Answer:
£10,200
Step-by-step explanation:
Simple interest = principal × rate × time
Principal = £6000
Rate = 7% = 0.07
Time = 10 years
Simple interest = principal × rate × time
= £6000 × 0.07 × 10
= £4,200
Total = simple interest + principal
= £4,200 + £6,000
= £10,200
He would have to pay back a total of £10,200 in 10 years
Calculate the average rate of change of y=x2+3x−2 on the interval 1≤x≤2
Answer:
The rate of change for the given function is 6.
Step-by-step explanation:
Given function is:
[tex]y = x^2+3x-2[/tex]
The interval on which we have to find the rate of change is:
1≤x≤2
Here
a = 1
b = 2
We have to find the values of function on both points
Putting 1 in place of input (x)
[tex]y_a= (1)^2+3(1)-2\\= 1+3-2\\=2[/tex]
Putting x = 2
[tex]y_b = (2)^2+3(2)-2\\= 4+6-2\\=8[/tex]
The rate of change is calculated by using the following formula
[tex]Rate\ of\ change = \frac{y_b-y_a}{b-a}\\=\frac{8-2}{2-1}\\= \frac{6}{1}\\=6[/tex]
Hence,
The rate of change for the given function is 6.
An apple tree measures 20 1/2 feet tal,over the next five years,it grew to the height of 28 feet. What was the average yearly growth of the apple tree
Answer:
6.4%
Step-by-step explanation:
We solve this question in using the population growth rate formula
P(t) = Po(1 + r)^t
P(t) = Population after t years = 28 ft
Po = Initial Population = 20 1/2 feet or 20.5 feet
r = Growth rate = ?
t = Time in years = 5
Hence:
28 = 20.5 (1 + r)⁵
Divide both side by 20.5
28/20.5 = 20.5 (1 + r)⁵/20.5
1.3658536585 = (1 + r)⁵
5th root both sides.
5√(1.3658536585) = 5√(1 + r)⁵
1.0643411027 = 1 + r
r = 1.0643411027 - 1
r = 0.0643411027
Converting to percentage
r = 0.0643411027 × 100
r = 6.43411027%
Approximately = 6.4%
The yearly growth rate of the apple tree = 6.4%
Damien is competing in both swimming and running at a competition. After analyzing himself and his competitors, he knows that he has a 65% chance of winning at swimming and an 85% chance of winning at running. What is the probability that he will win the running event, but lose the swimming event?
Answer:
[tex]Probability = 0.2975[/tex]
Step-by-step explanation:
Giving:
Swimming
[tex]P(Win[Swim])= 65\%[/tex]
Running
[tex]P(Win[Run])= 85\%[/tex]
Required
Determine the probability of winning at running and losing at swimming
First, we calculate the probability of losing at swimming using
[tex]P(Win) + P(Lose) = 1[/tex]
Substitute 65% for P(Win)
[tex]65\% + P(Lose[Swim]) = 1[/tex]
Collect Like Terms
[tex]P(Lose[Swim]) = 1 - 65\%[/tex]
[tex]P(Lose[Swim]) = 35\%[/tex]
The required probability is then calculated using:
[tex]Probability = P(Win[Run]) * P(Lose[Swim])[/tex]
[tex]Probability = 85\% * 35\%[/tex]
Convert to decimal
[tex]Probability = 0.85 * 0.35[/tex]
[tex]Probability = 0.2975[/tex]
12.12 ounces for 3 cups Unit rate
Answer:
4.04 oz per cup
Step-by-step explanation:
sry fam im not gonna give a step by step explanation cuz im in a rush, hope this is enough gl.
I need helppppppppppppppppppppp
Answer: x=20.6 miles and y=$22.05
Step-by-step explanation: Good luck!
Solve the equation below for y.
12(y−8) = 14y−2
Answer:
y=-47
Step-by-step explanation:
12(y-8)=14y-2
12y-96=14y-2
-96=14y-2-12y
-96=2y-2
-96+2=2y
-94=2y
-94/2=y
-47=y
y=-47
Answer:
-47
Step-by-step explanation:
please solve these problems
Answer:
1/3x - 2y - 5x + 8
Step-by-step explanation:
Given:
1/3x - 2y - 5x + 8
1. There are four (4) terms in the expression: 1/3x, -2y, -5x, 8
2. Like terms are terms which have the same thing in common such as 1/3x, -5x in the expression
3. A constant is a term without a variable. 8 is the constant in the expression
4. The variables in the expression are: x and y
5. The coefficients are; 1/3, -2, and -5
What is the value of x in:
3x + 2(x + 1) = 12?
A.12
B.6
C.10
D.2
Answer:
D
Step-by-step explanation:
3x + 2(x + 1) = 12 ← distribute and simplify left side
3x + 2x + 2 = 12
5x + 2 = 12 ( subtract 2 from both sides )
5x = 10 ( divide both sides by 5 )
x = 2 → D
d .2
d will be the answer
by simplify
Solve the following system of equations:
y=2x + 1
y = -x+4
x= ?
y=?
Answer:
x= 1, y=3
Step-by-step explanation:
y= 2x +1
y= -x +4
Those two equation are in a system that means they need to be true in the same time. Just like I would say look for a car that is red and is a truck in this case we look for x and y is true that y = 2x+1 and is true that y= =x+4.
so y= 2x+1 but y is -x+4 so substitute
-x+4 = 2x +1, add x on both sides
4= 2x+x +1, subtract 1 from both sides
4-1 = 2x +x, combine like terms
3 = 3x , divide both sides by 3
x=1
if x=1 we substitute in y= -1 +4 = 3
The perimeter of a college basket ball court is 96 m and the length is 14m
more than the width. What are the dimensions?
width=17m
length= 31m
Step-by-step explanation:
width = x
length= x+14
perimeter = 96m
2(x+x+14)=96
4x+28=96
4x=68
x=17
width=17m
length= 31m
what is the solution of x in 2-3(6-2x)=1/2(10x-8)
Answer:
answer is 12
....
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. :-)))
Triangle D E F is shown. Angle D E F is a right angle. The length of hypotenuse D F is 5 StartRoot 2 EndRoot and the lengths of sides D E and E F are 5.
Given △DEF, which is not equal to cos(F)?
sin(F).
sin(D).
tan(F).
cos(D).
Answer: tan(F)
Step-by-step explanation:
Answer: C). tan(F)
Step-by-step explanation:
The length of a rectangle is 6 ft longer than its width.
If the perimeter of the rectangle is 68 ft, find its length and width.
Answer:
the length is 23 ft and the width is 11 ft
Step-by-step explanation:
68/4 = 17
17 17 17 17
11 11 23 23
help me with this please :)
Answer:
Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction
Hope this helps!
helppp meeeee please
A real estate agency an agent salty house for 313,000. The commission rate is 4.5 for the real estate agency in the commission rate for the agent is 20% of the amount the real estate agent gets. How much did the agency make on the house? How much did the agent earn in comission
Answer:
313000/100 X 4.5 = 14085
14085/100 X 20 = 2817
14085 - 2817 = 11268
agency = 11268
agent = 2817
WILL MARK BRAINLIEST!!!!!! Which of the following graphs represent a function?
Answer:
The second one
Step-by-step explanation:
the semi circle
Please help I’m confused also if you can’t see it just click on the picture.
Find the slope: change in y over change in x:
Slope = 30 - -5/ 6- -1 = 35/7 = 5
Find y intercept (the y value when x is 0)
Y = 5(0) = 0
There is no y intercept
The function rule would be:
Y = 5x
Dakota received a mark of 68% on his math test.
The test had 25 questions.
How many questions did Dakota answer correctly?
Which part of this graph shows a nonlinear relationship?
Answer:
2
Step-by-step explanation:
Answer:
2, D
Step-by-step explanation:
Not only is it not in a line it doesn't hit any points(it curves)
How is the general shape of a cube root function different from the shape of a square root function?
Square root functions are in the shape of a parabola, like a giant U, while cube root functions are more wide and swiggly, like a stretched out S.
See :
The general shape of a cube root function is a "S" shape when graphed, while the general shape of a square root function is a "U" shape when graphed.
What is the cube root function?A cube root function is defined as f(x) = ∛x. It has a single value for each positive x and one value for each negative x, so it is defined for all real numbers. It has a vertical asymptote at x=0 and its graph is a reflection of the graph of f(x) = -∛x over the x-axis. It starts at -infinity as x approaches negative infinity, increases to zero as x approaches zero and then decreases to positive infinity as x approaches positive infinity.
A square root function is defined as f(x) = √x. It is defined for all non-negative x and it has a vertical asymptote at x=0. Its graph starts at zero as x approaches zero and increases to positive infinity as x approaches positive infinity.
In summary, the cube root function is defined for all real numbers and has a "S" shape while the square root function is defined for non-negative numbers and has a "U" shape.
Learn more about the function here:
brainly.com/question/12431044
#SPJ2
Take a look at the blue function below. The dashed green function is its parent
function. Are these sine or cosine functions?
1
2TT
-1
Sine
ОО
Cosine
Answer:
Step-by-step explanation:
They are both sine functions. The blue one is multiplied by 2 and shifted down one.
blue: y = 2 * sin(theta) - 1
green: y = sin(theta)
I'm not sure what the answers mean.
What is the measure of angle RST?
a. 87
b. 131
c. 93
d. 90
Option c. 93°.
Alright, so in this one um the angle um so uh this angle right here, let's see right here, right which these two angles these angles are going to be equal because those are vertical angles. So these this angle is equal to um So angle P. S. T. Is equal to one half the sum of those two arcs added together, so 43 plus 1 31 So one half of Uh was that 1 74, So 1 74, divide by two 87. So this is 87 and then you take 18687 And you get 93.
What is the measure of ∠ RST?Triangle RST is isosceles means that two of its angles are equal. (1) The measure of angle T is 100 degrees --> since no other angle can be equal to 100 degrees (because in this case, the sum of the angles will be more than 180 degrees) than the other two angles, R and S, are equal: R=(180-100)/2=40.
Learn more about the angle at
https://brainly.com/question/25716982
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easy question. what’s the value of x :)))
A rectangle is 14 inches long and 6 inches wide. Find it’s area
Someone help 100 points and marking brainliest
Answer:
ehh....130 is your answer alr bye
the answer to your question is 130
what is the ratio of the area of the larger pizza to the area of the smaller pizza ? choices are 2,3,4, and 9 .
What’s the answer for this?
Answer:
[tex] {y}^{3} [/tex]Step-by-step explanation:
[tex]2 {y}^{3} - {y}^{3} [/tex]
[tex] {y}^{3} \: (collect \: like \: terms)[/tex]
A basketball costs $15.00. If the sales tax is 6%, which equation can be used to find the amount of tax?
Answer:
Tax amount = $15.00 x 0.06 =0.9
Total amount of the basketball = $15.00 x 1.06 = $15.90
Answer:
Tax amount = $15.00 x 0.06 =0.9Total amount of the basketball = $15.00 x 1.06 = $15.90
Step-by-step explanation:
Non linear??????????
Answer:
Yes. That is correct
Step-by-step explanation: