The equation desbribing the total cost is:
[tex]y=10x+1250[/tex]This equation has the form:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept. Comparing both equations we conclude that in this case we have m=10 and b=1250.
The slope represents the change in cost for each book while the y-intercept represents the intial cost, therefore:
The change in the total cost for eah boog printed is 10.
The cost to get started before any books are printed is 1250.
the top ten medal winning nations in a tournament in a particular year are shown in the table. use the given information and calculate the mean number of gold medals for all nations round to the nearest tenth as needed
To calculate the mean number of gold medals for all nations, we need to add all the gold medals and then divide this number by the total number of nations. Then, we have that the total number of medals are:
T = 14 + 14 + 11 + 9 + 8 + 5 + 2 + 5 + 5 + 7 = 80
The total number of Nations is 10.
Then, the mean number of gold medals for all nations is:
[tex]m=\frac{80}{10}\Rightarrow m=8[/tex]If we round this number to the nearest tenth, the result is m = 8.
(If we round this number to the nearest ten, the result is m = 10).
The perimeter of the rectangle below is 64 units. Find the length of side PS. Write your answer without variables.
Given:
The perimeter of the rectangle, P=64 units.
From the figure, the length of the rectangle, l=PQ=3x+3.
The breadth of the rectangle, b=PS=2x-1.
Now, the expression for the perimeter of the rectangle can be written as,
[tex]\begin{gathered} P=2(l+b) \\ P=2(3x+3+2x-1) \\ P=2(5x+2) \\ P=2\times5x+2\times2 \\ P=10x+4 \end{gathered}[/tex]Now, put P=64 in the above equation and solve for x.
[tex]\begin{gathered} 64=10x+4 \\ 64-4=10x \\ 60=10x \\ \frac{60}{10}=x \\ 6=x \end{gathered}[/tex]Now, we know b=PS=2x-1.
Hence, PS can be calculated as,
[tex]\begin{gathered} PS=2x-1 \\ =2\times6-1 \\ =12-1 \\ =11 \end{gathered}[/tex]Therefore, the length of side PS is 11 units.
Lines AD and BC are parallel. What is the angle measurement of Angle ADEPoint D)?А45150°Bfс
Two Parallel lines , an angle between them
Two crossed lines. Find angle ADE
Two consecutive angles sum up an angle of 180 degrees
Mesurement of angle First find angle C = 180 - 150 = 30 °
hen Then find angle E = 180 - 45 - 30 = 110°
Now angle A = Angle F = 180° -150°= 30° ( because there are 2 parallel lines)
Now finally find angle D = 180° - 110° - 30° = 40 °
Angle D = 40 degrees
[tex] \frac{3}{2x} - \frac{1}{8 {x}^{2} } [/tex]If possible, a step by step for this would help immensely so I could do the rest of the problems like this one.
Problem
Solution
For this case we can take common factor in the denominator 2x and we got:
[tex]\frac{1}{2x}(\frac{3}{1}-\frac{1}{4x})[/tex]Then we can solve the fractions with this operation:
[tex]\frac{1}{2x}(\frac{3\cdot4x-1\cdot1}{1\cdot4x})=\frac{1}{2x}(\frac{12x-1}{4x})[/tex]then we can simplify on this way:
[tex]\frac{12x-1}{6x^2}[/tex]15. the product of k and eight decreased by three times k
We will have that the product of k and eighth decreased by three times k is the following:
[tex]8k-3k=5k[/tex]Student council is selling candy grams. They are using the formula f(c)=2.5c to determine the profit earned for the candy grams. They have to sell between 50 and 60 candy grams. What is the independent variable?
Given the formula:
f(c) = 2.5c
The independent variable is said to be the input. It is the variable that the dependent variable depends on.
Here the independent variable is the number of candy grams they have to sell, c.
Independent variable: c
The range will be the dependent variable. This is the set of output values which depends on the input(independent variable).
Given that they have to sell between 50 and 60 candy grams, the range will be the profit earned.
To find the range, calculate f(50) and f(60)
f(50) = 2.5 x 50 = 125
f(60) = 2.5 x 60 = 150
Therefore, the range is all numbers between 125 and 150.
ANSWER:
Independent variable: c
Range = [125, 150]
Write equations for the vertical and horizontal lines passing through the point (2,8).
Vertical equations x=2, Horizontal lines: y=8
1) For the coordinate point (2,8) let's write
Since we want the result for that is equal to 8. We can formulate
x | y
2 8
Since the question wants vertical and horizontal line, then
Vertical Lines
x=2
Horizontal
y=8
All the other possible equations will neither be horizontal, nor vertical lines. But lines with a certain slope.
how do I solve P= 1.5x -30,000
If you need to solve for x:
P= 1.5x -30,000
Add 30000 to both sides:
P + 30000 = 1.5x - 30000 + 30000
P + 30000 = 1.5x
Divide both sides by 1.5
P/1.5 + 20000 = x
Question 2 Write an equation that gives the amount of snow that h after x hours at this rate. Complete the equation below Use x as your variable. 1
ANSWER
y = 2x
EXPLANATION
We have that after 2 hours, 4 inches of snow had fallen.
We also have that the snow continues falling at this rate.
We are told to use x as the variable. This means that the hours the snow falls is represented by x.
It also means that the amount of snow is represented by y.
A linear equation is given generally as:
y = mx + c
where m = slope
c = y intercept
The slope basically means the rate of change of y values with respect to x values.
Since snow continues falling at the rate of 4 inches (y) every 2 hours (x), therefore, the rate (slope) is:
[tex]m\text{ = }\frac{y}{x}=\frac{4}{2}\text{ = 2}[/tex]Now, we will use the point-slope method to find the equation:
[tex]y-y_1=m(x-x_1)[/tex]where (x1, y1) is any set of points
We have a set of points already (x1, y1) as (2, 4) (remember 2 hours, 4 inches), so:
=> y - 4 = 2(x - 2)
y - 4 = 2x - 4
=> y = 2x - 4 + 4
y = 2x
Therefore, that is the equation that represents the amount of snow fallen after x hours.
You can buy 10 cherry tomatoes for $6. How much would it cost to buy 15 tomatoe Tisa anatish
The cost of 10 cherry is $6.
Determine the cost of one cherry by.
[tex]undefined[/tex]The brand name of a certain chain of coffee shops has a 60% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 8 Coffleton residents. Find the probability that a. exactly 4 of the 8 Coffleton residents recognize the brand name. b. At least 4 residents recognized the brand. c. Find the mean and the standard deviation of the binomial distribution above.
Given:
[tex]\begin{gathered} p=60\%=0.6 \\ n=8 \end{gathered}[/tex]To Determine: The probability that (a) exactly 4 of the 8 Coffleton residents recognize the brand name.
Solution
Using binomial probability, the probability that exactly 4 of the 8 recognize the brand name is
[tex]^8C_4p^4q^4[/tex]Note that
[tex]\begin{gathered} P_r=^nC_rp^rq^{n-r} \\ q=1-p \\ q=1-0.6=0.4 \end{gathered}[/tex]So,
[tex]\begin{gathered} P_4=^8C_4\times(0.6)^4(0.4)^4 \\ ^8C_4=\frac{8!}{4!4!}=\frac{8\times7\times6\times5\times4!}{4!\times4\times3\times2\times1}=\frac{1680}{24}=70 \end{gathered}[/tex][tex]\begin{gathered} P_4=70\times0.6^4\times0.4^4 \\ P_4=0.2322432 \end{gathered}[/tex]b) The probability of at least 4 residents recognized the brand
Using binomial distribution
[tex]\begin{gathered} P(x\ge4)=P(4)+P(5)+P(6)+P(7)+P(8) \\ P(x\ge4)=0.2322432+0.27869+0.209018+0.08958+0.0168 \\ P(x\ge4)=0.82632 \\ P(x\ge4)\approx0.826 \end{gathered}[/tex](c) Find the mean and the standard deviation of the binomial distribution
[tex]\begin{gathered} Mean=np \\ Mean=8\times0.6 \\ Mean=4.8 \end{gathered}[/tex][tex]\begin{gathered} Standard-deviation=\sqrt{npq} \\ Standard-deviation=\sqrt{8\times0.6\times0.4} \\ Standard-deviation=1.3856 \\ Standard-deviation\approx1.386 \end{gathered}[/tex]Hence, the probability that exactly 4 of the 8 Coffleton residents recognize the brand name is 0.232
(b) The probability that at least 4 residents recognized the brand is 0.826
(c) The mean is 4.8 and the standard deviation is 1.386
Write an equation of the line when given slope , m and y intercept (0,b) M=3 , b=5The equation is
Explanation
the slope-intercept form is a way to write the function of a line, it is given by
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \\ \text{and b is the y coordinate of the point where the line crosses the y-a}\xi s \end{gathered}[/tex]so, in this case we just need replace
Step 1
let
[tex]\begin{gathered} m=3 \\ b=5 \end{gathered}[/tex]now, replace in the expression
[tex]\begin{gathered} y=mx+b \\ y=3x+5 \end{gathered}[/tex]therefore, the equation is
[tex]y=3x+5[/tex]I hope this helps you
If (-5 , 3) is a point on the graph of a one-to-one function f, which of the following points is on the graph of f^-1Choose the correct answer below.A (-3 , 5)B (5, -3)C (5, -3)D (-5, -3)i don't need an explanation, just the answer, respectfully. thankyou
If (-5 , 3) is a point on the graph of a one-to-one function f, which of the following points is on the graph of f^-1
therefore
the answer is the point (3,-5)
There are multiple graphs, so I just need the drawing of the graph and explanation!!
GIVEN:
The cosine of the angle is:
[tex]\cos \theta=\frac{4}{7}[/tex]SOLUTION:
To find the measure of the angle, we can find the cos inverse of 4/7. Using a calculator:
[tex]\begin{gathered} \text{If }\cos \theta=\frac{4}{7}, \\ \text{then} \\ \theta=\cos ^{-1}(\frac{4}{7}) \\ \theta=55.15\degree \end{gathered}[/tex]The problem gives that sin θ is negative and we can see that cos θ is positive. The image below shows which angles are positive and in which quadrant:
Therefore, the angle is in the 4th quadrant.
In the fourth quadrant, the value of the angle is:
[tex]\theta_1=360-\theta[/tex]Therefore, the angle will be:
[tex]\begin{gathered} \theta_1=360-55.15 \\ \theta_1=304.85\degree \end{gathered}[/tex]The angle is 304.85°
Is the number in the following statement an exact quantity or a measured quantity?You are 5 feet 8 inches tall.exact quantitymeasured quanitity
Exact numbers have no uncertainty, this is never possible when measuring something since every measure we perform has a certain degree of uncertainty (You cannot measure fractions of a millimeter with a common ruler, for example).
Therefore, the answer is that that number is a measured one, a measured quantity
7,618,272,763km^2 in scientific notation to two digits after the decimal
In scientific notation we use powers of 10
first we need to count how many ciphers or numbers have the question
there are 10 numbers here
So we have 0.7618 x 10^10
BUT the problem says two digits after decimal, so we need to add two ZEROS after the decimal then it gives
0.007618 x 10^ 10 , and multiply this by 10^2
so then multiplying same base 10^10x (10^2)= 10^12
and the final result is
0.007618 x 10^12
Raj is making korma for a party. He puts 25 g of curry powder on a food scale. The food scale has marks every 0.1 g. To measure fo each recipe, Raj removes 1/4 g of curry powder from the scale 7 times. He says the mass of the remaining curry powder is between 18.2 g and 18.3 g.is Raj right?
He put 7G of curry powder on a food scale.
If he removes 1/4 seven times, then we can find the remaining curry powder using the next operation:
7(1/4) = 7/4
Then
25G - 7/4 = 23.25
Therefore, Raj is not right because 7 X 1/4= 7/4 and 25 - 7/4 = 23.25, which is between 23.2 g and 23.3 g.
I got this wrong can someone pls help me correct it?
Given the expression:
[tex](8n^6)^{\frac{5}{3}}[/tex]Let's simplify the expression.
First rewrite 2³ for 8:
[tex](2^3n^6)^{\frac{5}{3}}[/tex]To simplify the expression, apply distributive property and distribute the exponent outside the parentheses to the terms.
We have:
[tex]2^{3*\frac{5}{3}}*n^{6*\frac{5}{3}}[/tex]Simplify the exponents:
[tex]\begin{gathered} 2^5n^{\frac{6*5}{3}} \\ \\ 2^5n^{\frac{30}{3}} \\ \\ 2^5n^{10} \\ \\ =32n^{10} \end{gathered}[/tex]ANSWER:
[tex]undefined[/tex]The Garcia family has two cars. Last week, the first car consumed 35 gallons ofgas and the second consumed 25 gallons of gas. The two cars drove acombined total of 1,025 miles, and the sum of their fuel efficiencies was 35miles per gallon. What was the fuel efficiency of each of the cars last week?First car: 15 miles per gallonSecond car: 20 miles per gallonFirst car: 10 miles per gallonSecond car: 25 miles per gallonFirst car: 20 miles per gallonSecond car: 15 miles per gallonFirst car: 25 miles per gallonSecond car: 10 miles per gallon
Let x be the efficiency for the first car and let y be the efficiency for the second car.
We know that the firt car consumed 35 gallons, the second 25 gallons and that they drove a combined total of 1025 miles, then we have the equation:
[tex]35x+25y=1025[/tex]We also know that the sum of their efficiencies was 35, then we have:
[tex]x+y=35[/tex]Hence we have the system of equations:
[tex]\begin{gathered} 35x+25y=1025 \\ x+y=35 \end{gathered}[/tex]To find the solution of the system let's solve the second equation for y:
[tex]y=35-x[/tex]Plugging this in the first equation we have:
[tex]\begin{gathered} 35x+25(35-x)=1025 \\ 35x+875-25x=1025 \\ 10x=1025-875 \\ 10x=150 \\ x=\frac{150}{10} \\ x=15 \end{gathered}[/tex]Now that we have the value of x we plug it in the expression for y:
[tex]\begin{gathered} y=35-15 \\ y=20 \end{gathered}[/tex]Therefore the efficiency of the first car was 15 miles per gallon and the efficiency of the second car was 20 miles per gallon
The seven cards are [A A A B B R R] how do I solve this?
The given information is:
- The seven cards are A,A,A,A,B,B,R,R
Now, the 7 cards are shuffled, and 4 of the 7 cards are chosen at random and arranged in a random order in a straight line.
To find the total number of arrangements of these 4 cards, let's analyze the possibilities:
[tex]\begin{gathered} C(n,k)=\frac{n!}{(n-k)!k!} \\ \\ This\text{ is a combination since the order doesn't matter} \\ n\text{ is the total number of letters 7, and k is the number of letters we chose 4} \\ So: \\ C(7,4)=\frac{7!}{(7-4)!4!}=\frac{5040}{6*24}=\frac{5040}{144}=35 \end{gathered}[/tex]There are 35 possible arrangements for these 4 cards.
if length of AB/radius equal x/10 what is the ratio of the area of sector AOB to the area of the circle ?
Jamie downloaded 75.2 4GB of music onto her computer. The download took 3.8 hours. If the music downloaded at a constant rate, how many gigabytes of Music were downloaded in 1 hour? Use long division show your work.
To divide decimals using long division:
1. Convert the divisor into a interger: You multiply in this case dividend and divisor by 10):
[tex]\frac{75.24\cdot10}{3.8\cdot10}=\frac{752.4}{38}[/tex]2. Divide the first to digits of divident into divisor: How many times fits 38 in 75: 1 time (This is the first digit of the quotient)
3. Multiply 38 by 1 and susbtract that result from 75:
4. Put the next digit of the divident next to 37.
5. Divide 372 into 38 (how many times fits 38 in 372: 9 times) and repeat step 3 and 4 until you use the total of digits of dividend and a remainder of 0:
You put the decimal point in the quotient when you use the digit next to the decimal point in dividend.
Then, in 1 hour were downloaded 19.8GBsuppose that six people can stuff Flyers until 500 envelopes in five minutes assume all people work at the same steady rate. The relationship between the Number of people stuffing envelopes and the number of envelopes they can stuff in five minutes is what type of relationship how can you tail? Make a table and a graph to show the relationship and explain how to find several of the entries. Including entry for five people.
6 people stuff flyers into 500 envelopes in 5 minutes. They all work at the same rate.
From the question you can ascertain that if the number of people stuffing the Flyers into the envelopes increases the number of minutes they can stuff this Flyers in the envelopes decreases. Therefore the relationship between the number of people stuffing the envelopes and the number of minutes it takes to stuff the flyers in the envelope is an Inverse relationship. In other words the number of people stuffing the envelopes is inversely proportional to the number of minutes required to stuff the flyers into 500 envelopes . Mathematically,
Looking at the relationship 6 people takes 5 minutes . If the number of people decreases the number of minutes will increase. Therefore, 3 people which is half the number will take double the time which is 10 minutes . 1 person will take 6 times the time which is 30 minutes. Similarly, 2 people will take 3 times the time which is 15 minutes.
Donna runs each lap in 4 minutes. She will run less than 20 minutes today.What are the possible numbers of laps she will run today?Use n for the number of laps she will run today.Write your answer as an inequality solved for n .
Let the amount of laps she will run today be n. If Donna runs each lap in 4 minutes, the total minutes used to run n laps each minute will be 4n.]
Since she will run less than 20 minutes today, the inequality expression for the statement will be:
[tex]4n<20[/tex]To get the value of n, we will divide both sides of the inequality by 4 as shown:
[tex]\begin{gathered} \frac{4n}{4}<\frac{20}{4} \\ n<5 \end{gathered}[/tex]Hence the maximum number of laps she will run per day is 4
Note that the maximum value is 4 because n is less than 5
Which recursive rule can be used to find the bth term of the sequence, an
Answer:
[tex]A\text{ : a}_1\text{ = 9 , a}_n\text{ = a}_{n-1}\text{ + 6}[/tex]Explanation:
Here, we want to get the formula that could be used to represent the rule of the sequence
From the given terms:
4th term is 9 and the 5th term is 15
6th term is 21, 7th is 27 and 8th is 33
What this means is that the difference between each of the terms is 6
Hence, we add 6 to the current term to get the next term
Thus:
[tex]a_n\text{ = a}_{n-1}\text{ + 6}[/tex]Now, to get the first term, we can see that we are 3 differences away from the 3rd term
Hence, the value of the first term will be:
[tex]9-6(3)\text{ = -9}[/tex]Thus, we have the first term as -9
An airplane leaves and airport and flies due West 120 miles and then 150 miles in the direction south 39.17° west. How far is the plane from the airport (round to the nearest mile)
Okay, here we have this:
Considering the provided information we are going calculate how far is the plane from the airport, so we obtain the following using the law of cosines:
[tex]\begin{gathered} a=\sqrt[]{120^2+150^2-2\cdot120\cdot150\cdot\cos (129.17)} \\ a\approx244\text{ miles} \end{gathered}[/tex]Finally we obtain that the plane is approximately 244 miles far from the airport.
Are the checked statements correct or incorrect if so choose the correct answer
In this figure the side:
[tex]\sin (\text{GFH)}[/tex]Is equal to the segment GH so the equivalent expression will be:
[tex]\cos \measuredangle FGH[/tex]and no more
Alicia has $7.50. Bolts costs $0.30. How many bolts can she buy?
Answer:
25 bolts
Explanation:
The cost of a bolt = $0.30
Alicia has $7.50.
To determine the number of bolts she can buy, we divide the amount she has by the cost.
[tex]\begin{gathered} \frac{7.50}{0.30}=\frac{75}{3} \\ =25 \end{gathered}[/tex]Alicia can buy 25 bolts.
In May 2017, about 105 devil's lived on Maria island of those, 31% were captured and released into the wild to help struggling populations. How many is that?
Let be "x" the number devils that were captured and released into the wild.
According to the information given in the exercise, about 105 of them lived on Maria Islad. This number is the 100%.
Knowing that 31% were captured and released into the wild, you can set up the following proportion in order to find "x":
[tex]\frac{105}{100}=\frac{x}{31}[/tex]Now you must solve for the variable "x" in order to find its value. You get that this is:
[tex]\begin{gathered} (31)(\frac{105}{100})=x \\ \\ \frac{3255}{100}=x \\ \\ x=32.55 \\ x\approx33 \end{gathered}[/tex]The answer is: About 33 devils were captured and released into the wild.
find fractional notation 5.6%