For the given equation:
[tex]\begin{gathered} \text{Polar form: } \\ r=3 \\ \\ \text{Cartesian form:} \\ x^2+y^2=3^2 \\ x^2+y^2=9 \end{gathered}[/tex]The population of Somewhere, USA was estimated to be 658,100 in 2003, with an expected increase of 5% per year. At the percent ofincrease given, what was the expected population in 2004? Round your answer to the nearest whole number.
To solve for the expected population in 2004:
[tex]\begin{gathered} \text{Estimated population for 2003=658100} \\ \text{rate = 5 \%} \\ nu\text{mber of year = 1} \end{gathered}[/tex]Using compound interest formular to solve for the expected popupation:
Expected population = Amount
[tex]\begin{gathered} A=p(1+\frac{r}{100})^n \\ A\text{ = 658100 (1+}\frac{5}{100})^1 \\ A=658100\text{ (1+0.05)} \\ A=658100(1.05) \\ A=691005 \end{gathered}[/tex]Hence the expected population in 2004 = 691,005
Mark is roofing an old gymnasium that measures 270’x390’, and needs to calculate how many “squares “ he will need.(1 “square=100 ft square). The gym’s roof is a standard gable roof with 3’ of overhang on all sides. The roof angle measures 22.55 degrees from horizontal. How many squares of roofing does mark need ?
First, because of the roof having an inclination, we need to calculate the lenght of the surface we want to roof. The width will be the same.
Let's take a look at the situation:
Since we're on a right triangle, we can say that:
[tex]\cos (22.25)=\frac{G}{R}[/tex]Solving for R,
[tex]\begin{gathered} \cos (22.25)=\frac{G}{R}\rightarrow R\cos (22.25)=G \\ \\ \Rightarrow R=\frac{G}{\cos (22.25)} \end{gathered}[/tex]Since we already know that the lenght of the gym's floor is 390',
[tex]\begin{gathered} R=\frac{390^{\prime}}{\cos (22.25)} \\ \\ \Rightarrow R=421.38^{\prime} \end{gathered}[/tex]We get that the lenght of the surface we want to roof is 421.38'
Now, let's take a look at the surface we want to roof:
Since the roof is a standard gable roof with 3’ of overhang on all sides, we add 6' to each dimension:427
Our total roofing area would be:
[tex]427.38^{\prime}\cdot276^{\prime}=117956.88ft^2[/tex]We then divide this total area by the area of one of our "squares":
[tex]\frac{117956.88}{100}=1179.56[/tex]We round to the nearest integer from above, since we can't buy a fraction of a square.
(this is called ceiling a number)
[tex]1179.56\rightarrow1180[/tex]Therefore, we can conclude that Mark needs 1180 squares of roofing.
Which of the following expressions is equivalent to 2-3?A -2-31B-23C231D- 2-3
2 - 3
the correct answer is letter C
If we follow the rules of the exponents, the power is negative so we change the negative sign writing the numerator in the denominator,
use the following graph to find the mean, median, and mode
Given:
A graph
To determine the Mean, Median, and Mode based on the given graph, we first get the data set as shown below:
2,5,5,5,5,6,9,11,12,13,14,15,18,20
Next, we find the Mean by getting the average:
[tex]\begin{gathered} Mean=\frac{2+5+5+5+5+6+9+11+12+13+14+15+18+20}{14} \\ Simplify \\ Mean=\frac{140}{14} \\ Mean=10 \end{gathered}[/tex]Then, we get the Median by getting the average of the two middle values since there is an even number of data values:
[tex]\begin{gathered} Median=\frac{9+11}{2} \\ Simplify \\ Median=10 \end{gathered}[/tex]Now, we get the Mode by finding the number that appears most frequently. Hence, the Mode is 5.
Therefore, the answer is:
Mean:10, Median:10, Mode:5
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Order the numbers from least to greatest
Answer:
-1, √4/5, -6/5, √3, 2, -3√9, 2√125
Step-by-step explanation:
Which describes the product when two fractions greater than 0 and less than 1 are multiplied?
When you multiply two numbers, one of them greater than 0 and the other one lower than 1. The result is a number that is lower than the first one, that is, a number lower than the number greate than 0.
find the missing lenghts, the triangle in each pair are similar.
Since the triangles are similar, we have that
[tex]\frac{50}{40}=\frac{x}{52}[/tex]then
[tex]x=\frac{52\times50}{40}=65[/tex]then the answer will be D) 65Suppose that a regression line for some data transformed with logarithmspredicts that when x equals 4, log(y) will equal 2.671. What does theregression line predict y will equal when x equals 4?
Explanation:
The information that we have is that when the value of x is 4
[tex]x=4[/tex]The logarithm of y is 2.671
[tex]log(y)=2.671[/tex]The question is:
What does the regression line predict y will equal when x =4?
That means we need to solve for y in
[tex]log(y)=2.671[/tex]To find the predicted y-value.
To solve for y, we make 10 the base of the two sides of the equation as shown in the following expression:
[tex]10^{log(y)}=10^{2.671}[/tex]Due to the properties of logarithms, on the left side, we will be left only with 'y'
[tex]y=10^{2.671}[/tex]And finally, solving the operations on the right-hand side, the result is:
[tex]y=468.813[/tex]Answer:
[tex]y=468.813[/tex]21. Juanita is packing a box that is 18 inches long and 9 inches high. The total volume of the box.1,944 cubic inches. Use the formula V = lwh to find the width of the box. Show your work
The width of the box is 12 inches
Explanations:
The formula for calculating the volume of a rectangular box is expressed as:
[tex]V=\text{lwh}[/tex]where:
• l is the ,length ,of the box
,• w is the ,width, of the box
,• h is the ,height ,of the box
Given the following parameters
• length = 18 inches
,• heigh = 9 inches
,• volume = 1,944 cubic inches
Substitute the given parameters into the formula to calculate the width of the box as shown:
[tex]\begin{gathered} 1944=18\times w\times9 \\ 1944=162w \end{gathered}[/tex]Divide both sides by 162 to have:
[tex]\begin{gathered} 162w=1944 \\ \frac{\cancel{162}w}{\cancel{162}}=\frac{1944}{162} \\ w=12\text{inches} \end{gathered}[/tex]Hence the width of the box is 12 inches
A rectangular parking lot has length that is 3 yards less than twice its width. If the area of the land is 299 square yards, what are the dimensions of the land?The parking lot has a width of square yards.
Answer:
• Width = 13 yards
,• Length = 23 yards
Explanation:
Let the width of the parking lot = w yards.
The length is 3 yards less than twice its width.
[tex]\implies\text{Length}=(2w-3)\text{ yards}[/tex]The area of the land = 299 square yards.
[tex]w(2w-3)=299[/tex]We then solve the equation above for w.
[tex]\begin{gathered} 2w^2-3w=299 \\ \implies2w^2-3w-299=0 \end{gathered}[/tex]Factor the resulting quadratic expression.
[tex]\begin{gathered} 2w^2-26w+23w-299=0 \\ 2w(w-13)+23(w-13)=0 \\ (2w+23)(w-13)=0 \end{gathered}[/tex]Solve for w.
[tex]\begin{gathered} 2w+23=0\text{ or }w-13=0 \\ 2w=-23\text{ or }w=13 \\ w\neq-\frac{23}{2},w=13 \end{gathered}[/tex]Since w cannot be negative, the parking lot has a width of 13 yards.
Finally, find the length of the parking lot.
[tex]\begin{gathered} 13l=299 \\ l=\frac{299}{13}=23\text{ yards} \end{gathered}[/tex]The length of the parking lot is 23 yards.
Determine whether 17y = 3x − 19 is quadratic or not. Explain.No; there is no x2 term, so a = 0.No; there is no x-term, so b = 0.No; there is no constant term, so c = 0.Yes; it can rewritten in the form y = ax2 + bx + c.
The standard form of quadratic equation is given as,
[tex]ax^2+bx\text{ + c = 0 where a }\ne\text{ 0}[/tex]The equation is given as,
[tex]17y\text{ = 3x - 19}[/tex]Therefore,
[tex]\text{From the given equation x}^2\text{ is not present and also a = 0.}[/tex]Thus the given equation is not a quadratic equation.
A rectangle has a diagonal of length 10 cm and a base of length 8 cm . Find its height
Given:
The length of diagonal of rectangle is d = 10 cm.
The length of base is b = 8 cm.
Explanation:
The relation between length, height and diagonal of rectangle is given by pythagoras theorem. So
[tex]d^2=l^2+h^2[/tex]Substitute the values in the equation to obtain the value of h.
[tex]\begin{gathered} (10)^2=(8)^2+h^2 \\ 100=64+h^2 \\ h=\sqrt[]{100-64} \\ =\sqrt[]{36} \\ =6 \end{gathered}[/tex]So the height of rectangle is 6 cm.
Answer: 6 cm
A population of 2000 is decreasing by 4% each year. In how many years the population will be reduced in half?
the initial amount is 2000
the rate of change is 4%
t=time in years
Therefore we have the next exponential decay function
[tex]\begin{gathered} y=2000(1-0.04)^t \\ y=2000(0.96)t \end{gathered}[/tex]Half of the population is y=1000 so we need to find find the value of t
[tex]1000=2000(0.96)^t[/tex]we need to isolate the t
[tex]\frac{1000}{2000}=0.96^t[/tex][tex]\frac{1}{2}=0.96^t[/tex]Using logarithms
[tex]\begin{gathered} \ln (\frac{1}{2})=\ln (0.96^t) \\ \ln (\frac{1}{2})=t\ln (0.96^t) \end{gathered}[/tex][tex]t=\frac{\ln (\frac{1}{2})}{\ln (0.96^{})}=16.98\approx17[/tex]ANSWER
in 17 years the population will be reduced in half
A car has 34,000,miles on its odometer and accumulates an average of 100 more each week. What is the function rule that represents the total m miles the car will have on the odometer after w weeks?
Answer:
Step-by-step explanation:
M= 100m +34,000w
Answer: it would be A. for you, but for me it was C.:
m = 34,000 + 100w
what I mean is the answers were jumbled around.
Amy's cookie shop had expenses of the following: flour $45.00sugar $92.00butter $53 she earns $12 per dozen. what is her profit,if she sells 9 dozen?what is the total dollar amount for expenses?what is the total dollar amount for earnings or revenue?
If she earns $12 per dozen, the following will be the profit if she sells 9 dozen:
[tex]9\cdot12=108[/tex]Profit would be $108.
*The dollar amount of expenses would be:
[tex]e=\frac{190\cdot108}{12}\Rightarrow e=1710[/tex]The expenses would be $1710 if she were to sell 9 dozen.
*The total amount of revenue would be $108 for the 9 dozen sold.
A side of the triangle below has been extended to form an exterior angle of 133º. Find the value of x. 133° 21° xo
In order to find the value of x, we need to remember that the sum of the interior angles of a triangle is 180°
so we have the next equation
21+x+(180-133)=180
21+x+47=180
x=180-21-47
x=112°
what is the value of 6 3/4 (-11.5)
We are given the following expression
[tex]6\frac{3}{4}(-11.5)[/tex]As you can see, a mixed number is being multiplied with a negative decimal number.
First, convert the mixed number to a simple fraction then multiply with the decimal number
[tex]6\frac{3}{4}=\frac{6\cdot4+3}{4}=\frac{24+3}{4}=\frac{27}{4}[/tex]Now multiply it with the negative decimal number
[tex]\frac{27}{4}(-11.5)=-\frac{310.5}{4}=-77.625[/tex]So the resultant decimal number may be written back into the mixed form as
[tex]-77.625=-77\frac{5}{8}[/tex]Therefore, the result of the given expression is -77 5/8
Find the links of the sides of these special triangles
From the triangle, we express the tangent of 60° as:
[tex]\tan 60\degree=\frac{Z}{7}[/tex]But tan(60°) = √(3), then:
[tex]\begin{gathered} \frac{Z}{7}=\sqrt[]{3} \\ \Rightarrow Z=7\sqrt[]{3}\text{ ft} \end{gathered}[/tex]2. Jim is 8 years old, and his Uncle Bill is 512 times older than he his. What is his Uncle Bill's age?
Answer:
Uncle Bill has ignored the laws of nature and the known universe and reached a stunning 4096 years old
Step-by-step explanation:
Just multiply 8 * 512
500 * 8 = 4000, 12 * 8 = 96, 4000 + 96 = 4096
Answer:44
Step-by-step explanation:
What is the answer for 5p+10 = 8p+1
The equation is given to be:
[tex]5p+10\: =\: 8p+1[/tex]We can solve for p using the following steps:
Step 1: Subtract 10 from both sides of the equation
[tex]\begin{gathered} 5p+10-10=8p+1-10 \\ 5p=8p-9 \end{gathered}[/tex]Step 2: Subtract 8p from both sides of the equation
[tex]\begin{gathered} 5p-8p=8p-9-8p \\ -3p=-9 \end{gathered}[/tex]Step 3: Multiply both sides by -1
[tex]\begin{gathered} -1\times(-3p)=-1\times(-9) \\ 3p=9 \end{gathered}[/tex]Step 4: Divide both sides by 3
[tex]\begin{gathered} \frac{3p}{3}=\frac{9}{3} \\ p=3 \end{gathered}[/tex]ANSWER:
[tex]p=3[/tex]2(3 + v) =
Please help solve this problem and thank you
Answer:
6 +2v
Step-by-step explanation:
This is distributive property. That means you will multiply each term inside the parentheses by the term on the outside of the parentheses.
2(3 + v)
2(3) + 2(v)
6 +2v
16. Given the graph below, write the equation of the line graphed. Equation:
We have the following:
The equation has the following form
[tex]y=mx+b[/tex]where m is the slope and b is y-intercept
The slope formula is as follows
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The point are (-4, 8) and (6, -4)
replacing:
[tex]m=\frac{-4-8}{6-(-4)}=\frac{-12}{10}=-\frac{6}{5}[/tex]In the graph we can see that the y-intercept is equal to 4, therefore, the equation would be
[tex]y=-\frac{6}{5}x+4[/tex]The Neckware association of America reported that 3% of ties sold in the United States are bow ties. If 4 customers who purchased a tie randomly selected,find the probability that at least 1 purchased a bow tie
Pr (people with bow ties) = 3% = 0.03
p = 0.03
Pr (people without bow tie) = 1 - 0.03 = 0.97
q = 0.97
n = 4 customers
[tex]Pr(at\text{ least 1 purchased a bow tie) = 1 - Pr(none purchased a bow tie)}[/tex]To find the probability that at least 1 purchased a bow tie, we will use a binomial probability formula:
[tex]p(x=^{}X)=^nC_xp^xq^{n\text{ - x}}[/tex][tex]\begin{gathered} \text{Pr(none purchased a bow tie) = p(x = 0)} \\ \text{p(x = 0) = }^4C_0\times p^0\times q^{4\text{ - }0} \\ \text{p(x = 0) = 1 }\times\text{ 1}\times q^4=(0.97)^4 \\ \text{p(x = 0) = }0.8853 \\ \\ \text{Pr(none purchased a bow tie) = }0.8853 \end{gathered}[/tex][tex]\begin{gathered} Pr(at\text{ least 1 purchased a bow tie) = 1 - 0.8853} \\ Pr(at\text{ least 1 purchased a bow tie) = 0.1147} \end{gathered}[/tex]When should the Empirical Rule be used?
The empirical formula should be used after calculating the standard deviation and collecting the exact data needed for a forecast.
Explanations:What is the empirical rule?The empirical rule is a term used in statistics also known as the 68–95–99.7 rule. This rule is majorly used in forecasting the final outcome of events.
The empirical rule can be used to therefore determine a rough estimate of the outcome of the impending data to be collected and analyzed. This is done after calculating the standard deviation and collecting the exact data needed.
68–95–99.7 rule,
1. Tyra bought a lolli-pop with a diameter of 2 inches. What is the circumference of the lolli-pop to the nearest tenth of an inch? A. 3.9 inches B. 15.7 inches C. 6.3 inches D. 7.9 inches
A lollypop have a circular shape
Diameter D is the line in a circumference that divides it in half
then calculate directly π• D
to the nearest tenth
π•D = 3.14 x 2 = 6.28
then nearest number is 6.3 , or 6.30. Option C)
How many megagrams(Mg) are there in 3.6 tons?[ ? ] MgMass in MgEnter
Step 1
Given;
[tex]3.6\text{tons}[/tex]Required; To find how many megagrams(Mg) are in 3.6 tonnes
Step 2
Find how many megagrams(Mg) are in 3.6 tonnes
[tex]\begin{gathered} 1\text{ tonne=1000000}g \\ 1\text{ megagram=1}000000g \end{gathered}[/tex]Therefore,
[tex]1\text{ tonne = 1 megagram}[/tex][tex]\frac{1\text{ tonne}}{3.6\text{ tonnes}}=\frac{1\text{ megagram}}{x\text{ megagram}}[/tex][tex]\begin{gathered} x\text{ megagram(1 tonne)=1 megagram(3.6 tonnes)} \\ \frac{x\text{ megagram}(1\text{ tonne)}}{1\text{ tonne}}\text{=}\frac{\text{1 megagram(3.6 tonnes)}}{1\text{ tonne}} \\ x=\text{ 3.6 megagrams} \\ x=3.6Mg \end{gathered}[/tex]
Can you help me with this true and false problem?
FALSE.
Explanations:Given the linear relations 2x - 3y = 4 and y = -2/3 x + 5
Both equations are equations of a line. For the lines to be perpendicular, the product of their slope is -1
The standard equation of a line in slope-intercept form is expressed as
[tex]y=mx+b[/tex]m is the slope of the line
For the line 2x - 3y = 4, rewrite in standard form
[tex]\begin{gathered} 2x-3y=4 \\ -3y=-2x+4 \\ y=\frac{-2}{-3}x-\frac{4}{3} \\ y=\frac{2}{3}x-\frac{4}{3} \end{gathered}[/tex]Compare with the general equation
[tex]\begin{gathered} mx=\frac{2}{3}x \\ m=\frac{2}{3} \end{gathered}[/tex]The slope of the line 2x - 3y = 4 is 2/3
For the line y = -2/3 x + 5
[tex]\begin{gathered} mx=-\frac{2}{3}x \\ m=-\frac{2}{3} \end{gathered}[/tex]The slope of the line y = -2/3 x + 5 is -2/3
Take the product of their slope to determine whether they are perpendicular
[tex]\begin{gathered} \text{Product = }\frac{2}{3}\times-\frac{2}{3} \\ \text{Product = -}\frac{4}{9} \end{gathered}[/tex]Since the product of their slope is not -1, hence the linear relations do not represent lines that are perpendicular. Hence the correct answer is FALSE
Use Pythagorean theorem to find right triangle side lengthsFind the value of c in the triangle shown below.682Choose 1 answer:A = 28B= 64=9= 10
EXPLANATION
Given the Right Triangle, we can apply the Pythagorean Theorem in order to get the value of x as shown as follows:
[tex]\text{Hypotenuse}^2=Short_-leg^2+Long_-leg^2[/tex]Replacing terms:
[tex]x^2=6^2+8^2[/tex][tex]x^2=36+64=100[/tex]Applying the square root to both sides:
[tex]x=\sqrt[]{100}=10[/tex]Hence, the solution is x=10
- 2/3 (x+12)+2/3 x=-5/4 x+2
We will have the following:
[tex]-\frac{2}{3}(x+12)+\frac{2}{3}x=-\frac{5}{4}x+2\Rightarrow-\frac{2}{3}x-8+\frac{2}{3}x=-\frac{5}{4}x+2[/tex][tex]\Rightarrow-\frac{2}{3}x+\frac{2}{3}x+\frac{5}{4}x=2+8\Rightarrow\frac{5}{4}x=10[/tex][tex]\Rightarrow5x=40\Rightarrow x=8[/tex]So, the value of x is 8.
John has two apples, he gives Jane 251. How many apples does John have? Please help 2nd grade is so hard.
