The simplest ratio of squares to rectangles can be obtained as follows:
There are 14 squares and 18 rectangles. The ratio of squares to rectangles is:
[tex]\frac{14}{18}=\frac{7}{9}[/tex]Then, the simplest ratio is 7/9 because 7 is a prime number and the ratio cannot be simplified any more. To obtain 7/9 we divided the numerator by 2 and the denominator also by 2.
In college, we study large volumes of information- information that, unfortunately, we go not often retain for very long. The function f(x) = 80e +20 describes the percentage of information, fx), that a particular person remembers x weeks after learning the information. a. Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b. Substitute 1 for x and find the percentage of information remembered after 1 week C. Find the percentage of information that is remembered after 4 weeks. d. Find the percentage of information that is remembered after 1 year.
a)
[tex]f(0)=80\cdot e^{-0.5\cdot0}+20=100[/tex]b)
[tex]f(1)=80\cdot e^{-0.5}+20=68.52[/tex]c)
[tex]f(4)=80\cdot e^{-0.5\cdot4}+20=30.82[/tex]d)
[tex]f(48)=80\cdot e^{-0.5\cdot48}+20=20[/tex]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.
Suppose 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]I need to figure out the easiest way to solve this and apply the method to every problem
The function is given as,
[tex]f(x_{)=-3x^2-7x}[/tex]It is asked to find the value of the expression,
[tex]f(7)[/tex]This can be obtained by replacing 'x' by 7 in the given expression of the function,
[tex]f(7)=-3(7)^2-7(7)[/tex]Resolve the parenthesis,
[tex]\begin{gathered} f(7)=-3(49)-49 \\ f(7)=-147-49 \end{gathered}[/tex]Simplify the terms further,
[tex]f(7)=-196[/tex]Thus, the value of the expression f(7) is obtained as,
[tex]=-196[/tex]The half-life of a radioactive kind of iodine is 21 hours. How much will be left after 42 hours,if you start with 19,296 grams of it?In grams
The half-life of a radioactive material is the time that it takes to reduce to half
In this case, the half-life is 21 hs, and since 42hs is twice the half-life, the material will reduce to half after 21 hours and then to half again.
one half of one half is:
[tex]\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Then we multiply by the initial amount:
[tex]19,296\cdot\frac{1}{4}=4824gr[/tex]The amount left after 42 hours is 4824 grams.
Suppose angles a and B are the two acute angles in a right triangle and that b < a. Apply the relationship between sine and cosine todetermine which statements are correct.sin(6x - 10) = cos(4x + 10)A)x = 9B)a = 46°a = 48°D)B = 42°E)B = 44
The right statements are: A, B and E
Sin(A)=cos(B)
then we check if using x=9 this holds true:
sin(6x-10)=cos(4x+10)
sin((6*9)-10) = sin(44º)
cos(4x+10)=cos(46)
Sin(44)=0.694=cos(46)
then a is true
Now, we know that b
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°
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
pleaseee help meeee For questions 9 - 10, answer the question about inverses. 9. The function m(d) below relates the miles Bob can drive his rental car and the numbers of dollars it will cost. 10. The function a(h) below relates the area of a triangle with a given base 7 and the height of the triangle. It takes as input the number of dollars spent and returns as output the number of miles. It takes as input the height of the triangle and returns as output the of the triangle. m(d) = 40(d- 35) ain= Write the equation that represents the inverse function, d(m), which takes the number of miles driven, m, as input and returns the number of dollars owed, d. Write the equation that represents inverse function, h(a), which takes triangle's area as input and returns height of the triangle.
First problem:
Find the inverse of the function
m = 40 (d - 35)
Recall that for the inverse function we need to solve for d in terms of m (reverse the dependence), so we proceed to isolate d on the right hand side of the equation:
divide both sides by 40
m/40 = d - 35
now add 35 to both sides:
m/40 + 35 = d
The inverse function (dollars in terms of miles) is given then by:
d(m) = 1/40 m + 35
Second problem:
a = 7 * h / 2
in order to find the inverse function (as h in terms of a) we solve for h on the right hand side of the equation as shown below:
multiply both sides by 2:
2 * a = 7 * h
now divide both sides by 7 in order to isolate h on the right
2 a / 7 = h
So our inverse function of height in terms of area is given by:
h(a) = (2 a) / 7
76. A company has hired 10 new employees, I men and 3 women. The company mustassign 5 of them to the morning shift, 3 of them to the swing shift, and the restof them to the graveyard shift.(a) (2 points) Find the prob that at least one man is assigned to the swing shift?
Answer:
[tex]\frac{2519}{2520}[/tex]Explanation:
Here, we want to get the probability that at least one man is assigned to the swing shift
From the question, 3 of the employees are assigned to the swing shift
Thus we have to calculate the probability of:
1 man , 2 men or 3 men
Mathematically, we have that as:
1 - p(all of the swing shift employees are women)
For the swing shift, for all them to be women, we will be selecting 3 out of 3 so the combination here is 3 C 3 which is 1
We now calculate the probability by dividing this value by the total number of possible ways
Mathematically, we have that as follows:
[tex]\frac{1}{10\text{ C 5 }\times\text{ 5 C 3 }^\times\text{ 1}}\text{ = }\frac{1}{2520}[/tex]This is the probability of placing all of the women on the swing shift
So, the probability that at least 1 man is assigned will be:
[tex]1-\text{ }\frac{1}{2520}\text{ = }\frac{2519}{2520}[/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
2. Two of your classmates are arguing over the solution to a problem. Rhonda believes that the only method to solving the following theequation below is by using the quadratic equation. Max believes that you can use the quadratic formula but you can also factor theequation. Explain if Rhonda or Max is correct.2x^2-5x=88Some words/phrases to consider using in your response would be:factorFOIL MethodZero-Product PropertyStandard Formquadratic expressionquadratic equationscoefficientperfect square
Given data:
The given expression is x^2 -6x-7=0.
The given expression can be written as,
[tex]\begin{gathered} x^2-6x=7 \\ x^2-6x+(\frac{6}{2})^2=7+(\frac{6}{2})^2 \\ x^2-2(x)(3)+3^2=7+3^2 \\ (x-3)^2=16 \end{gathered}[/tex]Thus, the number 9 is added on both sides to complete square.
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]
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
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)
If sine= 2/3, which of the following are possible for the same value of ?
Given
[tex]\sin\theta=\frac{2}{3}[/tex]Find
which of the following are possible?
Explanation
as we know ,
[tex]\begin{gathered} \sin\theta=\frac{P}{H} \\ \end{gathered}[/tex]so , H = 3 , P = 2
then
[tex]\begin{gathered} B=\sqrt{H^2-P^2} \\ B=\sqrt{9-4} \\ B=\sqrt{5} \end{gathered}[/tex]so ,
[tex]\begin{gathered} \cos\theta=\frac{B}{H}=\frac{\sqrt{5}}{3} \\ \\ \tan\theta=\frac{P}{B}=\frac{2}{\sqrt{5}} \\ \\ sec\theta=\frac{1}{\cos\theta}=\frac{3}{\sqrt{5}} \end{gathered}[/tex]Final Answer
Hence , the correct options are B and C
Need help pleaseI was bad at math in school so lwant to learn
The probability of an event is expressed as
[tex]Pr(\text{event) =}\frac{Total\text{ number of favourable/desired outcome}}{Tota\text{l number of possible outcome}}[/tex]Given:
[tex]\begin{gathered} \text{Red}\Rightarrow2 \\ \text{Green}\Rightarrow3 \\ \text{Blue}\Rightarrow2 \\ \Rightarrow Total\text{ number of balls = 2+3+2=7 balls} \end{gathered}[/tex]The probability of drwing two blue balls one after the other is expressed as
[tex]Pr(\text{blue)}\times Pr(blue)[/tex]For the first draw:
[tex]\begin{gathered} Pr(\text{blue) = }\frac{number\text{ of blue balls}}{total\text{ number of balls}} \\ =\frac{2}{7} \end{gathered}[/tex]For the second draw, we have only 1 blue ball left out of a total of 6 balls (since a blue ball with drawn earlier).
Thus,
[tex]\begin{gathered} Pr(\text{blue)}=\frac{number\text{ of blue balls left}}{total\text{ number of balls left}} \\ =\frac{1}{6} \end{gathered}[/tex]The probability of drawing two blue balls one after the other is evaluted as
[tex]\begin{gathered} \frac{1}{6}\times\frac{2}{7} \\ =\frac{1}{21} \end{gathered}[/tex]The probablity that none of the balls drawn is blue is evaluted as
[tex]\begin{gathered} 1-\frac{1}{21} \\ =\frac{20}{21} \end{gathered}[/tex]Hence, the probablity that none of the balls drawn is blue is evaluted as
[tex]\frac{20}{21}[/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
Enter a range of values for x.1416202x+109/15-5
26
Here, we want to write a range of values for x.
The shape we have is not a parallelogram but we have two equal sides
If it was a complete parallelogram, the two marked angles will be equal
But since what we have is not a complete parallelogram,
then;
[tex]\begin{gathered} 2x\text{ + 10 < 62 } \\ 2x\text{ < 62 - 10} \\ \\ 2x\text{ < 52} \\ \\ x\text{ < }\frac{52}{2} \\ \\ x\text{ < 26} \end{gathered}[/tex]-2(k - 5) + 2K = 5k +5A)k=0B)k=4C)k1D)k=2
The equation we have is:
[tex]-2(k-5)+2k=5k+5[/tex]Now we can simply the equation by multiply the -2 into the parenthesis
[tex]\begin{gathered} -2k+10+2k=5k+5 \\ 10=5k+5 \end{gathered}[/tex]now we can solve for k
[tex]\begin{gathered} 10-5=5k \\ 5=5k \\ \frac{5}{5}=k \\ 1=k \end{gathered}[/tex]a. find a length of segment DF . use decimal rotation _______ unitsb. find the length of segment DF. use decimal rotation _______ units
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of
producing x units of tile is given by C(x) = 200x + 900, while the revenue in dollars, R(x), from the sale of x units of tile
is given by R(x)=230x. Find the break-even point and the cost and revenue at the break-even point.
The break-even point is
The cost at the break-even point is $
The revenue at the break-even point is
units.
www
The break-even point=30, The cost of producing x units of tile =6900$, revenue from the sale of x units of tile at the break-even point=6900$.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
What is revenue?Revenue is the total amount of money made from the sale of products and services that are essential to the business's core operations. Sales or turnover are other terms used to describe commercial revenue. Some businesses make money from royalties, interest, or other fees.
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of producing x units of tile is given by C(x) = 200x + 900, while the revenue in dollars, R(x), from the sale of x units of tile is given by R(x)=230x.
C(x) = 200x + 900
R(x)=230x
200x+900=230x
30x=900
x=30
C(x)=200*30+900
=6900
R(x)=230*30=6900
30 is the break-even point; At the break-even point, the cost of producing 30 units of tile is $6900, and the revenue from those sales is $6900.
To know more about revenue,
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Tasty Subs acquired a food-service truck on October 1, 2024, for $23,100. The company estimates a residual value of $1,500 and a six-year service life. Required:Calculate depreciation expense using the straight-line method for 2024 and 2025, assuming a December 31 year-end.
The company estimates a residual value of $1,500 and a six-year service life.
It is given that,
Cost of truck delivery = $ 23100
Salvage value = $ 1500
Useful life = 6 years
Depreciation expenses by using the straight-line method are calculated as,
[tex]Depreciation\text{ expenses p.a = }\frac{cost\text{ - salvage value }}{useful\text{ life}}[/tex]Substituting the value in the formula,
[tex]\begin{gathered} Depreciation\text{ expenses p.a = }\frac{23100\text{ - 1500}}{6} \\ Depreciation\text{ expenses p.a = }\frac{21600}{6} \\ Depreciation\text{ expenses p.a = 3600} \end{gathered}[/tex]Thu
Complete the equation, and tell which property you used.7. (3 X 10) X 8 = X (10 X 8)8. 16 + 31 = 31 +9. 0 +__= 9110. 21 x__= 9 X 21Problem Solving(RealWorld11. The Metro Theater has 20 rows of seats with 18seats in each row. Tickets cost $5. The theater'sincome in dollars if all seats are sold is (20 X 18)X 5. Use properties to find the total income.12. The numbers of students in the foursixth-grade classes at Northside School are 26,19, 34, and 21. Use properties to find the totalnumber of students in the four classes.
7. (3 X 10) X 8 = 3 X (10 X 8)
In this case, we use the associative property of the multiplication (you can group the factors in any way).
8. 16 + 31 = 31 + 16
Commutative property.
9. 0 + 91 = 91
Identity property
10. 21 x 9 = 9 X 21
Commutative property
11. The income is (20 * 18) * 5.
We can multiply the three numbers together, using the associative property.
20 * 18 * 5 = 1800
12. In this case, we have to add each of the groups:
26 + 19 + 34 + 21 = 100
We don't need to apply any properrty in particular. We can add them in any order taking into account the commutative property.
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:
TRIGONOMETRY Given a unite circle what is the value for y?
Let's put more details in the given figure:
To find y, we will be using the Pythagorean Theorem.
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{r}^2=x^2+y^2 \\ \end{gathered}[/tex]Where,
r = radius
x = 1/3
y = uknown
We get,
[tex]\text{r}^2=x^2+y^2[/tex][tex]\begin{gathered} y^2\text{ = r}^2\text{ - }x^2 \\ y^{}\text{ = }\sqrt{\text{r}^2\text{ - }x^2} \end{gathered}[/tex][tex]\text{ y = }\sqrt[]{1^2-(\frac{1}{2})^2}\text{ = }\sqrt[]{1\text{ - }\frac{1}{4}}[/tex][tex]\text{ y = }\sqrt[]{\frac{3}{4}}\text{ = }\frac{\sqrt[]{3}}{\sqrt[]{4}}[/tex][tex]\text{ y = }\frac{\sqrt[]{3}}{2}[/tex]Therefore, the answer is:
[tex]\text{ y = }\frac{\sqrt[]{3}}{2}[/tex]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]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]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,
The area of a circle is about 167.3306 square inches. The circle's circumference is ____ inches.Use 3.14 for π.
The area of a circle can be calculated using this formula:
[tex]A=\pi r^2[/tex]Where "r" is the radius of the circle.
The circumference of a circle can be found using this formula:
[tex]C=2\pi r[/tex]Where "r" is the radius of the circle.
In this case you know that the area of this circle is:
[tex]A\approx167.3306in^2[/tex]Then, you can substitute this value into the first formula and solve for "r". Use:
[tex]\pi=3.14[/tex]Then:
[tex]\begin{gathered} (167.3306in^2)=(3.14)r^2 \\ \\ \frac{(167.3306in^2)}{3.14}=r^2 \\ \\ r=\sqrt[]{(\frac{167.3306in^2}{3.14})} \\ \\ r=7.3in \end{gathered}[/tex]Now you can substitute this value into the formula for calculate the circumference of a circle:
[tex]\begin{gathered} C=(2)(3.14)(7.3in) \\ \end{gathered}[/tex]Finally, evaluating, you get:
[tex]C=45.844in[/tex]The answer is:
[tex]45.844in[/tex]