Select the ordered pair that is a solution
of this equation.
x-2y = -8
Click on the correct answer.
(2,1)
(2,5)
(5.2)
Answer:
(2,5)
Step-by-step explanation:
Choose values for x and substitute in to find the corresponding y values.
(2) - 2y = -8
2 = 2y - 8
10 = 2y
5 = y
(2,5)
I don't know what to put in theboxes.
I guess you have to put the amounts in the boxes based on your data :) hope that helped a little
I think it should go like
3|6
1|2
Solve this inequality.
8x + 6 < 54
A. x < 6
B. x < 7.5
C.x < 14
D. x < 384
Answer:
x < 6
Step-by-step explanation:
8x + 6 < 54
Subtract 6 from each side
8x+6-6 < 54-6
8x < 48
Divide each side by 8
8x/8 < 48/8
x < 6
A can of 3 tennis balls sells for $2. If Sal spent more than $24 on tennis balls, which inequality can be used to find n, the number of tennis balls Sal could have bought?
A. 2/3n > 24
B. 3/2n > 24
C. 2n >24
D. 3n > 24
Answer:
the answer is A
Step-by-step explanation:
i went but the all the other answers in and it was left to A
Option A is the correct answer.
What is the cost of one item if the cost of m items is x?
The cost of one item is obtained by dividing the total cost of m items by the number of items.
Given
The total amount spent by Sal > $24,
cost of 3 tennis balls = $2.
Cost of n tennis balls
Divide the cost of three tennis balls by 3 to get the cost of one tennis ball, which is $2/3.
Let the number of balls bought by Sal be n, and P be the cost of n tennis balls.
Total amount spent by him, P = cost of one ball × number of balls bought = ($2/3) × n = $(2/3)n.
Obtain the inequality
Since the total amount spent by him > $24, using the above value of P we obtain,
$(2/3)n > $24.
The inequality to be used to find n is (2/3)n > 24.
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Why is sexual reproduction citical in the process of evolution
Answer:
sexual reproduction provides evolutionary advantages to organisms that employ this mechanism to produce offspring.
Step-by-step explanation:
Answer: it creates birth
Step-by-step explanation: can i have brainliest
PLEASE HELP! WILL MARK THE FIRST CORRECT ANSWER BRAINLIEST!
There are n gallons of gas in a tank. After x gallons have been used, in terms of n and x, what percent of the gas has not been used?
Answer:
((n-x)/n)*100
Step-by-step explanation:
The Answer is:
((n-x)/n)100
The fraction models below represent two fractions of the same whole. How much of the Fraction 3 over 8 is in the Fraction 1 over 4?
Answer:
2/3
Step-by-step explanation:
Your model may show you that 1/4 = 2/8. Of course that will be 2 out of 3 of the 3/8 making up the other fraction of the same whole.
1/4 = 2/3 of the fraction 3/8
Please answer right, I've been stuck on this test for an hour.
Answer:
D
Step-by-step explanation:
f(x) has a horizontal asymptote of -4 while g(x) has horizontal asymptote of zero, in both functions, y is closer to infinity as x is closer to negative infinity,
A and B are definitely incorrect
while x gets closer to infinity, in f(x) y gets closer to -4, while in g(x) y gets closer to 0, thus they have a different end behavior as x approaches infinity
So, C is wrong, since it says that they have the same end behavior as x approaches infinity
Thus, D is correct
Write an exponential equation in the form y = abx whose graph passes through points (−3, 24) and (−2, 12). y = 3x y = 3(0.5)x y = 0.5(3)x y = −3(24)x
Answer:
Option B.
Step-by-step explanation:
The given exponential equation is
[tex]y=ab^x[/tex] ...(1)
It is given that the graph of above equation passes through points (−3, 24) and (−2, 12).
The graph passes through the point (-3,24), so substitute x=-3 and y=24 in equation (1).
[tex]24=ab^{-3}[/tex] ...(2)
The graph passes through the point (-2,12), so substitute x=-2 and y=12 in equation (1).
[tex]12=ab^{-2}[/tex] ...(3)
Divide equation (3) by equation (2).
[tex]\dfrac{12}{24}=\dfrac{ab^{-2}}{ab^{-3}}[/tex]
[tex]0.5=b[/tex]
Substitute b=0.5 in equation (2).
[tex]24=a(0.5)^{-3}[/tex]
[tex]24=\dfrac{a}{(0.5)^{3}}[/tex]
[tex]24=\dfrac{a}{0.125}[/tex]
[tex]24\times 0.125=a[/tex]
[tex]3=a[/tex]
Substitute a=3 and b=0.5 in equation (1).
[tex]y=3(0.5)^x[/tex]
Therefore, the correct option is B.
The graphs below have the same shape. What is the equation of the red
graph?
Answer:
A
Step-by-step explanation:
Since the shape of both graphs is the parent parabola form, and g(x) is just shifted up 2 instead of 5, its equation is [tex]2-x^2[/tex], or answer choice A. Hope this helps!
I NEED HELP ASAP :(
Use the distributive property to write the sum as a product.
(-1)·2+(-1)·ₓ
Answer:
−2 − x
Step-by-step explanation:
Answer:
-2-x
Step-by-step explanation:
distribute the the like terms and separate the problem then solve it.
What's the distance between - 14 and -5 on a number line?
A) 34
B) 11.7
D) 68
Question 15 (5 points)
Answer:
9
Step-by-step explanation:
Take -14 minus -5
-14 - (-5) Distribute the negative to -5
-14 + 5 Add
-9 Since distance can't be negative take the absolute value of -9
|-9| = 9
Answer:
the distance is 9
Step-by-step explanation:
its 9 because 14-5 = the distance of them on a number line
Help asap PLEASE, dhdbhehf
Answer:
3
Step-by-step explanation:
Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal. In this example, these are two pairs of Alternate Interior Angles: 2 and 3
Given the piecewise function shown, find the value of h(–6). A) 1 B) 26 C) -23 D) -6
Answer:
-22
Step-by-step explanation:
Which part of the function is valid when x = -6
The first part
h(-6) = 4x+2 and let x = -6
=4(-6) +2
= -24 +2
=-22
Answer:
-22
Step-by-step explanation:
simplify the expression 125^1/3
Step-by-step explanation:
We have:
(125)^1/3
= (5^3)^1/3
= 5^(3*⅓)
= 5 Ans.
A circular Petri dish has a diameter of 10 centimeters. If the dish contains 2.450 bacteria, what is the
population density of bacteria in the dish?
(1) 31 bacteria per square centimeter
(2) 42 bacteria per square
centimeter
(3) 48 bacteria per square centimeter
(4) 51 bacteria per square centimeter
Answer: 31 bacteria per square centimiter.
Step-by-step explanation:
The correct number of bacteria in the question is 2,450.
Hi, to answer this question we have to apply the next formula:
Area of a circle = π x (diameter/2) ^2
Replacing with the values given:
A = π x (10/2) ^2
A = π x (5) ^2
A = π x 25 = 78.54 cm2
Next, we have to divide the number of bacteria (2,450) by the area of the dish
2450 / 78.54 = 31.19 = 31 bacteria per square centimiter.
Feel free to ask for more if needed or if you did not understand something.
P
L
Z
H
E
L
P
M
E
!
!
!
Answer:
slope = - 4
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = - 1, 22) and (x₂, y₂ ) = (1, 14) ← 2 ordered pairs from the table
m = [tex]\frac{14-22}{1-(-1)}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4
