Lauren can add $30 each month to her savings account
Income made by Lauren from part-time job = $185
Money sent to Lauren by her parents = $120
Total income of Lauren = Money from job+ money received from parents = 120+185 = $305
Let her total expenses be x
Substituting the values in the formula we get:
Sum of Lauren's paycheck + Money she gets from her parents = Total expenses+ 11% more than her total expenses
185 + 120 = x+11% of x
305=x+11/100*x
305 = 1.11x
x=274.77 or 275
Money she can add in her savings account each month = Total money received - Expenses = 305 - 275 = $30
Learn more about linear equations:
https://brainly.com/question/13738061
#SPJ1
10^-6/10^-2 this is my question
Answer:
[tex] \frac{1}{10000} [/tex]
or Decimal
[tex]0.0001[/tex]
Step-by-step explanation:
Greetings !
look at the figure i have attached above
Hope it helps !!
How many positive real zeroes does f(x) = x⁵ - 4x³ + 7x² + 3x - 5 have?
Given -
f(x) = x⁵ - 4x³ + 7x² + 3x - 5
To Find -
How many positive real zeroes does f(x) have =?
Step-by-Step Explanation -
We have
f(x) = x⁵ - 4x³ + 7x² + 3x - 5
where the signs of coefficients are:
+ - + + -
We can see there are three changes in the sign in f(x).
So, from
Descarte's rule,
there are either 3 0r 1 positive real roots
Now,
f(-x) = -x⁵ + 4x³ + 7x² - 3x - 5
Signs: - + + - -
So, here f(-x) has two sign changes.
From this we can conclude there is at least 1 real root and either 4, 2 or 0 imaginary roots.
Final Answer -
Positive real zeroes f(x) have =
Minimum = 1
Maximum = 3
Find the opposite of –15.
Answer:15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
If there is a negative sign just add a positive sign or remove the sign. And if it's a positive number add a negative sign.
Easy There we go!
A cone has a volume of 3014.4 cubic inches and a radius of 12 inches.what is the height?
h = 20inches
Explanations:The formula for calculating the volume of a cone is expressed as:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where:
r is the radius
h is the height
Given the following
r = 12 inches
V = 3014.4 cubic inches
Substitute to determine the height
[tex]\begin{gathered} 3014.4=\frac{1}{3}\times3.14\times12^2\times h \\ 3014.4\times3=452.16h \\ h=\frac{9043.2}{452.16} \\ h=20inches \end{gathered}[/tex]Hence the height of the cone will be 20inches
Please answer correctly and tell me if its linear quadratic or exponential please.
Answer:
Exponential
Step-by-step explanation:
If the initial difference has the same value, the model will be linear.
If the value of the second difference is the same, the model will be quadratic.
If the difference has been calculated more than five times before duplicate values are discovered, the model might be exponential or involve another unique equation.
Hope this helps!
what is the arc measure of ct in radians? what is the arc length in feet?
We will determine the arch lenght (In radians) as follows:
*First: We transform the measure of the angle from degrees to radians, that is:
[tex]\theta=80\cdot\frac{\pi}{180}\Rightarrow\theta=\frac{4\pi}{9}[/tex]*Second: We find the arc length:
[tex]s=r\theta\Rightarrow s=(13.2)(\frac{4\pi}{9})[/tex][tex]\Rightarrow s=\frac{88}{15}\pi[/tex]So, the arc length for CT is 88pi/15 radians.
*Third: We find its measure in feet:
[tex]s\approx18.43[/tex]So, the arch length for CT in feet is approximately 18.43 feet.
Write a function to model the geometric sequence in the table. n: (1 2 3 4 5)a: (75 15 3 3/5 3/25)a) f(n) = 75 (1/5) nb) f(n) = 75 (1/5) n-1c) f(n) = 1/5 (75) nd) f(n) = 1/5 (75) n-1
First let's find the ratio of the sequence, by dividing one term by the term before:
[tex]\begin{gathered} \text{second term: 15} \\ \text{first term: 75} \\ ratio=\frac{15}{75}=\frac{1}{5} \end{gathered}[/tex]So the ratio is 1/5 and the first term is 75.
Now, we can use the following formula for the nth term of a geometric sequence:
[tex]a_n=a_1\cdot q^{n-1}[/tex]Where q is the ratio and a1 is the first term. So we have:
[tex]a_n=75(\frac{1}{5})^{n-1}[/tex]Substituting an by the function f(n), we have:
[tex]f(n)=75(\frac{1}{5})^{n-1}[/tex]So the correct option is b)
Hi, can you help me answer this question please, thank you!
Given that
[tex]\begin{gathered} \mu_d=\mu_2-\mu_1=21.1 \\ s_d=14.9 \\ n=8 \end{gathered}[/tex]a) The formula for the test statistics for this sample is,
[tex]t=\frac{\mu_d}{s_d\sqrt[]{n}}[/tex]Therefore,
[tex]\begin{gathered} t=\frac{21.1}{14.9\times\sqrt[]{8}}=0.50067 \\ t=0.50067\approx0.501(3\text{ decimal places)} \\ \therefore t=0.501 \end{gathered}[/tex]Hence, the test statistic for this sample is
[tex]t=0.501[/tex]b)
this. this is sucking my soul away.
Check the picture below.
let's recall that twin sides stemming from a common vertex, make twin angles at the base.
How do I solve this problem?By using the pythagorean identities.
Given the equation:
[tex]\sin ^2x(\csc ^2x-1)[/tex]Using the Pythagorean identities
so,
[tex]\csc ^2x-1=\cot ^2x[/tex]so, the equation will be:
[tex]\begin{gathered} \sin ^2x\cdot\cot ^2x \\ \\ =\sin ^2x\cdot\frac{\cos ^2x}{\sin ^2x} \\ \\ =\cos ^2x \end{gathered}[/tex]y=-2/3x+5 and goes through (0, -2)
with steps please
The equation of the line with coordinate (0, -2) that goes through y = -²/₃x + 5 is; y = -²/₃x - 2
What is the Equation of the Line?We know that the general formula for an equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, from the given equation of y = -²/₃x + 5, we can say that;
Slope; m = -²/₃
y-intercept = 5
Thus, equation of the new line would be;
y - (-2) = -²/₃(x - 0)
y + 2 = -²/₃x
y = -²/₃x - 2
Read more about Equation of Line at; https://brainly.com/question/13763238
#SPJ1
Create a data set that has 4 values with a mode of 3, a median of 6, and a meanof 10
We are to create a data set of 4
that is a, b, c, d
mode means a number that occur the most
Median means the middle number
Mean means the average number
in the set, we must have a mode of 3
3, 3,
to get a median of 6, we need a number when we add to three and divide by 2 will give us 6
the number is 9
3 + 9 / 2
12/ 2 =
3, 3 , 9, d
the last number is d and it is unknown
since means is 10
mean = summation of all the numbers in the data set / the total number
the total number is 4
mean = 10
10 = 3 + 3 + 9 + d / 4
cross multiplication
10 x 4 = 3 + 3 + 9 + d
40 = 6 + 9 + d
40 = 15 + d
isolate d
d = 40 - 15
d = 25
therefore, the data set with a mode of 3, median of 6 and a mean of 10 are
3 , 3 , 9, 25
Keisha is making potato casserole for a party. she needs 3/2 of a potato per guest. how many potatoes will she need for 15 guest
Keisha needs 3/2 of potato per guest ( i.e one guest is equivalent to 3/2 potato)
Thus, for 15 guests
she needs;
[tex]\begin{gathered} 15\text{ }\times\frac{3}{2} \\ \frac{15\times3}{2}=\frac{45}{2} \\ 22\frac{1}{2} \end{gathered}[/tex]Keisha needs 45/2 potatoes for 15 guests
Find LM tangent angle circle
Applying the two-tangent theorem, the length of LM is: A. 18.
What is the Two-Tangent Theorem?The two-tangent theorem states that if two tangents are drawn from a circle to meet at a point outside the circle, then the tangent segments are congruent to each other, that is they have equal lengths.
Segments LK and LM are tangent segments drawn to meet at the external point L. This means, the length of Lk and the length of LM would be equal to each other.
LK = 4x - 2
LM = 3x + 3
LK = LM
Substitute
4x - 2 = 3x + 3
Combine like terms
4x - 3x = 2 + 3
x = 5
LM = 3x + 3
Plug in the value of x
LM = 3(5) + 3
LM = 15 + 3
LM = 18
Learn more about the two-tangent theorem on:
https://brainly.com/question/4506246
#SPJ1
1. If DM = 35, what is the value of r?
DG=r + 3 GM=4r-28
Answer:
r=32
Step-by-step explanation:
when DM=35
then. 35=r+3
35-3=r
r=32 therefore, substitute into
second equation to solve GM
GM=4r-28
GM=128-28
GM=100
Solve for brainliest and 20 points please
Answer:
C.
Step-by-step explanation:
540
Answer:
540
Step-by-step explanation:
you can use this equation to find the sum of angles for a shape
(n-2)180 with n being the number of sides. Since a pentagon has 5,
its 5-2= 3 then times 180 is 540
Use the table to find the products od the two polynomials. Write your answer in descending order l.
Answer:
To use the given table to find product of the two polynomials.
Given that,
[tex](x^2+x-2)(4x^2-8x)[/tex]Explanation:
Using the table, we get it as,
we get,
[tex](x^2+x-2)(4x^2-8x)=4x^4-8x^3+4x^3-8x^2-8x^2+16x[/tex][tex]=4x^4-4x^3-16x^2+16[/tex]we get,
[tex](x^2+x-2)(4x^2-8x)=4x^4-4x^3-16x^2+16[/tex]Answer is:
[tex](x^2+x-2)(4x^2-8x)=4x^4-4x^3-16x^2+16[/tex]Can you please also give all forms of the end behavior such as ups/downs, as_,_ , and limits #25
The given function is a rational function
We will find the zeros of the denominator
[tex]\begin{gathered} 2x+1=0 \\ 2x=-1 \\ x=\frac{-1}{2} \end{gathered}[/tex]The end behavior of the function will be as follows:
[tex]\begin{gathered} x\rightarrow(-\frac{1}{2})^-;f(x)\rightarrow\infty \\ x\rightarrow(-\frac{1}{2})^+;f(x)\rightarrow-\infty \\ x\rightarrow\infty;f(x)\rightarrow\frac{1}{2} \\ x\rightarrow-\infty;f(x)\rightarrow\frac{1}{2} \end{gathered}[/tex]The graph of the function is as follows:
4. Find and interpret theaverage rate of change forthe interval. Show your work.1
Average rate of change = -2 celcius / hour
Interpretation: For every unit change in the time (x), there is a change of -2 celcius in the temperature
Explanations:The average rate of change is to be found for the interval:
[tex]1\text{ }\leq x\leq3[/tex]From the interval, we can deduce that:
[tex]x_1=1,x_2=3[/tex]Know the corresponding value of y for each value of x shown above:
[tex]\begin{gathered} \text{When x}_1=1,y_1=\text{ 6} \\ \text{When x}_2=3,y_2=\text{ 0} \end{gathered}[/tex]The average rate of cgange is given by the formula:
[tex]\begin{gathered} \frac{\delta y}{\delta x}=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \frac{\delta y}{\delta x}=\text{ }\frac{0-6}{3-1} \\ \frac{\delta y}{\delta x}=\frac{-6}{3} \\ \frac{\delta y}{\delta x}=-2 \end{gathered}[/tex]The rate of change for the interval is -2 celcius/hour
This can be interpreted as for every unit change in the time (x), there is a change of -2 celcius in the temperature
Help me asp please!!
It is an ongoing function. A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
What is function?In mathematics, a function is an expression, rule, or law that defines a connection between one variable (the independent variable) and another variable (the dependent variable).A function is defined as a relationship between a set of inputs and one output for each. A function is an input-output relationship in which each input corresponds to exactly one output.Every function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x is the input. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this.To learn more about function, refer to:
https://brainly.com/question/11624077
#SPJ13
A space shuttle is moving in a straight line and is traveling at a constant speed. It takes 3 hours to get from A to B and 1 hour to get from B to C. Relative to a suitable set of axes, A is the point (4,-1,7) and B is the point (16,-10,10). Find the coordinates of C.
We will solve as follows:
First: We will use the i, j, k vector notation to describe each point as a vector:
[tex]A=4i-j+7k[/tex][tex]B=16i-10j+10k[/tex]Now, we have that the time it takes to get from A to B is 3 hours (t1). And the time it takes from B to C is 1 hour (t2).
Second: We determine the speed from A to B:
[tex]v=\frac{B-A}{t_1}\Rightarrow v=\frac{(16-4)i+(-10+1)j+(10-7)k}{3}[/tex][tex]\Rightarrow v=\frac{12i-9j+3k}{3}\Rightarrow v=4i-3j+k[/tex]Third: We now determine the value of C:
[tex]C=B+vt_2\Rightarrow C=(16+4)i+(-10-3)j+(10+1)k[/tex][tex]\Rightarrow C=20i-13j+11k[/tex]So, we would have that the coordinates of C are:
[tex]C=(20,-13,11)[/tex]One weekend 5,780 people saw a new movie at (7 different theaters. Each theater sold tickets at ($7.50 a piece. If each theater received the same number of moviegoers, how much did each theater make?
Each theater sold tickets at ($7.50 a piece, if each theater received the same number of moviegoers, each theater make $6192.85 using arithmetic operations.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or more quantities. They cover topics like the study of numbers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry. Without applying the laws of arithmetic operations, we are unable to solve the issue. The four fundamental rules of mathematics are addition, subtraction, multiplication, and division.
Let the amount of each theater get be x,
No. of theaters are = 7
Cost of each ticket = $7.50
No. of people = 5780
Then we can say,
7x = 5780 ×7.50
x = [tex]\frac{5780\times7.50}{7}[/tex]
= $6192.85
To know more about arithmetic operations, visit:
https://brainly.com/question/20595275
#SPJ13
You have a tree in your yard that is 60 inches around. What is the diameter of the tree?
Given : a tree in your yard that is 60 inches around
60 inches represents the circumference of the tree
The circumference =
[tex]\pi\cdot d[/tex]Where d is the diameter of the tree
so,
[tex]\begin{gathered} \pi\cdot d=60 \\ \\ d=\frac{60}{\pi}\approx19.1 \end{gathered}[/tex]So, the answer is : the diameter of the tree is a bout 19.1 inches
A recipe that makes 10 pancakes calls for 13/4 cups of milk. If you want to scale down the recipe so that it makes only 2 pancakes, about how much milk should you use? A. 3/4 cup B. 1/2 cupC. 7/20 cup D. 3/10 cup E. 7/12 cup
13/20 cups
Explanations:The recipe makes 10 Pancakes with 13/4 cups of milk
The recipe will make 1 pancake with x cups of milk
[tex]\begin{gathered} x\text{ = }\frac{13}{4}\div10 \\ x\text{ = }\frac{13}{4}\times\frac{1}{10} \\ x\text{ = }\frac{13}{40} \\ \end{gathered}[/tex]The recipe will make 1 pancake with 13/40 cups of milk
The recipe will make 2 pancakes with (2 x 13/40) cups of milk
= 26 / 40
= 13 / 20
The recipe will make 2 pancakes with 13/20 cups of milk
A group of friends were working on a student film. They spent all their budget on equipment and props. They spent $369 on equipment and 55% of the total budget on props. What was the total budget for their student film
Answer: t = 820
Step-by-step explanation:
1) Set up the equation
369 + 55%t = t
2) Simplify the percentage
369+ 0.55t = t
3) Minus 0.55 t on both sides
369 = 0.45t
4) Set t by itself.
t = 820
The mean Exam score on the SOC 15 Exam 2 is 84.28 with a standard deviation of 6.71Your friend scored an 86 on the exam. What percentage of students scored lower than your friendon the exam?
First, find the z-score of 86
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{86-84.28}{6.71} \\ z=\frac{1.72}{6.71} \\ z=0.2563 \end{gathered}[/tex]Rounding to the nearest hundredth, that is 0.26
Next, find z = 0.26 to the left of z in the z-table and we have the following
Multiply by 100%, and we have
[tex]\begin{gathered} P(z<0.26)=0.60257 \\ \\ 0.60257\cdot100\%=60.257\% \end{gathered}[/tex]Therefore, the percentage of students who scored lower than 86 is 60.257%.
A line contains points F, G, H, I, J. The space between F G is 2. The space between H and I is 1. The space between F and I is 7.
If FG = 2 units, FI = 7 units, and HI = 1 unit, what is GH?
3 units
4 units
5 units
6 units
The measure of GH is 4 units.
The correct option is (B)
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Given:
FG = 2 units, FI = 7 units, and HI = 1 unit
Now,
FI = FG+ GH +HI
7= 2 + GH + 1
7= 3 + GH
GH = 7-3
GH = 4 units
Hence, the measure of GH is 4 units.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ1
Write the domain and range of g as intervals or unions of intervals
It's important to know that empty circles refer to open intervals or parenthesis.
In this case, we observe that the first interval of the domain is (-1, 1) and the second interval of the domain is (2, 5), so the whole domain would be the union of these two intervals.
[tex]\text{Domain}=(-1,1)\cup(2,5)[/tex]To obtain the range, let's observe the y-values. The function goes from y = -5 to y = 3, so the range would be
[tex]Range=(-5,3)[/tex]the store bought a bike from the factory for 90$ and sold it to Andre for 117 what percentage was the markup?
The markup percentage was
[tex]\begin{gathered} P=\frac{117-90}{90}\cdot100 \\ P=\frac{27}{90}\cdot100 \\ P=30 \end{gathered}[/tex]The markup percentage was 30%.
6.25 ft7.25 cm11 cm8.921.6 m
The area of the shaded region can determined by substracting the area of rectangle from the area of triangle,
[tex]\begin{gathered} A=A_r-A_t \\ =14\operatorname{cm}\times25\operatorname{cm}-(\frac{1}{2}\times11\operatorname{cm}\times25) \\ =212.5cm^2 \end{gathered}[/tex]Thus, the area of the shaded region is 212.5 square centimeters.