Using simple interest, it is found that she needs to earn $2,391.07 during the summer.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = A(0)(1 + rt)
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.For this problem, the objective is to have $1200 in 3 months = 0.25 years, hence the parameters are given as follows:
A(0.25) = 1200, t = 0.25, r = 0.03.
Hence we have to solve for A(0):
A(0)(1 + 0.03 x 0.25) = 1200
A(0) = 1200/(1 + 0.03 x 0.25)
A(0) = $1,191.07.
She also needs to earn $1,200 to pay the first-semester bill on time, hence:
1200 + 1191.07 = $2,391.07.
She needs to earn $2,391.07 during the summer.
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Pls help I need help rn
Evaluate 4x ^ 2 - 3x when x = 3
Answer:
27
Step-by-step explanation:
=4(3)^2-3(3)
=4(9)-9
=3(9)
=27
Refer to the number line. Find the coordinate of point C that’s is 7/8 of the distance from M to J
Answer:
C = 16
Step-by-step explanation:
Given point M=2 and J=18 on a number line, you want the coordinate of point C that is 7/8 of the distance from M to J.
DistanceThe distance from M to J is the difference of their coordinates:
J -M = 18 -2 = 16
7/8 of that distance is ...
(7/8)(16) = 7(16/8) = 7(2) = 14
You are being asked for the coordinate of the point that is 14 units from M in the direction of J.
PointTo find the coordinate of C, we add the desired distance to the coordinate of M:
C = M +14
C = 2 +14 = 16
The coordinate of point C is 16.
Help please this is due soon
The value of the given function is given as follows f(-5) ,g(2),f(4m) are 25,-3,-12m+10.
The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope. The vertex of a quadratic function is calculated by rearranging the equation to its general form, f(x) = a(x – h)2 + k; where (h, k) is the vertex.
The notation y=f(x) defines a function named f. This is read as “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable
F(x) is the notation for a function which is essentially the thing that does your operation to your input. You can think of a function as a little machine. You put in your input, it changes it around and gives you output in return. F(x) means it's a function f with respect to x.
f(x) = -3x+10
f(-5) = -3*-5 +10
= 15+10=25
g(x) = x^2-7
g(2)= 2^2-7
= 4-7
=-3
f(4m) = -3x+10
= -3*4m+10
=-12m +10
= -12m +10
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The values of the above functions are 25, 3, and 12m+10 for f(-5) and g(2) and f(4m), respectively.
By rearranging the equation to take on its general form, f(x) = mx + c, where m is the slope, one can determine the slope of a linear function. By rearranging the equation to its general form, f(x) = a(x - h)2 + k, where (h, k) is the vertex, one can determine the location of a quadratic function's vertex.
A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value or independent variable is denoted by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).
A function is essentially the item that applies your operation to your input, and its notation is F(x). A function can be compared to a tiny machine. You provide your input, which is altered and converted into output. F(x) denotes that a function is one that has respect to x.
f(x) = -3x+10
f(-5) = -3*-5 +10
= 15+10=25
g(x) = x^2-7
g(2)= 2^2-7
= 4-7
=-3
f(4m) = -3x+10
= -3*4m+10
=-12m +10
= -12m +10
larger of two numbers is 13 more than twice the smaller number. the sum of the numbers is 52. find each number
Answer:
13 and 39
Step-by-step explanation:
let the smaller number be n then the larger number is 2n + 13 , so
n + 2n + 13 = 52
3n + 13 = 52 ( subtract 13 from both sides )
3n = 39 ( divide both sides by 3 )
n = 13
2n + 13 = 2(13) + 13 = 26 + 13 = 39
then smaller number is 13 and larger number is 39
4500 = 3200(1+R/100)^4
Answer:
here is the answer for your question 4500=3200(1+R/100)^4, hope it helps
Let f(x)=12(4)x−1. Evaluate f(3)
Answer: f(3)=143
Step-by-step explanation:
f(x)=12(4)x−1
f(x)=48x−1
f(3)=48(3)−1
f(3)=144−1
f(3)=143
The breadth of the rectangular garden is 2
3
of its length. If its perimeter is 40 cm, what are its
dimensions.
Answer:
Length = 12cm
Width = 8cm
Step-by-step explanation:
Let the length be x
Let the width be 2/3x
Perimeter = 2 (l+b)
Length = 2 (x+2/3x) = 40
= x + 2/3x = 40/2
= x + 2/3x = 20
= x/1 + 2/3x = 20
LCM = 3
= 3x + 2x = 20
______
3
= 3x + 2x = 20 x 3
= 5x = 60
= x = 60/5
= x = 12
Width = 2/3 of 12
= 2/3 × 12
= 8
The function g(x)=−3(x−3)2+4 crosses the x-axis at x=1.845. What is true about the value of g(x) at that x-value? g(x)=0 g(x)=1.845 g(x)=−3.34 g(x)=−3
the value of the function is zero, then the correct option is the first one.
g(x)=0
What is true about the value of g(x) at that x-value?We know that the given function:
g(x) = -3*(x - 3)^2 + 4
Crosses the x-axis at x = 1.845
Now, remember that the x-axis is located at y = 0, to for the function:
y = g(x)
We should have that g(1.845) = 0
Then what we can conclude about the value of g(x) at x = 1.845 is that the value of the function is zero, then the correct option is the first one.
g(x)=0
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Find the numerical value if x=4 and y=5
Answer:
77
Step-by-step explanation:
2(4)^2+9(5)
2(16)+45
32+45
=77
Answer:
109
Step-by-step explanation:
First, you substitute x with 4 and y with 5
so your equation should be 2(4)squared +9(5)
PEMDAS
Parrentisies first so 2x4=8 and 9x5=45
then exponents so 8squared = 64
Addition next so 64 + 45 =?
? = 109
Find an equation of the line that has a slope of 5 and a
y
-intercept of
(
0
,
8
)
. Write your answer in the form
y
=
m
x
+
b
.
write the equation for the line perpendicular to y=-1/4x+9 and passing through the point (-9,9) in slope-intercept form.
Answer:
y = 4x + 45
Step-by-step explanation:
The slope for the equation y = -1/4x + 9 would be the number before the x. In this case, that number is -1/4. A perpendicular slope would be the opposite inverse to this number which would be 4. We know have the slope. We need the y- intercept.
To find the y-intercept we would need and x and y value that is on the line and the slope. We are given this information. From above, we see that the slope is 4. We can use the x and y from the ordered pair given (-9,9) The x value is -9 and the y value is 9.
y = mx + b Substitute in what we know.
9 = 4(-9) + b We are soling for b
9 = -36 + b Add 36 to both sides of the equation
45 = b We now know the y-intercept
The equation will be:
y = mx + b
y = 4x + 45
What is this number in standard form?
(8 × 10) + (2x 100) + (9 × 1.000)
5)
Enter your answer in the box.
Answer:
Depending on where the 5) is supposed to be, if it is multiplying the 9 x 1000, then total answer is 45280. If however the equation is 80 + 200 + 45000 then multiply by 5 it is 46400
Marty can buy lunch for 5 dollars in the cafeteria how many days can he buy lunch with 30 dollars
Answer: 6 days
Divide 30 by 5
Se desea estimar el ingreso familiar medio de los padres de familia de un barrio
de Arequipa con un error no exceda a 10 nuevos soles. ¿Qué tamaño, como
mínimo, debe tener la muestra para que la media sea estimada con una precisión
del 95%, si se sabe que la desviación estándar de los salarios mensuales es de 50
nuevos soles?
Using the z-distribution, it is found that a sample size of 97 is required.
What is a z-distribution confidence interval?The confidence interval is as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is given by the following rule:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.For this problem, considering a margin of error of 10, the parameters are given by:
[tex]M = 10, \sigma = 50[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Then we take the margin of error equation and solve for n as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]10 = 1.96\frac{50}{\sqrt{n}}[/tex]
[tex]10\sqrt{n} = 50 \times 1.96[/tex]
[tex]\sqrt{n} = 5 \times 1.96[/tex]
[tex](\sqrt{n})^2 = (5 \times 1.96)^2[/tex]
n = 96.04
Rounding up, as a sample size of 96 results in M > 10, we have that:
A sample size of 97 is required.
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Use the graph to determine the following
a. the functions domain
b. the functions range
c. the x-intercepts if any
d. the y-intercepts if any
e. the function values f(0) and f(4)
The answers are:
a) The domain is the set of all real numbers.
b) The range is R: (-∞, -2]
c) there are not any x-intercept.
d) The y-intercept is y = -5
e) f(0) = -5
f(4) = -4
How to determine the domain and range by using the graph?For a function f(x) =y, we define the domain as the set of the inputs and the range as the set of the outputs.
To identify the domain we need to look at the horizontal axis, and there we can see that the function covers it completely, then the domain is the set of all real numbers.
For the range, we look at the vertical axis. Here we can see that the function has a maximum at y = -2 and then goes down, then the range is:
R: (-∞, -2]
c) Now we want to get the xintercepts. As you can see in the graph, it never intercepts the x-axis (the horizontal one). Thus, there are not any x-intercept.
d) The y-intercept is when the graph intercepts the vertical axis, in this case the y-intercept is at y = -5
e) f(0) is the value of the y-intercept, which we already know is y = -5
for f(4) we need to find x = 4 in the horizontal axis and then find the correspondent value of the graph.
We can see that f(4) = -4.
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A toy manufacturer wants to see how long, on average, a new toy captures children's attention. He tests 16 children selected at random and finds that their mean attention span is 33 minutes with a standard deviation of 4 minutes. If we assume that attention spans are normally distributed, find a 95% confidence interval for the mean attention span of children playing with this new toy. Give the lower limit and upper limit of the 95% confidence interval.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.
Lower Limit:
Upper Limit:
Using the t-distribution, the limits of the 95% confidence interval are given as follows:
Lower: 30.9.Upper: 35.1.What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 16 - 1 = 15 df, is t = 2.1315.
The other parameters are given as follows:
[tex]\overline{x} = 33, s = 4, n = 16[/tex]
Hence the bounds of the interval are given as follos:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 33 - 2.1315\frac{4}{\sqrt{16}} = 30.9[/tex][tex]\overline{x} + t\frac{s}{\sqrt{n}} = 33 + 2.1315\frac{4}{\sqrt{16}} = 35.1[/tex]Which are the lower and the upper bound, respectively.
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A bakery is 12 meters wide and 19 meters long. The baker wants to put a wooden shelf around the inside of the bakery. The wooden shelving costs $23.37 per meter. How much will the baker's shelf cost?
The cost of the baker's shelf is $1,448.94
How to calculate the cost of the baker's shelf ?
The length of the bakery is 12 meters
The width of the bakery is 19 meters
The wooden shelf costs £23.37 per meter
The cost can be calculated as follows
2(12+19) × 23.37
= 2(31) × 23.37
= 62 × 23.37
= 1,448.94
Hence the cost of the baker's shelf is $1,448.94
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{ (-2, 4), (0, 2), (-1, 3), (4, -2)}
The set of ordered pairs above
The set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} belong to a function
[y = f(x)] considering the pairs are in the order of (x, y).
As per the question statement, we are provided with a set of ordered pairs: {(-2, 4), (0, 2), (-1, 3), (4, -2)}.
We are required to determine if the pairs in the set satisfy a function or not.
To solve this question, let us consider each pair in the form of (x, y) and then, we will have to find out a relation between x and y that will satisfy all the ordered pairs. If we are able to find out one such common relation or pattern, we will determine our ordered pairs as inputs and outputs of the same function, otherwise not.
We can say that, [tex][(-2)(-1)+2]=4,[/tex]
[tex][(0)(-1)+2]=(0+2)=2,[(-1)(-1)+3]=1+2)=3,\\[/tex]
And, [tex][4*(-1)]+2=[(-4)+2]=(-2)[/tex]
That is, all our ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} satisfy the function [y = f(x) = {x(-1) + 2}], being in the order of (x, y).
Therefore, the set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} are the inputs and outputs of the function [y = f(x) = {x(-1) + 2}].
Ordered Pairs: An Ordered Pair is a pair of elements (say a, b) having the property that [( a, b) = (p, q)] if and only if (a = p) and(b = q).
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The reciprocal of 2/19 is
(Type an integer or a fraction.)
Answer:
-19/2
Step-by-step explanation:
If you want the reciprocal you need to change the sign to the opposite and flip the numbers.
Julia went to ten houses on her street. 5 of them gave her a chocolate bar. What fraction of the houses gave her a chocolate bar
which of the following shows 3x^2-2x-5 factored completely?
Seven times the sum
of a number,n, and four
Answer:
7(n + 4) or 7×(n + 4)
Step by step explanation:
On Saturday, some adults and some children were in a theatre.
The ratio of the number of adults to the number of children was 4:3.
Each person had a seat in the Circle or had a seat in the Stalls.
2/3 of the children had seats in the Stalls.
114 children had seats in the Circle.
There are exactly 1100 seats in the theatre.
On this Saturday, were there people on more than 70% of the seats?
You must show how you get your answer
Answer:
Yes, there were people on more than 70% of the seats.
Step-by-step explanation:
Let's start with the children. We know that 2/3 of the children had seats in the Stalls, which means that the other 1/3 of the children had seats in the Circle. We know that 114 children had seats in the Circle. Therefore, we can calculate that there were 342 children total, since 114 (1/3 of the children) times 3 is 342.
In order to find how many adults there were, we can use the ratio of adults to children, 4:3. We're basically going to undo our math from the previous part. We divide 342 by 3 to determine how much 1 is. This gives us 114, which we multiply by 4 to find how many adults there were.
There were 456 adults.
There were 342 children.
456 + 342 = 798
There were 798 people in the theatre total.
To find what 70% of 1100 is, we multiply 0.7 x 1100. This gives us 770. Because 798 is more than 770, we know that there were people on more than 70% of the seats.
-X <-2x and 3x>2x
Solve, then graph and find interval notation
Answer:
-X < -2x
3x>2x
Step-by-step explanation:
3.4/feet
5 feet
Find the area of the triangle pictured above.
h
square feet
Area =
Answer:
8.5 square feet
Step-by-step explanation:
(3.4x5)/2
=8.5
use whole numbers and decimals to write 19.06 in expanded form
Answer:
19 + 0.06
taking out the whole number leaves you with 0.06
or you could do 10 + 9 +0.06
if you want to split it up more
The expanded form of the number 19.06 is 1×10 + 9×1 + 0/10 + 6/100.
What are the standard form and expanded form of numbers?Numerology can be expressed in a variety of ways. Word form is a means of expressing numbers verbally. Numbers can be written in expanded form by indicating the value of each digit. The digits 0 through 9 are used to write numerals in standard form, and each digit has a place value.
Given, A number in a decimal form which is 19.06.
This can be written as,
1×10¹ + 9×10⁰ + 0/10¹ + 6/10².
1×10 + 9×1 + 0/10 + 6/100.
Each digit has a face value and a place value.
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how far would the plane fly in 3 hours? in 3.5 hours?
A truck enters a highway driving 60 mph. A car enters the highway at the same place 8 minutes later and drives 71 mph in the same direction. From the time the car enters the highway, how long will it take the car to pass the truck?
It will take 44 minutes for the car to pass the truck.
What is relative speed ?Relative speed is the net speed difference between two objects when they are on the same direction we subtract and when they are on different direction we add.
According to the given question A truck enters a highway driving 60 mph which is (60/60) miles per minute = 1 mile per minute.
The car is going at a speed of 71 miles hour or (71/60) mile per minute = 1.183 miles per minute.
∴ Their relative speed difference is ( 1.183 - 1 ) = 0.183 miles.
Given the car enters the highway 8 minutes later on that time the truck will cover the distance of (1×8) = 8 miles.
so, the time needed for the car to pass the truck is (8/0.183) minutes which is = 43.7 minutes or 44 minutes.
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A city in Texas started the day at -5 degrees Fahrenheit. The temperature increased by 15.1 degrees by nightfall. What is the final temperature at nightfall?
Step-by-step explanation:
Add 15.1 to -5-5 + 15.1 = 10.1Answer:
The final temperature is 10.1 degrees Fahrenheit
how much would $500 invested at 4% interest compounded monthly be worth after 7 years ? A(t)=P*e^nt
The worth of the investment is $1.51 * 10^39
How to determine the compound amount?The given parameters are
Principal, P = $500
Rate, r - 4%
Time, t = 7 years
Number of times, n = 12
So, we have:
A(t)=P*e^nt
This gives
A(12) = 500 *e^(12 * 7)
Evaluate
A(12) = 1.51 * 10^39
Hence, the worth of the investment is $1.51 * 10^39
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