Simple interest formula:
[tex]I=P\times r\times t[/tex]I is the interest
P is the principal amount
r is the rate of interest in decimal form
t is the time in years
For the given situation:
P=10,000
r= (10/100)=0.1
t=3
[tex]\begin{gathered} I=10,000\times0.1\times3 \\ \\ I=3,000 \end{gathered}[/tex]Then, the interest on the loan is $3,000A piece of sheet metal, w = 20 inches wide, is bent to form the guttershown in the illustration. If the cross-sectional area is 18 square inches,find the depth of the gutter.Tho Yilar County News earns a profit of $20 per year for each of its 3,000
The width of the sheet is 20 inches:
[tex]w=20[/tex]The cross-sectional area is 18 square inches.
From the diagram provided, the cross-sectional area is calculated to be:
[tex]A=(w-2x)(x)[/tex]Therefore, we have that:
[tex](w-2x)(x)=18[/tex]Expanding the equation, we have:
[tex]wx-2x^2=18[/tex]If we substitute the value of w into the equation, we have:
[tex]20x-2x^2=18[/tex]We can divide through by 2 and rearrange the equation. Thus, we have:
[tex]x^2-10x+9=0[/tex]Solving the quadratic equation by factorization, we have:
[tex]\begin{gathered} x^2-9x-x+9=0 \\ x(x-9)-1(x-9)=0 \\ (x-9)(x-1)=0 \\ \therefore \\ x=9\text{ or 1} \end{gathered}[/tex]Therefore, the depth of the gutter can be 1 inch or 9 inches.
The measures of the angles of a triangle are in the extended ratio 5:6:7. What is the measure of the largest angle?A. 10 degreesB. 50 degreesC. 60 degreesD. 70 degreesthank you ! :)
Given:
The measures of the angles of a triangle are in the extended ratio 5:6:7.
Required:
We need to find the largest angle.
Explanation:
The measure of angles are 5x, 6x, and 7x.
We know that the sum of all three angles is 180 degrees.
[tex]5x+6x+7x=180\degree[/tex][tex]18x=180\degree[/tex]Divide both sides by 18.
[tex]\frac{18x}{18}=\frac{180\degree}{18}[/tex][tex]x=10\degree[/tex]The largest angle is 7x since 7 is larger than 5 anf 6.
[tex]7x=7\times10=70\degree[/tex]The largest angle is 70 degrees,
Final answer:
The measure of the largest angle is 70 degrees,
Operations with Radical Expressions I’m still learning about this concept and I’m having trouble understanding the complexity of the problem!
Answer:
Explanation:
Question 3.
Before we simplify the radical expression let us note the following.
[tex]\begin{gathered} 27=9\times3 \\ 45=9\times5 \end{gathered}[/tex]Therefore, we can write our radical function as
[tex]\begin{gathered} -\sqrt[]{27}-2\sqrt[]{27}+2\sqrt[]{45} \\ \Rightarrow-\sqrt[]{9\times3}-2\sqrt[]{9\times3}+2\sqrt[]{9\times5} \end{gathered}[/tex]Now,
[tex]\begin{gathered} \sqrt[]{9\times3}=\sqrt[]{9}\times\sqrt[]{3}=3\sqrt[]{3} \\ \sqrt[]{9\times5}=\sqrt[]{9}\times\sqrt[]{5}=3\sqrt[]{5} \end{gathered}[/tex]therefore, our expression becomes
[tex]\begin{gathered} -\sqrt[]{9\times3}-2\sqrt[]{9\times3}+2\sqrt[]{9\times5} \\ \Rightarrow-3\sqrt[]{3}-2(3\sqrt[]{3})+2(3\sqrt[]{5}) \end{gathered}[/tex]which simplifies to give
[tex]-3\sqrt[]{3}-6\sqrt[]{3}+6\sqrt[]{5}[/tex]since -3√3 - 6 √3 = - 9 √3 ( just add them up), the above becomes
[tex]-9\sqrt[]{3}+6\sqrt[]{5}[/tex]We cannot simplify the above function any further. Therefore, the above expression is our final answer.
Question 5.
Since -3√ 27 - 3√27 = -6 √27, our expression becomes
[tex]-3\sqrt[]{20}-6\sqrt[]{27}[/tex]Let us also note that
[tex]\begin{gathered} 20=4\times5 \\ 27=3\times9 \end{gathered}[/tex]therefore,
[tex]\begin{gathered} \sqrt[]{27}=\sqrt[]{3\times9} \\ \sqrt[]{20}=\sqrt[]{4\times5} \end{gathered}[/tex]therefore, our expression becomes
[tex]-3\sqrt[]{4\times5}-6\sqrt[]{3\times9}[/tex]Now since
[tex]\begin{gathered} \sqrt[]{4\times5}=\sqrt[]{4}\times\sqrt[]{5}=2\sqrt[]{5} \\ \sqrt[]{3\times9}=\sqrt[]{3}\times\sqrt[]{9}=3\sqrt[]{3} \end{gathered}[/tex]the above becomes
[tex]-3(2\sqrt[]{5})-6(3\sqrt[]{3})[/tex][tex]\Rightarrow-6\sqrt[]{5}-18\sqrt[]{3}[/tex]We cannot simplify the above function any further. Therefore, the above expression is our final answer.
the cost of a motorcycle $6,500 and markup prices 80%
Solving for retail price of a $6,500 motorcycle given a 80% markup:
We know that the original price of the bike is $6,500, and we want to obtain 80% of profit when we sell it.
Therefore, we ought to calculate the 80% of $6,500 , and then add this value to the original price.
A simple formula for the y percentage of x (y% of x) is:
[tex]x\times\frac{y}{100}[/tex]Applying it to this problem to find 80% of $6,500:
[tex]6500\times\frac{80}{100}=5200[/tex]Adding up the $6,500 of the original price with the markup of 80% ($5,200), we get:
[tex]6500+5200=11700[/tex]Thus, the retail price of the motorcycle, if we want to obtain an 80% markup, should be $11,700
Talia has a daily budget of $94 for a car rental. The car cost $34 per dayplus $1 per mile. How many miles can Talia drive in one day?
let
number of miles = x
budget = $94
Therefore,
[tex]\begin{gathered} 94=34+x \\ 94-34=x \\ x=60\text{ miles} \end{gathered}[/tex]A rectangle prism has a length of 4 cm and a width of 1 1/2 cm and a height of 2 1/2 cm.how many unit cubes with edge lengths of 1/2 cm will it take to fill the prism? what is the volume of the prism?the prism can be filled with _ unit cubes that have edge lengths of 1/2 cmThe volume of the prism is _ cm3
Volume of a Rectangular Prism
The dimensions of a rectangular prism are:
L = 4 cm
W = 1 1/2 cm
H = 2 1/2 cm
We'll convert the mixed fractions to improper fractions:
[tex]W=1\frac{1}{2}=1+\frac{1}{2}=\frac{3}{2}[/tex][tex]H=2\frac{1}{2}=2+\frac{1}{2}=\frac{5}{2}[/tex]The volume of the prism is:
[tex]V=L\cdot W\cdot H=4\cdot\frac{3}{2}\cdot\frac{5}{2}=15\operatorname{cm}^3[/tex]The unit cube has a length of 1/2 cm. The volume of each cube is
[tex]V^{\prime}=(\frac{1}{2})^3=\frac{1}{8}cm^3[/tex]To find the number of unit cubes that fill the prism, we divide both volumes as follows:
[tex]\frac{15}{\frac{1}{8}}=15\cdot8=120[/tex]The prism can be filled with 120 unit cubes
The volume of the prism is 15 cm3
Spiral Review Find the range of allowable values based on an expected mass of 250 grams for which values are allowed to vary by 5%.
Given:
An expected mass of 250 grams
It is allowed to vary by 5%
The variation may be increase or decrease
We will find 5% of the given mass
So,
[tex]5\%of250=0.05\times250=12.5\text{ grams}[/tex]So, the range will be from (250 - 12.5) to (250 + 12.5 )
if the allowable value = x
So, the range will be:
[tex]237.5\le x\le262.5[/tex]Use the model showing 2 wholes divided into thirds to find the quotient 2 ÷ (1/3)
Notice that after dividing two wholes into thirds, a total of six parts are created.
Additionally, remember that to divide by a fraction is the same as to multiply by its reciprocal. Then:
[tex]2\div\frac{1}{3}=2\times\frac{3}{1}=2\times3=6[/tex]Therefore, the correct choice is option D) 6.
Gary is building a new L-shaped desk for his room. He wants to make sure it is large enough to hold all his supplies. The dimensions of the desk, in feet, are shown in the diagram. What is the area of the desk?
In order to calculate the desk area, let's divide it in two rectangular areas:
A1 = vertical rectangle with dimensions 6 ft and 3 ft
A2 = horizontal rectangle with dimensions 6 ft and 2 ft
So we have:
[tex]\begin{gathered} A=A_1+A_2 \\ A=6\cdot3+6\cdot2 \\ A=18+12 \\ A=30\text{ ft2} \end{gathered}[/tex]So the desk area is 30 ft².
Question 8 of 10Which choices are equivalent to the expression below? Check all that apply.4-√√6A. √24B. √96C. √√32 √√3D. 96E. √4√36F. 166
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} 4\text{ }\sqrt{6} \\ =\text{ }\sqrt{16\text{ }}\text{ x }\sqrt{6}\text{ } \\ =\text{ }\sqrt{96}\text{ } \\ =\text{ }\sqrt{32\text{ }}\text{ x }\sqrt{3}\text{ } \end{gathered}[/tex]CONCLUSION:
The final answers are:
[tex][/tex]Suppose that 29% of people own dogs. If you pick two people at random, what is the probability that they both own a dog?Give your answer as a decimal (to at least 3 places) or fraction
Given:
29% of people own dogs = 0.29
The probability that both own a dog is given by:
[tex]P=P(owns\text{ dog\rparen}\times P(owns\text{ dog\rparen}[/tex]So:
[tex]P=0.29\times0.29=0.084[/tex]Answer: 0.084
What is the probability that a female is majoring in physics? Round the answer to the nearest hundredth of a percent.
Conditional probability:
Total of females: 15+24+20 = 59
Female majoring in physics: 24
Divide the number of females majoring in physics by the total number of females.
Probability that a female is majoring in physics: 24/59 = 0.41
8. Write the slope-intercept form of the equation of theline through (2, 2) and parallel to y = x + 4.
Answer:
y = x
Explanation:
The slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
Given the line;
[tex]y=x+4[/tex]We can see that the slope(m) = 1.
Note that the slopes of parallel lines are equal, therefore the slope of the line parallel to y = x + 4 will also be 1.
Let's go ahead and determine the y-intercept of the parallel line using the point (2, 2) and slope(m) = 1;
[tex]\begin{gathered} y=mx+b \\ 2=(1)(2)+b \\ b=2-2 \\ b=0 \end{gathered}[/tex]Having b = 0 and m = 1, the slope-intercept form of the equation of the parallel line can be written as y = x.
Vectors are shown in the graph.Which of the following is equivalent to v = ❬–3, –4❭?
Answer:
Vector s
Explanation:
Given the vector: ❬–3, –4❭
The vector ❬–3, –4❭ shows that there is a movement:
• In the left direction by 3 units
,• In the downwards direction by 4 units.
From the graph, the vector that shows these and hence is an equivalent vector is vector s.
The amount of water dispensed by a water dispenser is normallydistributed, with a mean of 11.60 ounces and a standard deviation of0.15 ounces. In which range will the amount of water dispensed befound 99.7% of the time?
Solution
For this case we have the following information:
mean = 11.6
sigma= 0.15
And we want to find the range of values that will cover 99.7% of the time and then we can do this:
11.6 -3*0.15= 11.15 ounces
11.6 +3*0.15= 12.05 ounces
And then the answer would be:
C. 11.15 ounces and 12.05 ounces
I already know that X=65 but I need to find out what the first step would be to solve the equation for X
We have the following:
[tex]\frac{4}{13}x=20[/tex]The first step is:
[tex]\begin{gathered} \frac{4}{13}x\cdot\frac{13}{4}=20\cdot\frac{13}{4} \\ x=65 \end{gathered}[/tex]Therefore, the answer is D. And solution is 65
Same-side interior angles always addup to 180°. If 44 and 46 are same-sideinterior angles, what is the measure of «6?{44=123°66 = [?]"O46sK
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the question, we can see that:
[tex]\begin{gathered} \angle\text{ 4 +}\angle6=180^0 \\ \text{But }\angle4=123^0 \\ \text{Then,} \\ 123^0+\text{ }\angle6=180^0 \end{gathered}[/tex][tex]\begin{gathered} \angle6=180^0-123^0 \\ \angle6\text{ = }57^0 \end{gathered}[/tex]CONCLUSION:
[tex]\angle6=57^0[/tex]
Solve 54 - 10x< 20 + 7x.O A. x 2O B. XS-2O c. xs2O D. XX-2
we have the inequality
54 - 10x< 20 + 7x.
solve for x
group terms
-10x-7x < 20-54
-17x < -34
Multiply by -1 both sides
17x > 34
x > 34/17
x > 2Archie's playing hide and seek with Valerie and Anya. Valerie's hiding 60 South of Archie and Anya is hiding Due West of Valerie. if Archie is 100 ft from Anya how far apart are Valerie and Anya?
Answer
The distance between Valerie and Anya = 80 ft.
Explanation
In order to answer this, we need to first represent the situation described with an image
We can seethat the whole situation can be described using a right angle triangle.
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = 60 ft
b = distance between Valerie and Anya = x = ?
hyp = 100 ft
a² + b² = (hyp)²
60² + x² = 100²
3600 + x² = 10000
x² = 10000 - 3600
x² = 6400
Take the square root of both sides
√(x²) = √(6400)
x = 80 ft
Hope this Helps!!!
what is 5% of 32. i need help thanks in advance.
5% of any number is that number multiplied by 5 and then divided by 100.
So 5% of 32 is given by:
[tex]32\times\frac{5}{100}=\frac{32}{20}=1.6[/tex]So 5% of 32 is 1.6.
Polygon ABCD with A (0,4), B (-4, 8), C (3, 3), and D (4, -2), is dilated by a scale factor of /2. What are the new coordinates? Is this a reduction or enlargement? *
The formula for dilations with center at origin is
[tex]\begin{gathered} D_{O,k}(x,y)=(kx,ky) \\ \text{ Where O is the center of dilation at (0,0) and} \\ k\text{ is the scale factor} \end{gathered}[/tex]Likewise when
*k > 1, the dilation is an enlargement
*k < 1, the dilation is a reduction
*k = 1, the dilation is a congruence
So, in this case, you have
[tex]k=\frac{1}{2}<1[/tex]Then, the dilation of the polygon is a reduction.
Now, finding the new coordinates of the polygon, you have
[tex]\begin{gathered} A(0,4)\rightarrow A^{\prime}(\frac{1}{2}\cdot0,\frac{1}{2}\cdot4)=A^{\prime}(0,2) \\ \end{gathered}[/tex][tex]B(-4,8)\rightarrow B^{\prime}(\frac{1}{2}\cdot-4,\frac{1}{2}\cdot8)=B^{\prime}(-2,4)[/tex][tex]C(3,3)\rightarrow C^{\prime}(\frac{1}{2}\cdot3,\frac{1}{2}\cdot3)=C^{\prime}(1.5,1.5)[/tex][tex]D(4,-2)\rightarrow D^{\prime}(\frac{1}{2}\cdot4,\frac{1}{2}\cdot-2)=D^{\prime}(2,-1)[/tex]Therefore, the correct answer is C. A'(0,2), B'(-2,4), C'(1.5,1.5), D'(2,-1): Reduction.
13. Vivian Roswell earns $2.57 per printer that she boxes up for shipment. On yesterday she boxe 85 printers.What was her total pay? (2 points)
SOLUTION
From the question she earns $2.57 per printer that she boxes up. That means she earns $2.57 if she boxes one printer. So if she boxes 85 printers, she will earn
[tex]\begin{gathered} 2.57\times85 \\ =218.45 \end{gathered}[/tex]Hence her total pay is $218.45
3 = 2-5x State The function f is given by f(x): the domain of f-1. A. {yly = 5, y E R} B. {yly = 0, y E R} C. {x|x = 0, X E R} D. {x|x + 5, x 6 R}
The function is given as
[tex]f(x)=\frac{3}{2-5x}[/tex]To find the inverse of the function, replace x with y.
[tex]x=\frac{3}{2-5y}[/tex]Now solve for y.
[tex]2-5y=\frac{3}{x}[/tex][tex]x=\frac{3}{2-5y}[/tex][tex]2x-5xy=3[/tex][tex]2x-3=5xy[/tex][tex]y=\frac{2x-3}{5x}=\frac{2}{5}-\frac{3}{5}x[/tex]Thus the inverse of the function is
[tex]-\frac{3-2x}{5x}[/tex]Now to find the domain of the function is
The domain of the function is the set of values of x for which the function is defined.
The domain of the inverse function is
[tex](-\infty,0)\cup(0,\infty)[/tex]Hence the correct option is B.
[tex]\lbrace y|y\ne0,y\epsilon R\rbrace[/tex]Factor f(x) into linear factors given that k is a zero of f(x).f(x) = 4x3 + 3x2 - 49x + 12; k= 3f(x) =(Factor completely.)
The final factorization is thus;
[tex]f(x)\text{ = (x-3)(4x-1)(x+4)}[/tex]Here, we want to factor the polynomial
From the question, we are told that k is a factor;
[tex]\begin{gathered} \text{if k = 3} \\ \text{that means x = 3 is a factor and that x-3 is the linear form} \end{gathered}[/tex]The given polynomial is a polynomial of degree 3; that means there are 3 linear factors
We already have the first factor and we are left with two others to determine
To determine these, we have to divide the given polynomial by the first linear factor
We can do this by the use of the long division method
We have the result of the long divison as follows;
Now, what we have left to factorize is the quadratic trinomial
We have this as;
[tex]4x^2+15x-4=4x^2+16x-x-4\text{ = 4x(x+4)-1(x+4) = (4x-1)(x+4)}[/tex]The difference of two supplementary angles is 8 degrees. Find the measures of the angels
Recall that the supplementary angles sum to 180°
Let x and y are the two angles, so we can write
[tex]x+y=180\degree\quad eq.1[/tex]We are given that the difference of the two supplementary angles is 8°
So we can write
[tex]\begin{gathered} x-y=8\degree \\ x=8\degree+y\quad eq.2 \end{gathered}[/tex]Substitute eq.2 into eq.1
[tex]\begin{gathered} x+y=180\degree \\ (8\degree+y)+y=180\degree \\ 8\degree+2y=180\degree \\ 2y=180\degree-8\degree \\ 2y=172\degree \\ y=\frac{172\degree}{2} \\ y=86\degree \end{gathered}[/tex]So, one angle is 86°, the other angle is
[tex]\begin{gathered} x=8\degree+y \\ x=8\degree+86\degree \\ x=94\degree \end{gathered}[/tex]Therefore, the measure of the two angles is
86°, 94°
Answer:
86 degrees and 94 degrees
The total distance in miles that a delivery van travels varies directly with the gallons of tule that the van uses.The van used 12 gallons of the fuel when it traveled 204 miles. How many miles will the van traveled when it has used 18 gallons of fuel?
It is said that the distance varies directly with the gallons of fuel. This is:
[tex]d=\frac{204\text{miles}}{12\text{gallons}}\times18gallons[/tex][tex]d=306mi[/tex]how do you solve the missing elements for this problem. use of 3.14 pie
Solution
Solution
1)
For this case r= 3 inches
D= 2*3= 6 in
C= 2pir= 2*pi*(3in)=2*3.14*3in= 18,84 in
A= pi (r^2)= pi*(3in^2)= 28.27 in
2)
r= 20 in
D= 2*20 in = 40in
C= 2*3.14*20in= 125.6in
A= pi*r^2 = 3.14*(20in^2)= 1256.66 in^2
mike has $36 dollars. he spends 1/3 of his money for a movie and 2/9 for a sandwich and drink. how much money did he spend for the movie?
Amount mike has = $36
The amount he spent for movie can be calculated below
[tex]\frac{1}{3}\times36=\frac{36}{3}=\text{ \$12}[/tex]Amount spent on movie = $12
find the vertex form f(x)=x2+4x-1
The vertex form of the equation of a parabola is,
[tex]f(x)=a(x-h)^2+k\ldots\ldots.(1)[/tex]where (h, k) are the corrdinates of the vertex.
The given equation is,
[tex]f(x)=x^2+4x-1\ldots\ldots(2)[/tex]The coefficient of x term is 4.
Add or subtract ((1/2)coeffiicent of x term)^2 from the above equation.
[tex](\frac{1}{2}\times4)^2=4[/tex]Adding and subtracting 4 from equ (2),
[tex]\begin{gathered} f(x)=x^2+4x-1+4-4 \\ f(x)=x^2+4x+4-1-4 \\ f(x)=(x^2+4x+4)-5 \\ f(x)=(x+2)^2-5 \end{gathered}[/tex][tex]\text{The equation f}(x)=(x+2)^2-5\text{ is in the form }f(x)=a(x-h)^2+k\text{.}[/tex]Therefore, the vertex form of the given equation is,
[tex]\text{f}(x)=(x+2)^2-5[/tex]can you please help me
so we get
[tex]\sin \theta=\frac{5}{13},\cos \theta=\frac{12}{13},\tan \theta=\frac{5}{12}[/tex]