We can match as follows:
1. divisor ----> d. the number of equal parts a number is being divided into
2. decimal fraction ----> e. a fraction in which the denominator is 10 or a power of 10
3. algorithm ----> c. a set of rules to be followed to solve a problem
4. fraction ----> g. a number that expresses the portion
5. quotient ----> a. the result of dividing two numbers
6. reminder ----> f. the amount left over after Division
For each ordered pair, determine whether it is a solution to 4x - 5y = -13.Is it a solution?x$(x, y)YesNo(-7, -3)(3, -4)OO(-2, 1)oO(6, 7)0
The equation is 4x - 5y = -13.
Substitute -7 for x and -3 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-7)-5\cdot(-3)=-13 \\ -28+15=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation so point (-7,-3) is solution of equation.
Substitute 3 for x and -4 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot3-5\cdot(-4)=-13 \\ 12+20=-13 \\ 32\ne-13 \end{gathered}[/tex]The ordered pair not satisfy the equation. So point (3,-4) is not a solution of the equation.
Substitute -2 for x and 1 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-2)-5\cdot1=-13 \\ -8-5=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation. So point (-2,1) is solution of equation.
Substitute 6 for x and 7 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot6-5\cdot7=-13 \\ 24-35=-13 \\ -11\ne-13 \end{gathered}[/tex]The orderedpair not satisfy the equation. So point (6,7) is not a solution of the equation.
On July 31, Oscar Jacobs checked out of the Sandy Beach hotel after spending four nights. The cost of the room was $76.90 per night. He wrote a check to pay for his four-night stay. What is the total amount of his check, expressed in words?
On July 31, Oscar Jacobs checked out of the Sandy Beach hotel after spending four nights. The cost of the room was $76.90 per night. He wrote a check to pay for his four-night stay. What is the total amount of his check, expressed in words?
step 1
Multiply $76.90 by 4
76.90*4=$307.6
so
expressed in words is
three hundred seven and six tenths5.Given the sample triangle below and the conditions a=3, c = _51, find:cot(A).
Depending on the angle we are analyzing on the right triangle, each side of it takes a different name. In this case, we are going to name them depending on the angle A. Then,
a: opposite side (to A)
b: adjacent side
c: hypotenuse
STEP 2: formula for cot(A)We know that the formula for cot(A) is:
[tex]\cot (A)=\frac{\text{adjacent}}{\text{opposite}}[/tex]Replacing it with a and b:
[tex]\begin{gathered} \cot (A)=\frac{\text{adjacent}}{\text{opposite}} \\ \downarrow \\ \cot (A)=\frac{b}{a} \end{gathered}[/tex]Since a = 3:
[tex]\cot (A)=\frac{b}{3}[/tex]STEP 3: finding bWe have an expression for cot(A) but we do not know its exact value yet. First we have to find the value of b to find it out.
We do this using the Pythagorean Theorem. Its formula is given by the equation:
[tex]c^2=a^2+b^2[/tex]Since
a = 3
and
c = √51
Then,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \downarrow \\ \sqrt[]{51}^2=3^2+b^2 \\ 51=9+b^2 \end{gathered}[/tex]solving the equation for b:
[tex]\begin{gathered} 51=9+b^2 \\ \downarrow\text{ taking 9 to the left} \\ 51-9=b^2 \\ 42=b^2 \\ \downarrow square\text{ root of both sides} \\ \sqrt{42}=\sqrt{b^2}=b \\ \sqrt[]{42}=b \end{gathered}[/tex]Then,
b= √42
Therefore, the equation for cot(A) is:
[tex]\begin{gathered} \cot (A)=\frac{b}{3} \\ \downarrow \\ \cot (A)=\frac{\sqrt[]{42}}{3} \end{gathered}[/tex]Answer: DThe table shows the cost for a clothing store to buy jeans and khakis. The total cost for Saturday's shipment, $1,800, is represented by the equation 15x + 20y = 1,800. Use the x- and y-intercepts to graph the equation. Then interpret the x- and y-intercepts.
[tex] log_{2 }(x - 6) + log_{2}(x - 4) = log_{2}(x) [/tex]x=8,3x=8No solution
Answer:
x=8,3
Explanation:
Given the expression:
[tex]\log _2\mleft(x-6\mright)+log_2\mleft(x-4\mright)=log_2\mleft(x\mright)[/tex]Applying the addition law of logarithm:
[tex]\log _2(x-6)(x-4)=log_2x[/tex]Next, cancel the logarithm operator on both sides:
[tex]\begin{gathered} (x-6)(x-4)=x \\ x^2-4x-6x+24=x \\ x^2-10x-x+24=0 \\ x^2-11x+24=0 \end{gathered}[/tex]We solve the resulting quadratic equation:
[tex]\begin{gathered} x^2-8x-3x+24=0 \\ x(x-8)-3(x-8)=0 \\ (x-3)(x-8)=0 \\ x-3=0\text{ or }x-8=0 \\ x=3\text{ or }x=8 \end{gathered}[/tex]The value of x is 3 or 8.
The length of a wire was measured using two different rulers. How many significant figures are in each measurement?
We will have the following
In the first image we can see that the maximum you will measure with a good degree of certainty is the unit, and in the next one we wil have that is the unit and a fraction of it, so:
Top: 1 significative figure.
Bottom: 2 significative figures.
Last month, Ebony had 110 dollars in achecking account. The current balance is146 dollars. What is the percent change inthe account balance from last month to thismonth? Round your answer to the nearest whole percent.
Problem
Last month, Ebony had 110 dollars in a
checking account. The current balance is
146 dollars. What is the percent change in
the account balance from last month to this
month? Round your answer to the nearest whole percent.
Solutiion
For this case we can use the following formula:
[tex]\text{Change}=\frac{\text{Actual}-\text{Before}}{\text{Before}}\cdot100[/tex]And replacing we got:
[tex]\text{Change}=\frac{146-110}{110}\cdot100=32.72[/tex]And then the answer wounded to the nearest percent would be:
33%
under normal conditions, 1.5 feet of snow will melt into 2 inches of water. after a recent snowstorm, there were 4 feet if snow. how many inches of water will there be when the snow MELTS? express your answer as a fraction reduced to lowest terms or decimal rounded correctly to two decimals places. Do not include units with this answer.
If 1.5 feet of snow melts into 2 inches of water, this implies that:
[tex]undefined[/tex]A 12 -inch ruler is closest in length to which one of the following Metric units of measure? 0.030 Kilometers30,000 millimeters30 centimeters30 meters
Inch is one of the units of measuring length.
Converting from inch to meters,
[tex]1inch=0.0254m[/tex]A 12-inch ruler converted to meters will be;
[tex]12\times0.0254=0.3048m[/tex]Converting the meter equivalent of the ruler into the sub-units of meters measurement,
[tex]\begin{gathered} 0.3048m \\ To\text{ kilometer} \\ 1000m=1\operatorname{km} \\ 0.3048m=\frac{0.3048}{1000}=0.0003048\operatorname{km} \\ \\ To\text{ millimeter} \\ 1m=1000\operatorname{mm} \\ 0.3048m=0.3048\times1000=304.8\operatorname{mm} \\ \\ \\ To\text{ centimeters} \\ \text{1m =100cm} \\ 0.3048m\text{ =0.3048}\times100=30.48\operatorname{cm} \\ \\ \\ To\text{ meters } \\ 12\text{ inch = 0.3048m} \end{gathered}[/tex]From the conversions of metric units of length above, the 12-inch ruler measures 30.48cm which is closest to 30cm
Therefore, the ruler is closest to 30 centimeters
the table shows the number of jeans sold at a store at different prices
To make a plot of the data you first must choose your axis. In this case we've chosen the X axis to be the average cost of the jeans and the Y axis to be the number of copies sold. To graph the data we match the information we're given in the table as shown in the drawing.
help I'm practicing
Remember that the volume of a rectangular pyramid is given by the expression:
[tex]v=\frac{1}{3}abh[/tex]Where:
• a ,and ,b ,are the lenght of the sides of the rcetangle (base)
,• h, is the height of the pyramid
Using this, and the data given, we'll get that:
[tex]\begin{gathered} v=\frac{1}{3}(14)(9.5)(15) \\ \Rightarrow v=665 \end{gathered}[/tex]The volume of the pyramid is 665 cubic feet
Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches. What is the actual measurement of that side of the courtyard? Show your work.
Okay, here we have this:
Considering that the scale is of 1 to 60, we obtain the following:
2.75 inches * 60 =165.
UsetheprimefactorsmethodtofindtheGCFof76,190,and931.
There are several ways to calculate the GCF
Let's use the Prime Factorization.
1) List the numbers in a row. As we can see, 76, 190 are both divisible by 2
So le's start dividing by the prime number 2, up to next divisible prime number as it follows:
As we can see the Greatest Common Divisor to both 76,190 and 931 is the prime number 19
Therefore, we can state the GCD of 76,190, 931 as 19
On the planet Alaber, there are 15 dubbles to every 13 rews. If farmer Mimstoon has 100 rews on his frent farm, how many dubbles are on the farm?
You have that on planet Alaber, there are 15 dubbles to every 13 rews. This proportion can be wrtten as 15:13, or 15/13.
In order to calculate how many dubbles are on the farm, while there are 100 rews. You use the previous ratio and proceed as follow:
15/13 = x/100 where x is the unknown number of dubbles
This is because the ratio between dubbles and rews must be the same.
You solve the previous equation as follow:
15/13=x/100 multiply both sides by 100 to cancel the denomitaro 100 right side
15/13(100) = x/100(100)
1500/13 = x
In order to write the previous result as a mixed number you divide numerator and denominator:
1500 | 13
143 115
70
65
5
Then, x = 1500/13 is also equal to:
x = 115 13/5
This means there are approximately 115 dubbles for 100 rews
Statistics: a professor recorded 10 exam grades but one of the grades is not readable. if the mean score on the exam was 82 and the mean of the 9 readable scores is 84 what is the value of the unreadable score?
To mean of a set is given by the sum of all values in the data-set divided by the number of values.
We have that the mean of the whole set is 82.
The mean of the 9 readable scores is 84.
So:
[tex]\begin{gathered} \frac{x}{9}=84 \\ x=84\cdot9 \\ x=756 \end{gathered}[/tex]So, we 9 readable scores add up to 801. If we add 756 to a number, y, and divide by 10, we'll have the mean score of the exam, 82.
[tex]\begin{gathered} \frac{756+y}{10}=82 \\ 756+y=820 \\ y=820-756 \\ y=64 \end{gathered}[/tex]So, the grade of the unreadable score was 64.
If your distance from the foot of the tower is 20 m and the angle of elevation is 40°, find the height of thetower.
We have to use the tangent of angle 40 to find the height of the tower.
[tex]\text{tan(angle) = }\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]The adjacent side is 20m, and the angle is 40 degrees, then
[tex]\tan (40)\text{ = }\frac{height\text{ of the tower}}{20m}[/tex][tex]\text{height = 20m }\cdot\text{ tan(40) = 20m }\cdot0.84\text{ = }16.8m[/tex]Therefore, the height of the tower is 16.8m
A landscaper has built a U-shaped raised bed in a vegetable garden as shown in the figure. How many cubic yards of soil should be ordered to fill the bed to a depth of 30 inches?
First calculate the area of the shaded region by considering the U-shaped bed as formed by three rectangles, as follow:
where the lengths of the sides of the rectangles corresponds with the dimensions of the U-shaped bed.
Then, for the area of the figure, use the formula for the area of a rectangle, for all three rectangles, as follow:
A = 5*18 + 3*20 + 5*18
A = 90 + 60 + 90
A = 240
Then, the area is 240 in^2
Next, convert the previous result to yd^2. Use the equivalence 1 yd = 36 in:
[tex]240in^2\cdot\frac{(1yd)^2}{(36in)^2}=0.185yd^2[/tex]Now, to find the volume convert 30 in to yards:
[tex]30in\cdot\frac{1yd}{36in}=0.83yd[/tex]Finally, multiply the previous result by the area of the figure:
[tex]0.185yd^2\cdot0.83yd=0.154yd^3[/tex]How many solutions will each equation have?x^2+6x+5
To solve the quadratic equation, factor the expression and then clear x from each of the factors obtained.
[tex]\begin{gathered} x^2+6x+5=0 \\ (x+5)(x+1)=0 \\ x+5=0 \\ x=-5 \\ x+1=0 \\ x=-1 \end{gathered}[/tex]This equation has 2 solutions which are -5 and -1.
A grocery store sales for $522,000 and a 25% down payment is made a 20 year mortgage at 7% is obtain compute and amortization schedule for the first three months round your answer to two Decimal place if necessary
The value of the mortgage (the real amount to be financed) is A = $391,500.
The annual interest rate is r = 7%. We must convert it to montly decimal rate:
r = 7 / 12 / 100 = 0.005833
Note: The decimals will be kept in our calculator. Only two decimal places will be shown in the results.
The monthly payment is R = $3,034.13 which includes interest and principal.
For the first month, the loan has not been paid upon, so the interest for this period is:
I = $391,500 * 0.005833 = $2,283.75
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,283.75 = $750.38
So the new balance of the loan is:
$391,500 - $750.38 = $390,749.62
Thus, for payment 1:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
Repeating the calcuations for the second payment:
The interest for this period is:
I = $390,749.62 * 0.005833 = $2,279.37
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,279.37 = $754.76
So the new balance of the loan is:
$390,749.62 - $754.76 = 389,994.86
The table is updated as follows:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
$2,279.37 - $754.76 - $389,994.86
For the third month:
The interest for this period is:
I = $389,994.86 * 0.005833 = $2,274.97
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,274.97 = $759.16
So the new balance of the loan is:
$389,994.86 - $759.16 = $389,235.70
The final updated table is:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
$2,279.37 - $754.76 - $389,994.86
$2,274.97 - $759.16 - $389,235.70
In the equation y = 2x, y represents the perimeter of a square.What does x represent?Ahalf the length of each sideBthe length of each sideСtwice the length of each sideDtwice the number of sides
Given:
An equation that represents the perimeter of a square:
[tex]y=2x[/tex]To find:
What x represents.
Solution:
It is known that the perimeter of the square is equal to four times the side of the square.
Let the side of the square be s. So,
[tex]\begin{gathered} y=P \\ 2x=4s \\ x=\frac{4s}{2} \\ x=2s \end{gathered}[/tex]Therefore, x represents twice the length of each side.
Ms. Morgan is the cafeteria manager. She keeps track of how many students select each type of drink. Today during breakfast, 32 children picked milk while 44 children picked juice. What is the ratio of the numbe of children who picked juice to those who picked milk?
Answer:
ratio of those who picked juice to milk
it refers to division
Circumference? (you must include units) Round to the tenthsas needed.
The circumference formula is given by:
[tex]L=2\pi r[/tex]Where r is the radius of the circle. From the problem, we have r = 10.9 ft. Then, using the formula:
[tex]\begin{gathered} L=2\pi\cdot10.9 \\ \\ \therefore L=68.5\text{ ft} \end{gathered}[/tex]The circumference is 68.5 ft
In the figure below, m2 = 49. Find mx 1.
By definition, a Right angle is an angle that measures 90 degrees.
Complementary angles are those angles that add up to 90 degrees.
For this case, you can identify that the angle 1 and the angle 2 are Complementary angles, because when you add them, you get 90 degrees (a Right angle).
Knowing the above, you can set up the following equation:
[tex]m\angle1+m\angle2=90\degree[/tex]Since you know that:
[tex]m\angle2=49\degree[/tex]You can substitute this value into the equation and the solve for the angle 1 in order to find its measure. You get that this is:
[tex]\begin{gathered} m\angle1+49\degree=90\degree \\ m\angle1=90\degree-49\degree \\ m\angle1=41\degree \end{gathered}[/tex]The answer is:
[tex]m\angle1=41\degree[/tex]The same set of data has been fit using two different functions. The following images show the residual plots of each function.
We have the residuals of each function graphed.
They represent the distance, taking into account the sign, of each data point to the line of best fit.
A good fit will have residuals that are close to the x-axis. Also, the distribution for the residuals should not have too much spread, meaning that all the points should have approximately the same residual in ideal conditions.
In this case, we see that Function A has most residuals around the horizontal axis. Except for one of the points, that may be considered an outliert.
In the case of Function B there is a clear pattern (a quadratic relation between x and the residual) that shows that the degree of the best fit function is not the adequate (maybe two degrees lower than what should be).
This results in residuals that have a wide spread depending on the value of x.
Then, we can conclude that Function A has a better fit because the points are clustered around the x-axis.
Answer: Function A has a better fit because the points are clustered around the x-axis [Third option]
Given a and b are first quadrant angles, sin a=5/13 and cos b=3/5 evaluate cos (a+b)1) 56/652) 33/653) 16/65
For the data shown in the scatter plot, which is the best estimate of r?The answer choices are .94 .-45 .-94 .45
Pearson's correlation coefficient, r, measures the linear relationship between two variables. The correlation coefficient can take a range of values from +1 to -1.
• A value of 0 indicates that there is no association between the two variables.
,• A value ,greater than 0, indicates a ,positive association., That is, as the value of one variable increases, so does the value of the other.
,• A value ,less than 0, indicates a ,negative association,; that is, as the value of one variable increases, the value of the other decreases.
Graphically,
In this case, you can see that as the value of a variable x increases, the value of the variable y other decreases. Then, the correlation coefficient of these two variables is negative.
Also, you can see that the values of the variables do not completely fit a line but are very close to one.
Therefore, the best estimate of r is -.94.
-27\sqrt(3)+3\sqrt(27), reduce the expression
Explanation
[tex]-27\sqrt[]{3}+3\sqrt[]{27}[/tex]Step 1
Let's remember one propertie of the roots
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]hence
[tex]\sqrt[]{27}=\sqrt[]{9\cdot3}=\sqrt[]{9}\cdot\sqrt[]{3}=3\sqrt[]{3}[/tex]replacing in the expression
[tex]\begin{gathered} -27\sqrt[]{3}+3\sqrt[]{27} \\ -27\sqrt[]{3}+3(3\sqrt[]{3}) \\ -27\sqrt[]{3}+9\sqrt[]{3} \\ (-27+9)\sqrt[]{3} \\ -18\sqrt[]{3} \end{gathered}[/tex]therefore, the answer is
[tex]-18\sqrt[]{3}[/tex]I hope this helps you
find the coordinates of a point on a circle with radius 18 corresponding to an angle of 190°
The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).
What is transforming coordinates?
Polar coordinates (r,θ) are transformed into Cartesian coordinates (x, y) using the formulas x = r cos(θ), and y = r sin(θ).
This problem is under the concept of transforming polar coordinates (r,θ) to cartesian coordinates (x, y).
For this problem the polar coordinates are r = 18 and θ = 190°.
Convert these polar coordinates into a cartesian coordinates as,
x = r cos(θ) = 18 cos(190°) = -17.73
y = r sin(θ) = 18 sin(190°) = -3.13
The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).
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10. A city has a population of 125,500 in the year 1989. In the year 2007, its population is 109, 185. A. Find the continuous growth/decay rate for this city. Be sure to show all your work.B. If the growth/decay rate continues, find the population of the city in the year 2021.C. In what year will the population of the city reach 97,890? Be sure to show all your work.
SOLUTION
A.
To solve this question, we will use the compound interest formula.
Which is:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ Since\text{ we are dealing with a yearly statistics, n = 1} \end{gathered}[/tex][tex]\begin{gathered} \text{From 1989 to 2007, there is a year difference of 18 years} \\ t=18 \\ A=109,185 \\ P=125,500 \\ We\text{ are looking for the continuous growth rate (r)} \\ \text{Now, we will substitute all these given parameters into the formula } \\ \text{above.} \end{gathered}[/tex][tex]\begin{gathered} 109,185=\text{ 125,500(1-}\frac{r}{100})^{18} \\ \frac{195185}{125500}=\frac{125500}{125500}(1-\frac{r}{100})^{18} \\ 0.87=(1-\frac{r}{100})^{18} \\ \text{take the natural logarithm of both sides:} \\ \ln 0.87=18\ln (1-\frac{r}{100}) \\ -0.1393=18\ln (1-\frac{r}{100}) \\ \frac{-0.1393}{18}=\ln (1-\frac{r}{100})_{}_{}_{}_{}_{} \\ -0.007737=\ln (1-\frac{r}{100}) \\ \end{gathered}[/tex][tex]\begin{gathered} e^{-0.007737}=(1-\frac{r}{100}) \\ 0.9922=1-\frac{r}{100} \\ \frac{r}{100}=1-0.9922 \\ \frac{r}{100}=0.007707 \\ r=100\times0.007707 \\ r=0.771\text{ \%} \end{gathered}[/tex]The continuous decay rate is 0.771%
B.
Using the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ t=2021-2007=14 \\ P=109,185 \\ n=1 \\ A=\text{?} \\ r=0.771 \\ \text{Substitute all the parameters into the formula above:} \end{gathered}[/tex][tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=109,185(1-\frac{0.771}{100})^{1\times14} \\ A=109,185\times0.89730607 \\ A=97,972.36 \\ A=97,972\text{ (to the nearest person)} \end{gathered}[/tex]The population of the city in the year 2021 is 97,972.
C.
We will use the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=97,890 \\ P=125,500 \\ r=0.771 \\ t=\text{?} \\ \text{Substitute all these parameters into the formula above:} \\ \end{gathered}[/tex][tex]\begin{gathered} 97890=125,500(1-\frac{0.771}{100})^t^{} \\ \frac{97890}{125500}=\frac{125500}{125500}(0.99229)^t \\ 0.78=0.99229^t \\ \ln 0.78=t\ln 0.99229 \\ -\frac{0.2485}{\ln 0.99229}=t \\ t=32.101 \\ SO\text{ the year that the population will reach 97,890 will be:} \\ 1989+32.101=2021.101 \\ \text{Which is approximately year 2021.} \end{gathered}[/tex]Question 16
Given AEFHAGFH below, what is the measure of GFH?
F
21.6°
E<
(6x - 12)° H
G
1 pts
The most appropriate choice for congruency of triangles will be given by-
[tex]\angle GFH =68.4^{\circ}\\[/tex]
What is congruency of triangles?
Two triangles are said to be congruent if all the corrosponding sides and the corrosponding angles of the triangle are equal.
There are five axioms of congruency. They are -
SSS axioms, SAS axioms, ASA axiom, AAS axiom, RHS axiom.
Here,
[tex]\Delta EFH \cong \Delta GFH[/tex] [Given]
[tex]\angle E = \angle G = 21.6^{\circ}[/tex] [Corrosponding parts of congruent triangles are congruent]
[tex]\angle GFH[/tex] = 180 - (90 + 21.6) [Sum of the three angles of a triangle is 180°]
[tex]\angle GFH = 180 - 111.6\\\angle GFH =68.4^{\circ}\\[/tex]
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