Answer: I = $ 1,102.50
Step-by-step explanation: First, converting R percent to r a decimal
r = R/100 = 7%/100 = 0.07 per year,
then, solving our equation
I = 4500 × 0.07 × 3.5 = 1102.5
I = $ 1,102.50
The simple interest accumulated
on a principal of $ 4,500.00
at a rate of 7% per year
for 3.5 years is $ 1,102.50.
The diamond method for factoring: Fill in the missing value
Consider a quadratic expression, let "m" and "n" represent the factors.
The diamond method of factoring is the following:
On the left of the diamond, there is one of the factors, for example, "m", of the right of the diamond you will find the other factor "n".
On the top of the diamond, you will find the product of both factors, on the bottom of the diamond you will find the sum of the factors.
Looking at the given diamond, you know the result of the product and the sum of both factors:
[tex]m*n=-15[/tex][tex]m+n=14[/tex]Using these expressions, you can find both factors.
- First, write the second expression for one of the variables, for example, for "n"
[tex]\begin{gathered} m+n=14 \\ m=14-n \end{gathered}[/tex]- Second, replace the expression obtained on the second equation:
[tex]\begin{gathered} m*n=-15 \\ (14-n)n=-15 \end{gathered}[/tex]Distribute the multiplication
[tex]14n-n^2=-15[/tex]Zero the expression and order the terms from greatest to least:
[tex]\begin{gathered} 14n-n^2+15=-15+15 \\ 14n-n^2+15=0 \\ -n^2+14n+15=0 \end{gathered}[/tex]- Third, use the quadratic expression to determine the possible values of n:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Where
a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant
For the quadratic expression obtained, where "n" represents the x-variable.
[tex]-n^2+14n+15=0[/tex]The coefficients are:
a= -1
b=14
c=15
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ n=\frac{-14\pm\sqrt{14^2-4*(-1)*15}}{2*(-1)} \\ n=\frac{-14\pm\sqrt{196+60}}{-2} \\ n=\frac{-14\pm\sqrt{256}}{-2} \\ n=\frac{-14\pm16}{-2} \end{gathered}[/tex]Solve the sum and difference separately to determine both possible values for "n"
→Sum:
[tex]\begin{gathered} n=\frac{-14+16}{-2} \\ n=\frac{2}{-2} \\ n=-1 \end{gathered}[/tex]→Difference:
[tex]\begin{gathered} n=\frac{-14-16}{-2} \\ n=\frac{-30}{-2} \\ n=15 \end{gathered}[/tex]- Finally, determine the possible value/s of m:
For n=-1
[tex]\begin{gathered} m+n=14 \\ m+(-1)=14 \\ m-1=14 \\ m=14+1 \\ m=15 \end{gathered}[/tex]For n=15
[tex]\begin{gathered} m+n=14 \\ m+15=14 \\ m=14-15 \\ m=-1 \end{gathered}[/tex]So, the factors are -1 and 15 and the diamond is:
Can someone pls help me . Thank you so much .FIRST PROBLEM
Answer:
Step-by-Step explanation:
We are given the following equation:
Daisy is buying a video game in the shop. The price before tax is $21, and after sales tax is $24.74. What is the sales tax plied to the video game? Round to the nearest hundredth
Recall that:
[tex]\text{salesprice}=\text{originalprice+taxes.}[/tex]Therefore Daisy pays:
[tex]24.74-21=3.74\text{ dollars}[/tex]in taxes for the videogame.
Now, recall that to determine the percentage that a represents from b we use the following expression:
[tex]\frac{a}{b}\cdot100.[/tex]Therefore, the sales tax applied to the videogame is:
[tex]\frac{3.74\text{dollars}}{21\text{dollars}}\cdot100\approx17.81[/tex]percent.
Answer: The tax applied to the videogame is 17.81%, in this case, the sales tax is 3.74 dollars.
Solve the system of equations. If the system has no solution say that it's inconsistent. [tex]\begin{gathered}x + 5y = 2 \\ 3x + 15y = 6\end{gathered}[/tex]
Answer:
Explanation: Given the system of equations:
[tex]\begin{gathered} x+5y=2 \\ 3x+15y=6 \end{gathered}[/tex]Question 8 According to a textbook, this is a challenging question; according to me, it is the easiestquestions, among the easy questions!Suppose that the equations ax + by = c, where a, b, and c are real numbers, describes a directvariation. What do you know about the value of c?That c is
The Solution:
Given the equation below:
[tex]ax+by=c_{}[/tex]We are asked to say what we know about the value of c.
From the above equation, it is clear that:
c is a variable that depends on the values of the variables x and y.(where a and b are possibly constants.
what is 5/8 out of 100
5/8 of 100 can be obtained by applying the rule of three:
[tex]\begin{gathered} 1\text{ ----- 100} \\ 5/8\text{ ----x} \end{gathered}[/tex]then, x is given by
[tex]\begin{gathered} x=\frac{\frac{5}{8}\cdot100}{1} \\ x=62.5 \end{gathered}[/tex]then, the answer is 62.5.
Freiese Um Which of the following is the graph of F(x) = 3x2 ?
To determine which is the graph of the function we can give some values to x to find point through the graph.
If x=0 then we have:
[tex]\begin{gathered} F(0)=3(0)^2 \\ F(0)=0 \end{gathered}[/tex]This means that the graph passes through the point (0,0).
If x=1 then we have:
[tex]\begin{gathered} F(1)=3(1)^2 \\ F(1)=3(1) \\ F(1)=3 \end{gathered}[/tex]This means that the graph passes through the point (1,3)
If x=-1 then we have:
[tex]\begin{gathered} F(-1)=3(-1)^2 \\ F(-1)=3(1) \\ F(-1)=3 \end{gathered}[/tex]This means that the graph passes through the point (-1,3)
Hence we conclude that the graph has to pass through the points (0,0) (1,3) and (-1,3)
Looking at the graphs given we notice that the third graph fullfils these condition; therefore, the graph of the function is shown in option C
The sugar sweet company needs to transport sugar to market. The graph below shows the transporting cost (in dollars) versus the weight of sugar being transported (in tons) a.)What is the cost of transporting 0 tonsb.) What is the cost of transporting 1 tons c.) Hos much does the cost increase for each ton of sugar being transported d.) Are the amounts given in parts b. and c. equal?
The cost of transport of tons is the point of intersection between the line and the X axis
Now we see that the point O tons, corresponds in the line to the point Y=1600
this the answer a)
For answer b) the point 1 corresponds to 2000
for answer c) the cost increase per ton is 400 , that is because 2000-1600= 400, and the line is inclined with a slope equal to 1
Claim: The mean pulse rate (in beats per minute) of adult males is equal to bpm. For a random sample of adult males, the mean pulse rate is bpm and the standard deviation is bpm. Find the value of the test statistic.
For solving this question, you should apply the equation:
The question gives
Next step - replace the values in the equation
[tex]z_T=\frac{70.4-69}{\frac{10.8}{\sqrt[]{129}}}=\frac{1.4}{\frac{10.8}{\sqrt{129}}}=1.47[/tex]Angles of Polygons The figure below is a pentagon whose interior angles have the same measure.What is the sum of the measures of these 5 angles?
Given the number of sides of a pentagon:
Number of sides = 5
Let's find the sum of the measures of the 5 equal angles.
To find the sum of the measures of interior angles of a polygon, apply the formula:
[tex]S=(n-2)*180[/tex]Where:
n is the number of sides = 5
Thus, we have:
[tex]\begin{gathered} S=(5-2)*180 \\ \\ S=(3)*180 \\ \\ S=540^o \end{gathered}[/tex]Therefore, the sum of the interior angles of the pentagon is 540 degrees.
ANSWER:
540°
A bridge being designed will crossthe river at a right angle. Theequation of the left bank of theriver is y = 2x + 8. The center ofthe bridge will pass through (0, 2).What is the equation of the linerepresenting the bridge?
Let's begin by listing out the information given to us:
Left side: y = 2x + 8
Center of the bridge: (0, 2)
[tex]\begin{gathered} y=2x+8 \\ m=2 \\ \text{However, the bridge is perpendicular to }y=2x+8\colon \\ m(perpendicular)=-\frac{1}{m} \\ m(perpendicular)=-\frac{1}{2} \end{gathered}[/tex]Use the point-slope formula to get the equation of the bridge:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(0,2);m=m(perpendicular)=-\frac{1}{2} \\ y-2=-\frac{1}{2}(x-0) \\ y-2=-\frac{1}{2}x \\ y=-\frac{1}{2}x+2 \\ \\ \therefore\text{ equation of the line representing the bridge is }y=-\frac{1}{2}x+2 \end{gathered}[/tex]Given the parametric equations x = 7cos θ and y = 5sin θ, which of the following represents the curve and its orientation?
We have the following parameters
[tex]\begin{gathered} x=7cos\theta \\ y=5sin\theta \end{gathered}[/tex]the general equation of a circle with center (0,0) is the following,
[tex]x^2+y^2=r^2[/tex]Let's use the following tigonometric identity,
[tex]sin^2\theta+cos^2\theta=1[/tex]solving for cos and sin in the equations we are given,
[tex]cos\theta=\frac{x}{7},sin\theta=\frac{y}{5}[/tex]replace,
[tex](\frac{y}{5})^2+(\frac{x}{7})^2=1[/tex]Since we have two different numbers in the denominator, this is not a circle equation but an elipse, of the form,
[tex]\frac{y^2}{a^2}+\frac{x^2}{b^2}=1[/tex]where,
a is the vertex and,
b is the covertex
thus, in the x axis, the vertex is 7 and the y-axis the covertex is 5
Now, let's determine the direction by replacing
when Θ = 0 , then x = 7*cos0 = 7*1 = 7 , and y = 5*sin0 = 5*0 = 0
when Θ = 90° or π/2 , then x = 7*cos90° = 7*0 = 0 , and y = 5sin90° = 5*1 = 5
If we draw this, we can see that the direction is counterclockwise as in the bottom right image.
QUESTION 6Emily has enrolled in a first year math class. The course has 5 assignments each worth 2%, 3 tests worth 20% and 2 tests worth 15%. Emily thus far has completed 3 assignments scoring: 72%, 84%, and 58%. In addition to the assignments, Emily has completed 2 tests: Test 1 (worth 20%) she scored 85% and Test 2 she scored 68% (worth 15%). What is Emily's current grade? Keep the answer in percent and round to the tenth if necessary. Do not input the percent (%) into the answer.
ANSWER:
76.8
STEP-BY-STEP EXPLANATION:
Given:
3 Assignments (2%)
1. 72%
2. 84%
3. 58%
1 Test (20%)
85%
1 Test (15%)
68%
We can calculate Emily's current grade using the weighted average principle, just like this:
[tex]p=\frac{\sum ^{}_{}x_i\cdot w_i}{\sum ^{}_{}w_i}[/tex]In this case, the value of x are the scores and w are the percentages associated with that value, we replace:
[tex]\begin{gathered} g=g=\frac{72\cdot2\%+84\cdot2\%+58\cdot2\%+85\cdot20\%+68\cdot15\%}{2\%+2\%+2\%+20\%+15\%} \\ g=\frac{72\cdot0.02+84\cdot0.02+58\cdot0.02+85\cdot0.2+68\cdot0.15}{0.02+0.02+0.02+0.2+0.15} \\ g=\frac{31.48}{0.41} \\ g=76.78 \\ g\cong76.8\% \end{gathered}[/tex]Therefore, Emily's current grade is 76.8%.
please help figure out this problem i’m trying to determine if the lines that appear to be tangent are tangent
Suppose that the two lines that form the missing angle are tangents to the circle. Then, the measure of the missing angle can be found using the following equation:
[tex]\measuredangle ABC=\frac{arc\text{ AEC - arc AGC}}{2}[/tex]Notice that we can complete the information about the arcs of the circle with the central angle:
then, we can find the angle x with the following expression:
[tex]\begin{gathered} \measuredangle x=\frac{243-117}{2}=\frac{126}{2}=63 \\ \Rightarrow\measuredangle x=63\degree \end{gathered}[/tex]therefore, the measure of the missing angle is 63 degrees.
Is the function y= –10x10–10 linear or nonlinear?
The function y = -10*x¹⁰ - 10
Is not a linear function, as we can see the exponent is 10.
Is the function linear or non-linear?Remember that a linear function is of the form:
y = m*x + b
Where x is the variable.
So a linear function is a polynomial of degree 1.
Particularly, here we have the function:
y = -10*x¹⁰ - 10
So we have an exponent of 10, which means that this is not a linear function.
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A music store has 40 trumpets, 39 clarinets, 24 violins, 51 flutes, and 16 trombones in stock. Write each ratio in simplest formTrumpets to violins
SOLUTION
Given the question in the question tab, the following are the solution steps to get the ratio of Trumpets to violins
Step 1: Write the given data
40 trumpets
39 clarinets
24 violins
51 flutes
16 trombones
Step 2: Write the ratio of trumpets to violins
Trumpets=40
Violins=24
[tex]\begin{gathered} \text{ratio}=40\colon24=\frac{40}{24} \\ By\text{ s}implification, \\ \frac{40}{24}=\frac{5}{3} \end{gathered}[/tex]Hence, the ratio of trumpets to violin in its simplest from is:
[tex]5\colon3[/tex]What is the measure of ∠N, if ∠M and ∠N are angles in a linear pair and the m∠M is 30°? *.
Given:
[tex]\angle M=30\degree[/tex]And angle M and N are angles in a linear pair.
Required:
To find the angle N.
Explanation:
The sum of angles of a linear pair is always equal to 180°.
Therefore,
[tex]\begin{gathered} \angle M+\angle N=180\degree \\ \\ 30\degree+\angle N=180\degree \\ \\ \angle N=180\degree-30\degree \\ \\ \angle N=150\degree \end{gathered}[/tex]Final Answer:
[tex]\angle N=150\degree[/tex]Writing about Finding a Percen Explain how to find 27% of 16 using multiplication by a decimal. Then explain how to use estimation to check your answer.
To find 27% of 16 using multiplication by a decimal, we can proceed as follows:
First, convert the number 27 in decimal:
[tex]16\cdot\frac{27}{100}=16\cdot0.27=4.32[/tex]A way to estimate the possible value, we can multiply the number 16 by the nearest tenth, that is, 0.3. We know that the possible value is a little greater than the actual value.
We can do this in the following way:
[tex]16\cdot\frac{30}{100}=\frac{48}{100}=4.8[/tex]Then, after the estimation, we can say that the value must be less than 4.8. Multiplying by 3 or 30 is easier than by 27. This is a way to check the answer.
We can also say that if we multiply 16 by 3 is 48 (equivalently to 4.8, after doing the correct operations), and this is a quick value to know, that, approximately 4.32 is 27% of 16.
You want to buy a $364,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan for the rest. (Enter numeric answers to 2 decimal places.)
a) How much is the loan amount going to be?
Considering buying a home for $364,000 and paying 5% down payment. The amount to be paid for loan is going to be $345 800
How to find the loan amountThe following is gotten from the question:
cost of the home = $ 364 000
percentage to pay as down payment = 5 %
Solving for the down payment
The down payment refers to the initial payment and is a percentage, We convert the percentage to decimal as follows
5 % = 5 / 100
= 0.05
The percentage of the money is calculated by multiplying as follows
5 % of $364 000
= 0.05 * 364 000
= $18 200
Solving for the loan amount
The loan amount is calculated by subtracting the down payment from the cost of home
= cost of the home - down payment
= $ 364 000 - $ 18 200
= $ 345 800
Conversion from percentage to decimal followed by multiplication helped to get the down payment, then subtracting the down payment from the cost of home helped to get the loan amount to be $345 800
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Determine the a coordinates of the critical points/numbers for the function f(x)= x/x^2+5
○ x=0, x= -√5, and x = √5
○ x=0
○ No critical points
○ x = √5
○x= -√5 and x = √5
The critical points for the given function f(x) are -√5 and √5.
so option d is the correct answer.
What is the critical point?A critical point is the part of the domain of a function where the derivative is either equal to zero or the function is not differentiable.
Differentiate the given function f(x)=x/(x²+5)
f'(x)=((x²+5)-x(2x))/(x²+5)²
Using the Quotient Rule for differentiation.
What is Quotient Rule?A method for finding the derivative or differentiation of a function that is given as a ratio or division of two differentiable functions in calculus is known as the quotient rule.
We get f'(x)=5-x²/(x²+5)²
So the derivative is zero at -√5 and √5 and non differentiable at -√5
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I'm needing help with graphing equation
what is the equation?
a) y = 2x
x y
1 2(1) = 2
2 2(2) = 4
3 2(3) = 6
4 2(4) = 8
5 2(5) = 10
b) y = x - 2
x y
2 2 - 2 = 0
3 3 - 2 = 1
4 4 - 2 = 2
5 5 - 2 = 3
6 6 - 2 = 4
a) line a
line b
c)
y = 3x + 2
x y
1 3(1) + 2 = 5
2 3(2) +2 = 8
3 3(3) + 2 = 11
4 3(4) + 2 = 14
5 3(5) + 2 = 17
line d
y = 5x - 3
x y
0 5(0) - 3 = -3
2 5(2) - 3 = 7
4 5(4) - 3 = 17
6 5(6) - 3 = 27
which is the solution of 3(t + 1) = 6 - 13.5?A <-5.5B t2-5.5Ci< 5.5D (>55
Let's begin by identifying key information given to us:
[tex]\begin{gathered} 3\mleft(t+1\mright)\le6t-13.5 \\ 3t+3\le6t-13.5 \\ \text{Put like terms together, we have:} \\ 3+13.5\le6t-3t \\ 16.5\le3t \\ \frac{16.5}{3}\le\frac{3t}{3} \\ 5.5\le t\Rightarrow t\ge5.5 \\ \therefore t\ge5.5 \end{gathered}[/tex]Therefore, D is the correct answer
"∆ABC~∆DEF. The area of ∆ABC is given. Find the area of ∆DEF. Do not lable the final answer."
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
∆ABC~∆DEF
triangle 1:
AC = 10
area = 65 in²
triangle 2:
DF = 20
area = ?
Step 02:
We must apply the rules of similar triangles to find the solution. .
[tex]\frac{triangle\text{ 1 AC}}{\text{triangle 2 DF }}=\frac{triangle\text{ 1 area}}{\text{triangle 2 area}}[/tex][tex]\frac{10}{20}=\frac{65in^2}{triangle\text{ 2 area}}[/tex]triangle 2 area * 10 = 65 in² * 20
triangle 2 area = (65 in² * 20 ) / 10
= 130 in²
The answer is:
The area of the big triangle is 130 in² .
The diameter of the pool is 5 feet. What is the circumference of the pool?
Use the standard algorithm to solve the equation 36 x 25 =
Answer: 900
Step-by-step explanation:
Column method
x=-3
f(x)= -2
f’(x)=2
g(x)=3
g’(x)=-1
h(x) = g(x)/2f(x)
Find h'(-3)
Answer: [tex]-1[/tex]
Step-by-step explanation:
Using the quotient rule,
[tex]h'(x)=\frac{2f(x)g'(x)-2g(x)f'(x)}{(2f(x))^2}\\\\h'(3)=\frac{2f(3)g'(3)-2g(3)f'(3)}{(2f(3))^2}\\\\=\frac{2(-2)(-1)-2(3)(2)}{2(-2)^2}\\\\=-1[/tex]
Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.(3,-5) , (4,5)
We will determine th equation in slope-intercept from of the line as follows:
First, we find the slope:
[tex]m=\frac{5-(-5)}{4-(3)}\Rightarrow m=10[/tex]Then:
[tex]y-5=10(x-4)\Rightarrow y-5=10x-40[/tex][tex]\Rightarrow y=10x-35[/tex]So, the equation of the line in slope-intercept form is:
[tex]y=10x-35[/tex]4x squared- 5x +4-(9x squared +3x -1)
hello
the question here requires the subtraction of polynomials
[tex]\begin{gathered} 4x^2-5x+4 \\ - \\ 9x^2+3x-1 \end{gathered}[/tex]if we are to do this, we have to subtract the polynomials based on their degree
this would be equal to
[tex]-5x^2-8x+5[/tex]the above polynomial is the result after subtraction, but we can as well, decide to multiply through by -1, to make or eilimate the negative sign on the second degree polynomal
[tex]\begin{gathered} (-5x^2-8x+5)\times-1 \\ = \\ 5x^2+8x-5 \end{gathered}[/tex]Round to the nearest thousand to estimate the difference between 7,333 and 4,983
Rounded to the nearest thousand the given numbers are:
[tex]\begin{gathered} 7,333 \\ 3<5\colon Round\text{ by leaving the digit in thousand position} \\ \\ 7,333\approx7,000 \end{gathered}[/tex][tex]\begin{gathered} 4,983 \\ 9>5\colon\text{ Round increasing the digit in thousand position} \\ \\ 4,983\approx5,000 \end{gathered}[/tex]Estimate the difference between 7,000 and 5,000:
[tex]7,000-5,000=2,000[/tex]Estimated difference: 2,000Jeremy Sold x tickets for a fundraiser. Kelly sold twice as many tickets as Jeremy Altogether. Jeremy and Kelly sold 192 tickets which equation could be used to determine how many tickets Jeremy sold?
If x represents Jeremy's sold tickets, then the expression 2x + x represents the part Kelly sold twice as many tickets as Jeremy.
If the sold 192 tickets together, then the expression is 3x = 192.
Hence, the answer is B.