The first company offers the better value deal based on price
Here, we want to compare the prices from the two companies
We can have the unit in the same system
For the first company, we have a price of $3.85 per meter
We want to convert this price to per foot
From the conversion;
1 foot = 0.3 meters
Thus;
[tex]\begin{gathered} 10\text{ foot = 3 meters} \\ or\text{ 1 meter = }\frac{1}{0.3\text{ }}\text{ fe}et \\ \\ \text{Thus;} \\ 3.85\text{ per meter will be} \\ 3.85\text{ divided by }\frac{1}{0.3} \\ \\ =\text{ 3.85 }\times\frac{0.3}{1} \\ =\text{ 1.155} \end{gathered}[/tex]So, for the first company, the price per foot is $1.155
As we can see, this is lesser than what the second company charges
Thus, the first company offers the better value deal based on price
I need help answering this, having trouble It’s trig from my ACT prep guideI will send you another pic of the graph that goes along
Question:
Solution:
Step 1: graph the parent function f(x)=cos(x)
Step 2: We want to graph y = f(x+c) where c is π/2. To do this, shift the graph of y =f(x)=cos(x) to the left π/2 units:
So that, we can conclude that the correct answer is:
The length of a rectangle is seven
times the width. If the width is represented by x
,
then write an algebraic expression that describes the length.
If the width is represented by [tex]x[/tex], then write an algebraic expression that describes the length is [tex]7x[/tex].
In the given question,
The length of a rectangle is seven times the width.
The width is represented by [tex]x[/tex].
We have to write an algebraic expression that describes the length.
Firstly we know about the rectangle,
A rectangle is a shape in which two sides are equal. It has four sides.
It is given that the length of rectangle is seven time the width of rectangle. The seven times means the length of rectangle is multiplied by [tex]7[/tex].
The width of rectangle is [tex]x[/tex].
So the length of the rectangle is [tex]7x[/tex].
So an algebraic expression of length is [tex]7x[/tex].
Hence, if the width is represented by [tex]x[/tex], then write an algebraic expression that describes the length is [tex]7x[/tex].
To learn more about rectangle link is here
brainly.com/question/17117320
#SPJ1
Simplify the given expression:csc(tan^-1)(w)=
The problem is given to be:
[tex]\csc (\tan ^{-1}(w))[/tex]Let
[tex]\begin{gathered} \theta=\tan ^{-1}w \\ \therefore \\ \tan \theta=w \end{gathered}[/tex]We can write the above to be:
[tex]\tan \theta=\frac{w}{1}[/tex]Using the above, we can draw a right-angled triangle as shown below:
To find the value of x, we can use the Pythagorean Theorem:
[tex]\begin{gathered} x^2=w^2+1^2 \\ x=\sqrt[]{w^2+1} \end{gathered}[/tex]Recall:
[tex]\csc (\tan ^{-1}(w))=\csc \theta[/tex]The identity of cosec is given to be:
[tex]\csc \theta=\frac{1}{\sin \theta}[/tex]From the triangle,
[tex]\sin \theta=\frac{w}{x}=\frac{w}{\sqrt[]{w^2+1}}[/tex]Therefore,
[tex]\csc \theta=\frac{\sqrt[]{w^2+1}}{w}[/tex]Therefore, the answer is given to be:
[tex]\csc (\tan ^{-1}(w))=\frac{\sqrt[]{w^2+1}}{w}[/tex]mr. Martin's math class math test which is worth a hundred points has 29 problems each problems is worth either five points or two points let X be the number of questions worth 5 Points and let y be the number of questions worth two points x + y equals 29 5x + 2 y equals 100 how many problems of each point value are on the test
Let x be the number of questions worth 5 points and y be the number of questions worth 2 points.
[tex]\begin{gathered} x+y=29\quad eq.1 \\ 5x+2y=100\quad eq.2 \end{gathered}[/tex]Let us solve this system of equations using the substitution method.
[tex]\begin{gathered} x+y=29 \\ y=29-x\quad eq.1 \end{gathered}[/tex]Substitute eq. 1 into eq. 2
[tex]\begin{gathered} 5x+2y=100\quad eq.2 \\ 5x+2(29-x)=100 \\ 5x+58-2x=100 \\ 5x-2x=100-58 \\ 3x=42 \\ x=\frac{42}{3} \\ x=14 \end{gathered}[/tex]So, there are 14 questions worth 5 points.
Now substitute the value of x into eq. 1 to get the value of y
[tex]\begin{gathered} y=29-x\quad eq.1 \\ y=29-14 \\ y=15 \end{gathered}[/tex]So, there are 15 questions worth 2 points.
Therefore, the correct answer is
14 questions worth 5 points and 15 questions worth 2 points.
WUa. Give another name for UV.b. Name a ray with endpoint X.c. Match each ray with its opposite ray.UZUVUXIII「画 4 □白首
Another name for line segment UV is VU.
Graph the inequality on the numberline and then write it in interval notation. 4-3y<-8
First, let's simplify the inequality
[tex]\begin{gathered} \frac{4}{3}y<-8 \\ \Rightarrow4y<-24 \\ \Rightarrow y<-6 \end{gathered}[/tex]The graph looks like this:
Notice that the white dot is placed above the -6, it is important to include it like that.
Now, as an interval:
[tex]\begin{gathered} y<-6 \\ \Rightarrow y\in(-\infty,-6) \end{gathered}[/tex]In 2000, Jose Gonzalez earned $54,700 as a self-employed worker. He also earned $40,150 as an employee. How much FICA tax did he pay for both earnings? Note: Self-employed tax rate is 15.3% and the employee tax rate is 7.65%.$10,992.75$11,025.50$11,155.90$11,440.58None of these choices are correct.
Answer:
$11,440.58
Explanation:
Amount earned as a self-employed worker = $54,700
Self-employed tax rate = 15.3%
Amount earned as an employee = $40,150
The employee tax rate = 7.65%.
[tex]Total\; \text{Tax Paid=(}15.3\%\times54700)+(7.65\%\times40150)[/tex]We solve for our result:
[tex]\begin{gathered} Total\; \text{Tax Paid=(}\frac{15.3}{100}\times54700)+(\frac{7.65}{100}\times40150) \\ =\text{(}0.153\times54700)+(0.0765\times40150) \\ =8369.1+3071.48 \\ =11440.58 \end{gathered}[/tex]The total FICA tax he paid for both earnings is $11,440.58.
what is the circumstance if the diameter is 21in and pi is 3.14
The result is 346.19 in^2
what is the name of a number that is grater then zero
It's often called Positive number
I will like help with the second question -3 1/2...
Answer:
Step-by-step explanation:
hope this helps
What are the steps to solve x^2+19x=-90
we have the equation
[tex]x^2+19x=-90[/tex]step 1
Rewrite in standard form
[tex]x^2+19x+90=0[/tex]step 2
we have
a=1
b=19
c=90
substitute in the formula
[tex]x=\frac{-19\pm\sqrt{19^2-4(1)(90)}}{2(1)}[/tex][tex]x=\frac{-19\pm1}{2}[/tex]The values of x are
x=-9 and x=-10Round the following percentages two decimal placesA. 16.981%B. 13.655%C. 0.569%D. 98.990%E. 98.999%
Given the percentages provided in the exercise, you need to follow these steps in order to round them to two decimal places:
1. Identify the digit in the Thousandths Place.
2. If the digit is greater than or equal to 5, you must round up. This means that you must add 1 unit to the digit in the Hundredths Place, and the other digits on the right become zero.
3. If the digit is less than 5, you must round down. This means that the digit in the Hundredths Place stays the same and the other digits on the right become zero.
Therefore, applying those steps, you get:
A.
[tex]16.981\text{\%}\approx16.98\text{\%}[/tex]B.
[tex]13.655\text{\%}\approx13.66\text{\%}[/tex]C.
[tex]0.569\text{\%}\approx0.57\text{\%}[/tex]D.
[tex]98.990\text{\%}\approx98.99\text{\%}[/tex]E.
[tex]98.999\text{\%}\approx99.00\text{\%}[/tex]Hence, the answers are:
A.
[tex]16.981\text{\%}\approx16.98\text{\%}[/tex]B.
[tex]13.655\text{\%}\approx13.66\text{\%}[/tex]C.
[tex]0.569\text{\%}\approx0.57\text{\%}[/tex]D.
[tex]98.990\text{\%}\approx98.99\text{\%}[/tex]E.
[tex]98.999\text{\%}\approx99.00\text{\%}[/tex]Using suitable identity evaluate the following : 98^3
941,192
Steps:
[tex](a-b)^3=a^3-b^3-3a^2b+3ab[/tex][tex]\begin{gathered} (98)^3=(100-2)^3 \\ (100-2)^{3\text{ }}=(100)^3-(2)^3-3\cdot(100)^2\cdot2+3\cdot100\cdot2^2\text{ } \\ (100)^3-(2)^3-3\cdot(100)^2\cdot2+3\cdot100\cdot2^2\text{ = 1,0}00,000\text{ - 3 - 60,000 +1,200} \\ \text{ 1,0}00,000\text{ - 3 - 60,000 +1,200 = 941,192} \end{gathered}[/tex]A manufacturer made a television set at a cost of $6,000.00 and sold it to a wholesaler at a profit of 10%.The wholesaler sold it to a retailer at a profit of 15%. The retailer marked the set to be sold at a profit of 25%.find the cost to the wholesaler, the selling price of the wholesaler and the marked price of the retailer
cost to the wholesaler:6600
selling price of the wholesaler : 7590
the marked price of the retailer is $ 9487.5
Explanation
Step 1
a)A manufacturer made a television set at a cost of $6,000.00 and sold it to a wholesaler at a profit of 10%
to find the new price, we can use the formula:
[tex]\text{new price= original price}\cdot(1+\frac{\text{ \% }}{100})[/tex]so,let
original price= 6000
%=10
replace
[tex]\begin{gathered} \text{new price= original price}\cdot(1+\frac{\text{ \% }}{100}) \\ \text{New}=6000\cdot(1+\frac{10}{100})=6000(1.1)=6600 \end{gathered}[/tex]so, the manufacturer sold the TV set for $6600
Step 2
b)The wholesaler sold it to a retailer at a profit of 15%
again we need apply the formula
this time, let
original price= 6600
% of profit=15
replace
[tex]\begin{gathered} \text{new price= original price}\cdot(1+\frac{\text{ \% }}{100}) \\ \text{New}=6600(1+\frac{15}{100})=6600(1.15) \\ \text{New}=7590 \end{gathered}[/tex]therefore,
the wholsaer sold it for $7590
Step 3
c)The retailer marked the set to be sold at a profit of 25%
hence,let
original= 7590
% of profit= 25%
replace and calculate
[tex]\begin{gathered} \text{new price= original price}\cdot(1+\frac{\text{ \% }}{100}) \\ \text{New}=7590\cdot(1+\frac{25}{100})=7590(1.25) \\ \text{New}=9487.5 \end{gathered}[/tex]therefore, the marked price of the retailer is $ 9487.5
I hope this helps you
How long will it take for an investment of 1600 dollars to grow to 7600 dollars, if the nominal rate of interest is 8.3 percent compounded quarterly? FV = PV(1 + r/n )^ntAnswer= ________years. (Be sure to give 4 decimal places of accuracy.)
18.9669 years
Explanation:principal = $1600
future value = $7600
rate = 8.3% = 0.083
n = number of times compounded = quarterly
n = 4
time = ?
To determine the time it will take, we will apply the compound interest formula:
[tex]FV\text{ = P(1 +}\frac{r}{n})^{nt}[/tex]substitute the values into the formula:
[tex]\begin{gathered} 7600\text{ = 1600(1 +}\frac{0.083}{4})^{4\times t} \\ 7600=1600(1+0.02075)^{4t} \\ \\ \text{divide both sides by 1600:} \\ \frac{7600}{1600}=\frac{1600(1+0.02075)^{4t}}{1600} \\ 4.75\text{ = }(1+0.02075)^{4t} \\ \end{gathered}[/tex][tex]\begin{gathered} 4.75\text{ = }(1.02075)^{4t} \\ \text{take log of both sides:} \\ \log 4.75\text{ = log }(1.02075)^{4t} \\ \log 4.75\text{ = 4t log }(1.02075) \\ \\ \text{divide both sides by log }(1.02075)\colon \\ \frac{\log 4.75\text{ }}{\text{ log }(1.02075)}\text{=}\frac{\text{ 4t log }(1.02075)}{\text{ log }(1.02075)} \\ 75.8677\text{ = 4t} \end{gathered}[/tex][tex]\begin{gathered} \text{divide both sides by 4:} \\ \frac{75.8677}{4}\text{ = }\frac{4t}{4} \\ t\text{ = 18.9669} \end{gathered}[/tex]It will take 18.9669 years (4 decimal place)
The bakers want to sell their house for $145,500. After 2 months, the Bakers decided to mark down the price of their house 8% to sell more quickly. How much are the Bakers selling their Fouse for now?
The details provided are as follows;
The sales price of the house = 145500
Mark down price = -8%
This means the bakers were willing to sell their price not at a 100% price of 145500, but at a price which is -8% of 145500. We would start by calculating 8% of 145500 as follows;
20. Given A(4, 2) and B(-1, y) and the graph of line t below, find the value of y so that AB is perpendicular to t
two lines are perpendicular when the multiplication of their slopes is equal to -1.
the slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\text{ }\frac{y_2-y_1}{x_2-x_1}[/tex]Then, the slope of the lines that passes through A(4,2) and B(-1,y) is:
[tex]m_1=\frac{y-2}{-1-4}=\frac{y-2}{-5}[/tex]From the picture, t passes through (-1, 2) and (2,4), then its slope is:
[tex]m_2=\frac{4-2}{2-(-1)}=\frac{2}{3}[/tex]Then
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ \frac{y-2}{-5}\cdot\frac{2}{3}=-1 \\ \frac{(y-2)\cdot2}{-15}=-1 \\ (y-2)\cdot2=(-1)\cdot(-15) \\ y-2=\frac{15}{2} \\ y=\frac{15}{2}+2 \\ y=\frac{19}{2} \end{gathered}[/tex]Write the point-slope form of an equation of the line through thepoints (-1, 4) and (-2, 2).
The slope of the line is given by:
[tex]m=\frac{4-2}{(-1)-(-2)}=2[/tex]If a line has slope m and passes through the point (a,b), its equation in the point slope form is given by: (y-b) = m(x - a)
Then, if (a,b) = (-1,4), we have: y - 4 = 2(x + 1) (option C)
Can you help me solve this problem. Part b only
Answer:
C. (x, -y)
Explanation:
Given quadrilateral ABCD, we want to determine the coordinate describing the vertex when it is reflected over the x-axis.
When a point (x,y) is reflected across the x-axis, the transformation rule is given below:
[tex](x,y)\to(x,-y)[/tex]Given that (x,y) describes a coordinate of quadrilateral ABCD, the coordinates of A''B''C''D'' will be:
[tex](x,y)\to(x,-y)[/tex]The coordinate of the corresponding vertex is (x, -y).
Option C is correct.
The perimeter of a regular pentagon is 10x + 15. what is the length of each side of the pentagon?
A regular pentagon has 5 equal sides. recall, perimeter is the sum of the distance around a shape. This means that the perimeter of the regular pentagon is the sum of the 5 equal sides. If the perimeter is 10x + 15, then,
length of each side = (10x + 15)/5
length of each side = 2x + 3
answer options are belowA. -4B. -3C. -1D. The limit does not exist (this is from my act prep guide, I’m having trouble on calculus right now)
Given a graph of the function;
[tex]\lim _{x\to-1}f(x)[/tex]From the graph, as x is approaching -1, f(x) is approaching -3. Thus;
The limit of a function
[tex]\lim _{x\to-1}f(x)=-3[/tex]CORRECT OPTION: B
Describe the transformations of the graph f(x) = (x - 2)^2 - 5
Answer:
• Horizontal translation right 2 units
,• Vertical Translation down 5 units
Explanation:
Given the parent function x²
If we translate the parent function by a horizontal translation right 2 units, we have:
[tex](x-2)^2[/tex]If we carry out a Vertical Translation down 5 units, we then have:
[tex]f(x)=(x-2)^2-5[/tex]What is fifty dollars less and 5 cents more than $144.50
Solution
Step 1
5cents is the same as $0.05.
Fifty dillars = $50
Step 2
For fifty dillars less than $144.50, you will subtract $50 from $144.50.
= $144.50 - $50
= $94.5
Step 3
5 cents more than is by adding $0.05 to the above result.
= $94.5 + $0.05
= $94.55
Final answer
$94.55
Maria Invests $600 in a bank account that earns simple interest. She earns $30 at the end of 12 months . How much money will Janae earn on her $350 investment after the 12 months.
Given data:
The given amount of money Maria have p=$600.
The interest earn by Maria is i=$30.
The given amount of money Janae have p'=$350.
The given time is t=12 months=1 year.
The expression for the interest is,
i=(pxrxt)/100
30=(600)(r)(1)/100
30 =6r
r=5
The expression for interest earn by Janae is,
i'=(p'xrxt)/100
Substitute the given values in the above expression.
i'=(350)(5)(1)/100
=$17.5
Thus, Janae earn $17.5 money from her investment.
Use the pattern from part a to find the sum of the squares of the first 16 Fibonacci numbers
GIVEN:
We are given a Fibonacci sequence as shown in the attached image.
Required;
To use the pattern derived to find the sum of the squares of the first 16 Fibonacci numbers.
Step-by-step solution;
We have a Fibonacci sequence whose first term is 1.
The sequence and the sum of the squares of a given number of terms is derived as follows;
[tex]\begin{gathered} 1^2+1^2=1\times2 \\ \\ 1^2+1^2+2^2=2\times3 \\ \\ 1^2+1^2+2^2+3^2=3\times5 \\ \\ 1^2+1^2+2^2+3^2+5^2=5\times8 \\ \\ 1^2+1^2+2^2+3^2+5^2+8^2=8\times13 \\ \\ 1^2+1^2+2^2+3^2+5^2+8^2+13^2=13\times21 \end{gathered}[/tex]Next, we determine the sequence from the 1st to 16th term as follows;
[tex]\begin{gathered} 1^2+1^2+2^2+3^2+5^2+8^2+13^2+21^2+34^2+55^2+89^2 \\ \\ +144^2+233^2+377^2+610^2+987^2=987\times1597 \end{gathered}[/tex]The sum of the squares of the first 16 terms therefore is
[tex]987\times1597=1,576,239[/tex]ANSWER:
[tex]1,576,239[/tex]How to solve for problem 21? Calculate the surface area of the hemisphere with the knowledge that the circumference of a great circle is 40.8 inches.
In order to get the surface area of a hemisphere, let's determine its radius first.
Based on the question, the circumference of a great circle is 40.8 inches. Since circumference = 2πr, then 40.8 inches = 2πr. From this, we can solve for the radius.
[tex]40.8=2\pi r[/tex]To solve for the radius, divide both sides of the equation by 2π. Use π = 3.14159
[tex]\frac{40.8}{2\pi}=r[/tex][tex]\frac{40.8}{2(3.14159)}\Rightarrow\frac{40.8}{6.28318}\Rightarrow6.4935[/tex]Therefore, the length of the radius is 6.4935 inches.
Now that we have the radius, let's calculate the surface area of the hemisphere. The formula is:
[tex]SA_{hemisphere}=3\pi r^2[/tex]Let's plug into the formula r = 6.4935 inches and π = 3.14159
[tex]SA_{hemisphere}=3(3.14159)(6.4935in)^2[/tex]Then, solve.
[tex]SA_{hemisphere}=(9.42477)(42.1655in^2)[/tex][tex]SA_{hemisphere}\approx397.4in^2[/tex]Therefore, the surface area of the hemisphere is approximately 397.4 square inches.
2. Determine the points of intersection of each pair of functions. a) y = 4x2 – 15x + 20 and y = 5x – 4
In order to determine the points of intersection proceed as follow:
Equal both equations:
[tex]4x^2-15x+20=5x-4[/tex]Write the previous equation as an standard quadratic equation:
[tex]\begin{gathered} 4x^2-15x+20=5x-4 \\ 4x^2-15x-5x+20+4=0 \\ 4x^2-20x+24=0 \\ x^2-5x+6=0 \end{gathered}[/tex]to obtain the last equation you divide by 4 both sides.
Now, use the quadratic formula, with a = 1, b = -5 and c = 6, to find the solution for x:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} x=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(1)(6)}}{2(1)} \\ x=\frac{5\pm\sqrt[]{25-24}}{2} \\ x=\frac{5\pm1}{2} \\ x_1=\frac{5-1}{2}=\frac{4}{2}=2 \\ x_2=\frac{5+1}{2}=\frac{6}{2}=3 \end{gathered}[/tex]The previous solutions mean that for the values of x = 2 and x = 3 the given functions intersect each other.
By replacing the values of x into any of the functions, for instance, in
y = 5x - 4, you get:
y = 5(2) - 4 = 10 - 4 = 6
y = 5(3) - 4 = 15 - 4 = 11
Then, the points of intersection are:
(2 , 6)
(3 , 11)
The graph is shown below:
Tell Esther the ordered pair is a solution of y=-4x+5 a) (1,2) b) (0,-4)
the expression is,
y = -4x + 5
poitn a is
a(1,2)
put x = 1
y = -4(1) + 5
y = -4 + 5
y = 1
so it is not the satisfying the equation thus, this pair is not the solution
point b is
b(0,-4)
put x = 0
y = -4(0) + 5
y = 5
so it is not the satisfying the equation thus, this pair is not the solution
both the points are not the solution of the given equation
there is rope running from the top of a flag pole to a hook in the ground. The flagpole is 9 meters high, the hook is 12 meters from it's base, and the rope is_______ meters long
Answer:
The rope is 15 meters long
Explanation:
Below is a sketch of the situation
Now, the Pythagorean theorem says that if we have a right triangle of side lengths a and b then the hypotenuse is given by
[tex]a^2+b^2=c^2[/tex]Now, in our case, the rope, the pole, and the distance to the hook forms a right triangle; therefore, the length of the rope is given by
[tex]12^2+9^2=c^2[/tex]
Solve the formula for the indicated variable.W = XYZ for ZZ=
Answer:
Z = W/(XY)
Step-by-step explanation:
We have the following equation:
W = XYZ
To solve for Z, we switch XY to the other side of the equality, doing the inverse multiplication(it multiplies Z, so it switches dividing). Then
Z = W/(XY)
Is the solution for Z.