The account will be worth $12,909.81, rounded to the nearest cent, after five years based on the function.
Using the compound interest formula A = P(1 + r/n), we may calculate the value of the account after five years (nt)
Where A represents the overall sum, P represents the principal (original investment), r represents the annual interest rate, n represents the number of times the interest is compounded annually, and t represents the passage of time in years.
Inputting the values provided yields:
\(A = 10,000(1 + 0.032/4)^(4*5)\\A = 10,000(1.008)^(20)\\\\ A = $12,909.81\)
Exponential growth is the function that most accurately depicts the growth of the investment. This is due to the investment's ability to generate compound interest, which entails that interest is added to the principle and then generates additional interest over the course of the following period. The exponential growth function that emerges from this compounding impact.
Learn more about function here:
https://brainly.com/question/12431044
#SPJ1
The average rent in a city is $1,570 per month with a standard deviation of $230. Assume rent follows the normal distribution. Use the empirical rule for normal distributions to answer the following questions.
a. What percentage of rents are between $1,340 and $1,800? (Round your answer to the nearest whole percent.)
Percentage of rents b. What percentage of rents are less than $1,340? (Round your answer to 1 decimal place.)
Percentage of rents c. What percentage of rents are greater than $2,030? (Round your answer to 1 decimal place.)
Percentage of rents
Answer:
Below
Step-by-step explanation:
a) the empirical rule would say that these rents are +- 1 SD from the mean....this area encompasses + - 34.1% or 68.2 % (see image)
b) this is one S.D. below the mean which would be 50% - 34.1 % = 15.9% are below 1340
c) from graph: this is two S.D. ABOVE the mean and would include 2.2% are more than 2030
NOTE: What YOU have been taught might have slightly different numbers for the 'empiracal rule' ....like 34% rather than 34.1 % etc.....you will have to apply what you have been given and expected to use.....I do not have that information !
Carlos needs an average of 90% or greater on his quiz scores to earn an A in science class for the quarter. Each quiz is worth 20 points. The scores of his first four quizzes are shown in the table. There is one more quiz this quarter. Quiz Score 1 2 3 4 18 at least 19 17 20 What is the mininum score Carlos can earn on the final quiz to earn at least a 90% average? points
Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.
We have,
Let's start by finding the total number of points that Carlos can earn in the class:
Total points
= 5 quizzes x 20 points per quiz
= 100 points
If Carlos needs an average of 90% or greater, that means he needs to earn at least 90 points out of 100.
Total points earned.
= 18 + 19 + 17 + 20
= 74 points
To find the minimum score Carlos needs on the final quiz, we can set up an inequality:
(74 + x) / 5 ≥ 0.9
where x is the score on the final quiz.
Simplifying this inequality.
74 + x ≥ 90
x ≥ 16
Therefore,
Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ1
Commutative property 1/7 + -1 +2/7 would commutative property help this equation?
Explanation
The commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.
So for the question
\(\frac{1}{7}-1+\frac{2}{7}\)we are asked if the commutative property will help the equation
If we re-arrange the expression as
\(\begin{gathered} \frac{1}{7}+\frac{2}{7}-1 \\ \\ or \\ \\ -1+\frac{1}{7}+\frac{2}{7} \end{gathered}\)
What input is NOT allowed for f(x) = 3/ x-5
Answer:
x ≠ 5
Step-by-step explanation:
x ≠ 5
The reason for this is because if we use the input 5, this will be the result:
f(x) = 3/(5) - 5
f(x) = 3/0 = Undefined
Jane wants to add chocolate chips to her trail mix. A 3-pound bag of chocolate chips cost $3.22 . What is the unit price ?
Answer:
It would be 1.073 you can also rojnd ot to 1.07
Answer:
$1.07 per pound
Step-by-step explanation:
$3.22/3lb is about $1.07 per lb.
Graph the line whose y intercept is -9 and whose x intercept is 7
The graph of the linear equation y = 9/7x - 9 is attached below
Graph of a Linear EquationA linear graph is the graphical representation of a straight line. It showcases a linear equation in two variables and shows the linear association between two quantities. A linear function often have a straight line with a slope and y-intercept.
To solve this, we can simply write an equation of the linear equation which is often given as
y = mx + c
m = slopec = y-interceptLet's substitute the values and find the equation;
y = 9/7x - 9
Kindly find the attached image below;
Learn more on graph of a linear equation here;
https://brainly.com/question/14323743
#SPJ1
Predict the next three numbers in the pattern.
4, 10, 14, 24, 38, 62,
Answer:
100, 162, 262
Step-by-step explanation:
to find each number you add the previous number
4+10=14
10+14=24
14+24=38
24+38=62
38+62=100
62+100=162
100+162=262
I will give the brainiest if you get it right.
Answer:
1 ≤ x < 7/4
Step-by-step explanation:
The function f(x) is defined as increasing on the domain (-8, 4), so the ordering of the arguments is not changed by the function. We can solve the inequality as though f(x) = x, which is increasing everywhere.
Inequality solutionsf(4x -3) ≥ f(2 -x²)
4x -3 ≥ 2 -x² . . . . . . using our assumed definition of f(x)
x² +4x -5 ≥ 0 . . . . . subtract 2-x²
(x -1)(x +4) ≥ 0 . . . . factored form; zeros at -4, +1
The values of x that make this true are ones that make the factors have the same signs: x ≤ -4 or x ≥ 1.
Domain restrictionsThe domain of f(x) is -8 < x < 4, so we require the arguments of f be restricted to those values
Left side
-8 < 4x -3 < 4
-5 < 4x < 7
-5/4 < x < 7/4
Right side
-8 < 2 -x² < 4 . . . . . right side is always true
x² < 10 . . . . . . . . . . . add x² +8
|x| < √10 . . . . . . . . . . less restrictive than the the left-side restriction
SolutionWith the given domain restrictions on f(x), the inequality will be true on the interval ...
1 ≤ x < 7/4
__
Additional comment
The attached graph shows the left-side function argument (dashed blue) and the right-side function argument (dashed green) with the given domain restrictions. The red curve is the difference in function values for the function defined as above. It is only non-negative between 1 and 1.75 as we found above.
This general behavior is applicable for any f(x) that can be described as in the problem statement. For example, f(x) = √(x+8) also gives an increasing curve for the difference f(4x-3)-f(2-x²) on the interval (-5/4, 7/4) with an x-intercept of +1.
<95141404393>
For each value of u determine whether it is a solution to -2u-6<-20
Answer:
u > 7
Step-by-step explanation:
-2u -6 < -20 Add 6 to both sides
-2u - 6 + 6 < -20 + 6
-2u < -14 Divide both sides by -2. When you multiply or divide both sides by a negative number, you must flig the sign.
\(\frac{-2u}{-2}\) > \(\frac{-14}{-2}\)
u > 7
Helping in the name of Jesus.
The answer is:
u > 7
In-depth explanation:
You haven't told me what the values of u are, but I'll solve the equation for u.
Add 6 on each side:
\(\bf{-2u-6 < -20}\)
\(\bf{-2u < -14}\)
Divide each side by -1 and reverse the sign:
\(\bf{2u > 14}\)
Now divide each side by 2
\(\bf{u > 7}\)
A radial saw has a blade with a 6-in radius.
Suppose that blade spins at 1000 rpm.
Find the angular speed of the blade in
rad/min.
Answer:
The angular speed of the blade is of 166.67 rad/min
Step-by-step explanation:
The velocity, is given by the following equation:
\(v = rw\)
In which r is the radius and w is the angular speed.
We use this relation to solve this question;
We have that:
\(v = 1000, r = 6\). We want to find w. So
\(v = rw\)
\(1000 = 6w\)
\(w = \frac{1000}{6}\)
\(w = 166.67\)
The angular speed of the blade is of 166.67 rad/min
On parallelogram ABC∧
mΔA=42 mΔB=___ mΔC___ mΔD=___
The measures of the remaining angles of the parallelogram are m ∠ B = 138°, m ∠ C = 42° and m ∠ D = 138°
How to determine the measure of missing angles in a parallelogram by geometric theorems
In this problem we know the measure of an angle and we should find the values of the three remaining angles. According to Euclidean geometry, the sum of internal angles in a parallelogram equals 360° and there exists the following property between each pair of angles:
m ∠ A = m ∠ Cm ∠ B = m ∠ Dm ∠ A + m ∠ B = m ∠ B + m ∠ C = m ∠ C + m ∠ D = m ∠ A + m ∠ D = 180°Then, the measures of the missing angles are, respectively:
m ∠ B = 180° - m ∠ A
m ∠ B = 180° - 42°
m ∠ B = 138°
m ∠ D = 138°
m ∠ C = 42°
Remark
The statement is poorly formatted, presents typing mistakes and image is missing, correct form is shown below:
On parallelogram ABCD, m ∠ A = 42, m ∠ B = ____, m ∠ C = _____, m ∠ D = _____
A representation of the parallelogram is shown in the image attached below.
To learn more on parallelograms: https://brainly.com/question/1563728
#SPJ1
One end of a right circular cone has been cut off by a plane parallel to the base of the cone as shown in the figure below.
What is the approximate circumference of the smaller circular base of the remaining section of the cone?
a. 3.03 feet
b.6.06 feet
c. 3.36 feet
d. 5.28 feet
Answer: The circumference of the smaller circular base of the cone can be found using the formula:
C = 2 * π * r
where "r" is the radius of the circle. The radius can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
Since the cut plane is parallel to the base of the cone, the height of the cone and the height of the remaining section of the cone are equal. Let's call this height "h". Then, using the Pythagorean theorem, we have:
r^2 + (h/2)^2 = (h/2)^2
Simplifying, we get:
r^2 = (h/2)^2
Taking the square root of both sides:
r = h/2
Substituting "h/2" for "r" in the formula for the circumference:
C = 2 * π * (h/2) = π * h
Since we do not have a specific value for "h", we cannot find an exact value for the circumference. However, based on the given options, the closest approximate value to π * h is c) 3.36 feet.
Step-by-step explanation:
Please help!! The question is the image below VVV
Answers are also images after the picture.
Step-by-step explanation:
When adding two fractions with different bases (bottom numbers), we can use this function:
\(\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}\)
So, to apply this to the given question:
\(\frac{x+3}{x-6} +\frac{1}{x-2}\)
= \(\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}\)
From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.
Multiply top using: (a + b)(c + d) = ac + ad + bc + bd= \(\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}\)
Simplify.= \(\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}\)
Remove parentheses.= \(\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}\)
Simplify again.= \(\frac{x^2 +2x-12}{(x-6)(x-2)}\)
Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.
Factor.= \(\frac{x(x+2)}{(x-6)(x-2)}\)
Answer:
A) \(\frac{x(x+2)}{(x-6)(x-2)}\)
Help whats the answer and an explanation to it
Answer:
C
Step-by-step explanation:
the answer is c
PLEASE HELP ASAP. DUE IN A FEW MINS
5(k + 2)
(5 * k) + (5 * 2)
= 5k + 10
______________________________
8(4 - 1.2h)
(8 * 4) - (8 * 1.2h)
= 32 - 9.6h
______________________________
3(1 - 7m)
(3 * 1) - (3 * 7m)
= 3 - 21m
______________________________
(b + 9)(6)
(6 * b) + (6 * 9)
= 6b + 54
Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium?
Hint: Think about the point where they both meet. For example, if you were to place the graphs on top of each other, what would be the point of intersection?
Type the correct number below without the dollar sign.
Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.
Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.
Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.
At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.
To learn more about equilibrium of demand and supply:
https://brainly.com/question/30237240
Graph y=-3x+4
Please Help
Answer:
(-2,10)
(-1,7)
(0,4)
(1,1)
(2,-2)
(3,-5)
Step-by-step explanation:
Answer:
your anwer is x=-1/3y+4/3
Step-by-step explanation:
Help plssssssss thanks 15 points
Step-by-step explanation:
before buying any songs (0 number of songs) she has $50.
after buying 5 songs she has $37.50 left.
after buying 10 songs she has $25 left.
so, we see, each song costs $2.50 (5×2.5 = 12.5, 50-12.5 = 37.5, 10×2.5 = 25, 50 - 25 = 25).
that ratio continues also for 15 and 20 songs.
so, yes, the problem definition is right, it is a linear function.
the function is
m(x) = y = 50 - 2.5x
"m" standing for "money left".
x = number of songs bought.
the y-intercept is the y-value, when x = 0.
that is in our case 50. or $50.
that stands in this case (as the first sentence in this explanation shows) for the initial amount of money she had before buying any songs.
Help help help math math help
Answer:
x = - 4
Step-by-step explanation:
i hope its helped. thank you !
Small cubes of side 1 cm are stuck together to form a large cube
of side 4cm. Opposite faces of the large cube are painted the
same colour, but adjacent faces are different colours. The three
colours used are red, black and green.
(a) How many small cubes have just one red and one green
face?
(b) How many small cubes are painted on one face only?
(c) How many small cubes have one red, one green and one
black face?
(d) How many small cubes have no faces painted?
hola buenas noches como estan
Evaluate the number
24 · 32
Answer:768
Step-by-step explanation:
You just multiply the to numberers
Can someone help me with this please?
Answer:
The triangles are similar.
Explanation:
Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.
A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1080 feet of fencing material, what should be the length and width of the field?
The width of the field is 230 feet and the length is 310 feet.
Let's denote the width of the field as "x" feet.
The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.
To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:
2(length) + 2(width) = perimeter
Substituting the given values:
2(x + 80) + 2(x) = 1080
2x + 160 + 2x = 1080
4x + 160 = 1080
4x = 920
x = 920/4
x = 230
Therefore, the width of the field is 230 feet.
Now we can find the length by adding 80 feet to the width:
Length = Width + 80 = 230 + 80 = 310 feet.
So, the width of the field is 230 feet and the length is 310 feet.
To learn more on Area click:
https://brainly.com/question/20693059
#SPJ1
If Margo walks 1/4 mile in 1/12 of an hour, what is her unit rate
To find the unit rate, we need to determine how much distance Margo covers in one unit of time. We can do this by dividing the distance by the time.
Distance = 1/4 mile
Time = 1/12 hour
Unit rate = Distance ÷ Time
Unit rate = (1/4 mile) ÷ (1/12 hour)
We can simplify this division by multiplying both the numerator and denominator by the least common multiple of 4 and 12, which is 12.
Unit rate = (1/4 mile) ÷ (1/12 hour) x (12/12)
Unit rate = (3/4 mile) ÷ 1 hour
Unit rate = 3/4 mile per hour
Therefore, Margo's unit rate is 3/4 mile per hour. This means that she can cover a distance of 3/4 mile in one hour of walking.
Answer:
3mph
Step-by-step explanation:
1/12 of an hour will be 5 min. In 5 min she can walk 1/4 mile then in one hour she can walk 1/4 x 12. This means her rate will be 3 miles per hour.
60/12 = 5
12 x 1/4 = 12/4 = 3
The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
How to determine the legs of the triangle?The complete question is in the attached image
The given parameters are:
Area = 24
Legs = x and x + 2
The area of the triangle is calculated as:
Area = 0.5 * Base * Height
This gives
0.5 * x * (x + 2) = 24
So, we have:
0.5(x)(x + 2) = 24
Divide through by 0.5
(x)(x + 2) = 48
Expand
x^2 + 2x = 48
Subtract 48 from both side
x^2 + 2x - 48 = 0
Hence, the equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
Read more about area at:
https://brainly.com/question/24487155
#SPJ1
at a given high school the probability that a student is taking a geometry class is 0.24 the probability that a student is taking a chemistry class and a geometry class is 0.18 if a student is taking a geometry class what is the probability that the student is also taking a chemistry class
Answer:
0.24
Step-by-step explanation:
Answer: 0.24
Step-by-step explanation:
HELP ASAP DO NOT SPAM YOU WILL BE REPORTED 15 POINTS I WILL MARK BRAINIEST Graph the solution to this inequality on the number line. w – 0.7 > -1.1 First select the correct ray. Then select the location of the endpoint to plot the inequality on the number line.
Answer:
K12 Answer
Step-by-step explanation:
The correct answer would be an option (A) which is the location of the endpoint to plot the inequality on the number line.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.
Any directed number's location can be determined using a number line. There are positive and negative axes in it.
We have been given that inequality on the number line.
⇒ w – 0.7 > -1.1
⇒ w > -1.1 + 0.7
⇒ w > -0.4
⇒ w < 0.4
Therefore, the correct answer would be option (A) which is the location of the endpoint to plot the inequality on the number line.
Learn more about the number line here:
brainly.com/question/17617832
#SPJ2
Help and explain too (using elimination to solve systems of equations ) !!!!!
Answer:
x=3 y=5
Step-by-step explanation:
it's simultaneous equations so you first try matching the x or the y on both equations
on the first equation the ys are matching so:
4x+y=17
2x+y=11
2x=6
x=3
now that you have x you substitute it back into the equation to get y
6+y=11
-6 -6
y=5
Answer:
(3,5)
(3,2)
(7,0)
(8,1)
Step-by-step explanation:
1.)
Subtract the two equations
(4x+y)-(2x+y)=17-11
2x=6
x=3
plug this into the first equation
4(3)+y=17
y=5
2.) we need one set of the same variable's coefficents to match (so that when we add/subtract the two equations a variable cancels out). To do this multiply the first equation by 1.5
1.5(3x+2y)=13*1.5
4.5x+3y=19.5
Subtract the second equation
(4.5x+3y)-(2x+3y)=19.5-12
2.5x=7.5
x=3
plug this into the first equation
3(3)+2y=13
2y=4
y=2
3.)
Mulitply the first equation by 3
3(x-2y)=7*3
3x-6y=21
subtract this and the second equation
(3x-6y)-(3x+y)=21-21
-7y=0
y=0
plug this into the first equation
x-2(0)=7
x=7
3.)
add the two equations
(x+5y)+(x-5y)=13+3
2x=16
x=8
plug this into the first equation
8+5y=13
5y=5
y=1
math question!
pls help
question is in the pic
(either answer it or can you tell how to find the answer or both pls & thxxu)
Step-by-step explanation:
use the a method called tan which to find the answer u will divide 4 divide by 2 and then you find the tan of 2 to get the answer then you find tan inverse with calculator yo get the correct answer
A bowling ball of mass 9 kg hits a wall going 11 m/s and rebounds at a speed
of 8 m/s. What was the impulse applied to the bowling ball?
The Answer is 171 kg m/s