The equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
What is an linear equation is one variable?
An linear equation is an equation of degree one. the highest exponent is 1 and one variable is number of variable is 1 in the equation
We are given that, Simba pays $15 per month for the phone he bought. His cell phone plan costs $49 per month.
He pay additional $5 for 1 gb data after 15gb data limit got over
Let the number of gb's used be x
Hence the total bill will be given by the equation
B= 15+49+5x
B= 64+5x
If he uses 23 gb of data the first 15 Gb are covered in his phone plan
And he has to pay $5 for each gb
The total cost is 8*5=$40
Hence the total phone bill is B=64+40
B=$104
Hence the equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
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A basketball player shooting from the foul line has a 40% chance of getting a basket. He takes five shots. Whether he scores on one shot is independent of what he does on another shot. What is the probability that he misses at most one basket (rounded off to three decimals)?
The probability that the basketball player misses at most one basket is 0.077 as it is a mutually exclusive event.
what are mutually exclusive events in probability?Two events are said to be mutually exclusive if they cannot occur at the same time or simultaneously. This implies they are disjoint events and the probability of both events occurring at the same time will be zero.
Let us represent the probability of the player getting a basket to be p(y) and that of not getting a basket to be p(x)
then p(y)=40%=40/100=2/5
p(x)=1-(2/5)=3/5
The probability the player misses at most one basket implies his highest miss is one out of the five shots he took
So, the probability that he missed the:
1st shot= (3/5)×(2/5)×(2/5)×(2/5)×(2/5)=48/3125
2nd shot= (2/5)×(3/5)×(2/5)×(2/5)×(2/5)=48/3125
3rd shot= (2/5)×(2/5)×(3/5)×(2/5)×(2/5)=48/3125
4th shot= (2/5)×(2/5)×(2/5)×(3/5)×(2/5)=48/3125
5th shot= (2/5)×(2/5)×(2/5)×(2/5)×(3/5)=48/3125
The probability that he misses at most one basket= (48/3125)+(48/3125)+(48/3125)+(48/3125)+(48/3125)+(48/3125)= 249/3125=0.0768.
Finally, from the workings the probability that the player misses at most one basket is 0.077 rounded up to three decimals
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The diameter of a circle has endpoints P(-12, -4) and Q(6, 12).
ANSWER
[tex](x+3)^{2}+(y-4)^{2}=145[/tex]EXPLANATION
The equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) = center of the circle
r = radius of the circle
The center of a circle is the midpoint of the endpoints of the diameter of the circle. Hence, to find the center of the circle, we have to find the midpoint of the diameter:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) and (x2, y2) are the endpoints of the diameter.
Hence, the center of the circle is:
[tex]\begin{gathered} M=(\frac{-12+6}{2},\frac{-4+12}{2}) \\ M=(\frac{-6}{2},\frac{8}{2}) \\ M=(-3,4) \end{gathered}[/tex]To find the radius of the circle, we have to find the distance between any endpoint of the circle and the center of the circle.
To do this apply the formula for distance between two points:
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, the radius of the circle is:
[tex]\begin{gathered} r=\sqrt{(6-(-3))^2+(12-4)^2}=\sqrt{9^2+8^2} \\ r=\sqrt{81+64}=\sqrt{145} \end{gathered}[/tex]Hence, the equation of the circle is:
[tex]\begin{gathered} (x+3)^2+(y-4)^2=(\sqrt{145})^2 \\ (x+3)^2+(y-4)^2=145 \end{gathered}[/tex]What is the surfacearea of the cone?2A 225π in²B 375m in²C 600T in²D 1000 in 225 in.15 in.
We are given a cone whose radius is 15 inches and slant height is 25 inches. We need to solve for its surface area.
To find the surface area of a cone, we use the following formula:
[tex]SA=\pi rl+\pi r^2[/tex]where r = radius and l = slant height.
Let's substitute the given.
[tex]\begin{gathered} SA=\pi(15)(25)+\pi(15^2) \\ SA=375\pi+225\pi \\ SA=600\pi \end{gathered}[/tex]The answer is 600 square inches.
what is the density of a 10g box measuring 10 cm by 5 cm by 5 cm
Answer:1 g/cm^3
Step-by-step explanation:
Solve. 2x – 5=-3x + 15
Explanation:
First we have to add 3x on both sides of the equation:
[tex]\begin{gathered} 2x-5+3x=-3x+3x+15 \\ 5x-5=15 \end{gathered}[/tex]Now add 5 on both sides:
[tex]\begin{gathered} 5x-5+5=15+5 \\ 5x=20 \end{gathered}[/tex]And finally divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{20}{5} \\ x=4 \end{gathered}[/tex]Answer:
x = 5
Answer:
[tex] \sf \: x = 4[/tex]
Step-by-step explanation:
Given equation,
→ 2x - 5 = -3x + 15
Now the value of x will be,
→ 2x - 5 = -3x + 15
→ 2x + 3x = 15 + 5
→ 5x = 20
→ x = 20 ÷ 5
→ [ x = 4 ]
Hence, the value of x is 4.
The proof below shows that sin theta -sin^3 theta=sin2theta cos^2 theta/2cos theta
Given:
Given the steps of the proof of the equation
[tex]\sin\theta-\sin^3\theta=\frac{2\sin2\theta\cos^2\theta}{2\cos\theta}[/tex]Required: Expression missing on the thrd step
Explanation:
The second step is
[tex]\sin\theta-\sin^3\theta=\sin\theta(1-\sin^2\theta)\frac{2\cos\theta}{2\cos\theta}[/tex]from which leads to
[tex]\sin\theta-\sin^3\theta=\frac{(2\sin\theta\cos\theta)(1-\sin^2\theta)}{2\cos\theta}[/tex]The expression missing on the third step is
[tex]\frac{(2\sin\theta\cos\theta)(1-\sin^2\theta)}{2\cos\theta}[/tex]Option D is correct.
Final Answer:
[tex]\frac{(2\sin\theta\cos\theta)(1-\sin^2\theta)}{2\cos\theta}[/tex]The graph of f(a) = > has been transformed to create the graph of g(s) =
EXPLANATION
The graph of the parent function: f(x) = 1/x has the following form:
Translating the function two units to the left, give us the Image function:
This function is obtained by adding two units to the denominator.
In conclusion, the solution is -2
f(x) = log 2(x+3) and g(x) = log 2(3x + 1).(a) Solve f(x) = 4. What point is on the graph of f?(b) Solve g(x) = 4. What point is on the graph of g?(c) Solve f(x) = g(x). Do the graphs off and g intersect? If so, where?(d) Solve (f+g)(x) = 7.(e) Solve (f-g)(x) = 3.
Given
[tex]\begin{gathered} f(x)=log_2(x+3) \\ and \\ g(x)=log_2(3x+1) \end{gathered}[/tex]a)
[tex]\begin{gathered} f(x)=4 \\ \Rightarrow log_2(x+3)=4 \\ \Leftrightarrow x+3=2^4 \\ \Rightarrow x+3=16 \\ \Rightarrow x=13 \end{gathered}[/tex]The answer to part a) is x=13. The point on the graph is (13,4)
b)
[tex]\begin{gathered} g(x)=4 \\ \Rightarrow log_2(3x+1)=4 \\ \Leftrightarrow3x+1=2^4 \\ \Rightarrow3x+1=16 \\ \Rightarrow3x=15 \\ \Rightarrow x=5 \end{gathered}[/tex]The answer to part b) is x=5, and the point on the graph is (5,4).
c)
[tex]\begin{gathered} f(x)=g(x) \\ \Rightarrow log_2(x+3)=log_2(3x+1) \\ \Rightarrow\frac{ln(x+3)}{ln(2)}=\frac{ln(3x+1)}{ln(2)}] \\ \Rightarrow ln(x+3)=ln(3x+1) \\ \Rightarrow x+3=3x+1 \\ \Rightarrow2x=2 \\ \Rightarrow x=1 \\ and \\ log_2(1+3)=log_2(4)=2 \end{gathered}[/tex]The answer to part c) is x=1 and graphs intersect at (1,2).
d)
[tex]\begin{gathered} (f+g)(x)=7 \\ \Rightarrow log_2(x+3)+log_2(3x+1)=7 \\ \Rightarrow log_2((x+3)(3x+1))=7 \\ \Leftrightarrow(x+3)(3x+1)=2^7 \\ \Rightarrow3x^2+10x+3=128 \\ \Rightarrow3x^2+10x-125=0 \end{gathered}[/tex]Solving the quadratic equation using the quadratic formula,
[tex]\begin{gathered} \Rightarrow x=\frac{-10\pm\sqrt{10^2-4*3*-125}}{3*2} \\ \Rightarrow x=-\frac{25}{3},5 \end{gathered}[/tex]However, notice that if x=-25/3,
[tex]log_2(x+3)=log_2(-\frac{25}{3}+3)=log_2(-\frac{16}{3})\rightarrow\text{ not a real number}[/tex]Therefore, x=-25/3 is not a valid answer.
The answer to part d) is x=5.
e)
[tex]\begin{gathered} log_2(x+3)-log_2(3x+1)=3 \\ log_2(\frac{x+3}{3x+1})=3 \\ \Leftrightarrow\frac{x+3}{3x+1}=2^3=8 \\ \Rightarrow x+3=24x+8 \\ \Rightarrow23x=-5 \\ \Rightarrow x=-\frac{5}{23} \end{gathered}[/tex]The answer to part e) is x=-5/23
The population of Canada, as estimated every five years since 1960, is shown in the table. 1. . Calculate the finite differences for the data set.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data set
STEP 2: Find the finite difference
We first find the differences in the output values which is the population as seen below
[tex]\begin{gathered} 19.68-17.91=1.77 \\ 21.32-19.68=1.64 \\ 23.21-21.32=1.89 \\ 24.59-23.21=1.38 \\ 25.94-24.59=1.35 \\ 27.79-25.94=1.85 \\ 29.35-27.79=1.56 \\ 30.77-29.35=1.42 \\ 32.31-30.77=1.54 \\ 34.01-32.31=1.70 \\ 35.75-34.01=1.74 \end{gathered}[/tex]STEP 3: Find the second order difference
[tex]\begin{gathered} 1.64-1.77=-0.13 \\ 1.89-1.64=0.25 \\ 1.38-1.89=-0.51 \\ 1.35-1.38=-0.03 \\ 1.85-1.38=0.47 \\ 1.56-1.85=-0.29 \\ 1.42-1.56=-0.14 \\ 1.54-1.42=0.12 \\ 1.70-1.54=0.16 \\ 1.74-1.70=0.04 \end{gathered}[/tex]STEP 4: Find the third order difference
[tex]undefined[/tex]Preston drove to his new college and then back home.Round trip he traveled 642 miles. Preston drives aHonda Civic and gets 38 miles for every gallon of gas. IfPreston needs to make 15 round trips a year how muchwill it cost him in gas assuming the price of gas stays at$2.48 a gallon for all his trips?$Round all answers to the nearest hundredthsDo not put a label, just the numeric value
1) Gathering the data
Preston
642 miles
38 miles/gallon
15 round trips
1 gallon = $2.48
2) Considering that each round trip consists of 642 miles
So Preston in 15 roundtrips is going to make
15 x 642 miles =9,630 miles
His car gets 38 miles per gallon. So we can write a proportion for that:
38 miles ---------1 gallon
9,630 miles ----- x
Cross multiplying it:
38x = 9,630 Divide by 38
x =9630/38
x=253.42 gallons
Finally, let's set another proportion to find out the cost of it
1 gallon -------------- $2.48
253.42 -------------- y
y= 253.42 x 2.48
y=628.4816
3) Rounding off to the nearest hundredth
$628. 48 That's how much Preston will spend.
can you help me to find midpoint
First, locate the given points.
Then, draw the line that connects them
Next, add the two x-coordinates of the endpoints and divide by 2. In this case, (1 + 4)/2 = 5/2 = 2.5
Then, draw a line perpendicular to the x-axis that passes through x = 2.5, until it intersects the other line. The intersecting point is the midpoint.
In this case, the coordinates of the midpoint are (2.5, 0.5), as can be seen in the figure
A 4-pound bag of potatoes costs $3.96. What is the unit price?
Given that 4-pound bag of potatoes costs $3.96 then the unit price which is same as the cost of a pound
= $3.96/4
= $0.99
The unit price is $0.99
I need help Options for the first box: -3, 1/3, 3, -1/3 Options for the second box -303, 363, 183, -60
To find the common ratio of the sequence, divide each of the elements of the sequence by the element that precedes it:
[tex]\begin{gathered} \frac{-9}{3}=-3 \\ \frac{27}{-9}=-3 \\ \frac{-81}{27}=-3 \end{gathered}[/tex]Since the quotient is always -3, then the common ratio is equal to -3.
To find the fifth term of the sequence, multiply the fourth term, which is -81, times -3:
[tex]-81\times-3=243[/tex]Once that we know the first five terms of the sequence, add them to find their sum:
[tex]\begin{gathered} 3-9+27-81+243 \\ =-6+27-81+243 \\ =21-81+243 \\ =-60+243 \\ =183 \end{gathered}[/tex]Therefore:
The common ratio of the sequence is -3.
The sum of the first five terms of the sequence is 183.
Based on the experimental probability, predict the number of times that you will roll a 5 if you roll the number cube 300 timesExperiment result on previews question: The number 5 was rolled 9 times out of 20 on a previous question
Explanation: To understand this problem we need to know that there are two different types of probability. The experimental probability and the theoretical probability.
- The experimental probability occurs once you conduct the experiment and after the experiment, you calculate the probability using the result of the experiment.
- The theoretical probability occurs before the experiment. Once you have information about the situation so you calculate the probability the get a specific result before trying.
Step 1: For this question, once we have a number cube with faces 1,2,3,4,5 and 6 and we want to know the experimental probability to get a 5 once you roll the cube 300 times you would need to get in real life a number cube and to roll it 300 times. After this experiment we would get all the results of each time we roll it and we would know how many times (from 300 times) we got a number 5. After that, we would use the following formula
[tex]Experimental_{probability}=\frac{number\text{ of times we got a number 5}}{300}[/tex]Once the get this result we finish the question.
Which of the following sets of ordered pairs represents a function?
A.
{ (0, -2), (-27, -13), (-10, -5), (-27, -12) }
B.
{ (-7, -14), (-9, -18), (-5, -10), (-6, -12) }
C.
{ (1, -1), (1, -27), (1, -26), (1, -17) }
D.
{ (81, 1), (81, -1), (83, 4), (86, 6) }
Answer: B
Step-by-step explanation:
For the set of ordered pairs to be a function, each x-value has to correspond to only one y-value.
In option A, the x-value of -27 corresponds to both -13 and -12.
In option C, the x-value of 1 corresponds to -1, -27, -26, and -17.
In option D, the x-value of 81 corresponds to both 1 and -1.
In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Find BC.
The length of BC is 29 units (solved using trigonometry and its applications).
What is trigonometry?
Trigonometry (from Ancient Greek v (trgnon) 'triangle' and (métron)'measure') is a field of mathematics that explores the correlations between triangle side lengths and angles. The topic arose in the Hellenistic civilization during the third century BC from geometric applications to astronomical research. The Greeks concentrated on chord computation, whereas Indian mathematicians established the first-known tables of values for trigonometric ratios (also known as trigonometric functions) such as sine. Trigonometry has been used throughout history in geodesy, surveying, celestial mechanics, and navigation. Trigonometry is well-known for its many identities. These trigonometric identities are frequently used to rewrite trigonometrical expressions with the goal of simplifying an expression, finding a more usable form of an expression, or solving an equation.
Let the point where AB is cut through line from C be D
This can be solved using trigonometry and its applications.
In triangle ACD,
tan 45° = CD/AD
or, CD = tan 45° x AD
= 1 x 20
= 20 units
In triangle CDB,
tan Ф = CD/BD
or, Ф = tan⁻¹(CD/BD)
= tan⁻¹(20/21)
= 43.6°
so, sin 43.6° = CD/BC
or, BC = CD/sin 43.6°
= 20/0.689
= 29 units
The length of BC is 29 units.
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Answer:
29
Step-by-step explanation:
BC is a side of ACB, which is a 45 45 90 triangle. BC = AB/SQRT2
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 2". Let B be the event "the outcome is greater than 4". Find P(A or B). Outcome Probability 1 0.15 2 0.31 3 0.35 4 0.08 5 0.11
The general rule of P(A or B) is given by the formula
[tex]undefined[/tex]A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings
below:
Pepperoni
Sausage
Chicken Green pepper
Mushroom Pineapple
Ham
Onion
Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is
going to randomly choose 2 different toppings.
What is the probability that Rosa's mom chooses sausage and onion?
Choose 1 answer:
The Probability that Rosa's mom chooses sausage and onion is [tex]\frac{1}{^{8} C_{2} }[/tex]
What is Probability?Probability is the likelihood of an event occurring, measured by the ratio of the favorable cases to the whole number of cases possible.
The probability of an event happening = number of possible outcomes/total number of outcomes.
The number of possible outcomes is 8 exactly 1 of the total possible groups of toppings is sausage and onion.
The total number of outcome is 8 ways, because she has to choose the 2 toppings from possible 8 toppings
So the probability that Rosa's mom will chooses sausage and onion is [tex]\frac{1}{^{8} C_{2} }[/tex]
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Picture translating A ABC three units to the left and five units up.What are the coordinates of A'?A(2,-2)
The coordinates of point A are (2, -2)
If the picture is translated 3 units to the left, we need to subtract 3 units to the x coordinate as:
( 2 - 3, -2) = (-1, -2)
Then, if the picture is translated 5 units up, we need to sum 5 units to the y-coordinate as:
( -1 , -2 + 5) = (-1, 3)
So, the coordinates of A' are (-1, 3)
Answer: (-1, 3)
1. Knowledge: Use your Factoring Flowchart or Concept Map to factor the following Quadratic Polynomials. Copy down the question and show any necessary steps if it is a multi-step factoring process (not just a single-step solution). Question F to I
Solution
We are asked to factorize the following questions
Question F:
[tex]\begin{gathered} 4+6x+2x^2 \\ \text{ 2 is common among the terms, so we can factorize it out} \\ \\ 2(2+3x+x^2) \\ \text{ The term }3x\text{ can also be written as }2x+x.\text{ And the terms }2x\text{ and }x\text{ multiply to get }2x^2 \\ \text{ Thus, we have,} \\ \\ 2(2+3x+x^2)=2(2+2x+x+x^2) \\ \text{ In this new expression, }2\text{ is common to }2+2x\text{ while }x\text{ is common to }x+x^2 \\ \text{ Thus, we can factorize them out} \\ \\ 2(2+2x+x+x^2)=2(2(1+x)+x(1+x)) \\ \text{ Lastly, }(1+x)\text{ is common to }2(1+x)\text{ and }x(1+x) \\ \\ 2(2(1+x)+x(1+x))=2((2+x)(1+x)) \\ \\ \therefore4+6x+2x^2=2(2+x)(1+x) \end{gathered}[/tex]Question G:
[tex]\begin{gathered} 3x^2-1x-10 \\ \text{ The term }-1x\text{ can also be written as }-6x+5x\text{ and the terms }-6x\text{ and }5x\text{ multiply to get} \\ -30x^2.\text{ Thus, we have,} \\ \\ 3x^2-1x-10=3x^2-6x+5x-10 \\ 3x\text{ is common to }(3x^2-6x)\text{ and }5\text{ is common to \lparen}5x-10) \\ \text{ Thus, we can factor them out} \\ \\ 3x^2-6x+5x-10=3x(x-2)+5(x-2) \\ (x-2)\text{ is common to both terms, so we can factor again} \\ \\ 3x(x-2)+5(x-2)=(x-2)(3x+5) \\ \\ \therefore3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]Final Answer
The answers to questions F and G are:
[tex]\begin{gathered} 4+6x+2x^2=2(2+x)(1+x) \\ \\ 3x^2-1x-10=(x-2)(3x+5) \end{gathered}[/tex]
The functions s and t are defined as follows.Find the value of t(s(- 4)) .t(x) = 2x ^ 2 + 1s(x) = - 2x + 1
EXPLANATION
Since we have the functions:
[tex]s(x)=-2x+1[/tex][tex]t(x)=2x^2+1[/tex]Composing the functions:
[tex]t(s(-4))=2(-2(-4)+1)^2+1[/tex]Multiplying numbers:
[tex]t(s(-4))=2(8+1)^2+1[/tex]Adding numbers:
[tex]t(s(-4))=2(9)^2+1[/tex]Computing the powers:
[tex]t(s(-4))=2*81+1[/tex]Multiplying numbers:
[tex]t(s(-4))=162+1[/tex]Adding numbers:
[tex]t(s(-4))=163[/tex]In conclusion, the solution is 163
call Scott's is collecting canned food for food drive is class collects 3 and 2/3 pounds on the first day in 4 and 1/4 lb on second day how many pounds of food has they collected so far
The food collected on first day,
[tex]\begin{gathered} 3\frac{2}{3} \\ =\frac{3\times3+2}{3} \\ =\frac{9+2}{3} \\ =\frac{11}{3} \end{gathered}[/tex]The food collected on second day,
[tex]\begin{gathered} 4\frac{1}{4} \\ =\frac{4\times4+1}{4} \\ =\frac{16+1}{4} \\ =\frac{17}{4} \end{gathered}[/tex]The total amount of food collected can be calculated as,
[tex]\begin{gathered} T=\frac{11}{3}+\frac{17}{4} \\ =\frac{11\times4+17\times3}{3\times4} \\ =\frac{44+51}{12} \\ =\frac{95}{12} \\ =7\frac{11}{12} \end{gathered}[/tex]Therefore, the total amount of food collected so far is 7 11/12 pounds.
Subtract the following polynomial. Once simplified, name the resulting polynomial. 5.) (10x² + 8x - 7) - (6x^2 + 4x + 5)
The given polynomial expression: (10x² + 8x - 7) - (6x^2 + 4x + 5)
[tex]\begin{gathered} (10x^2+8x-7)-(6x^2+4x+5) \\ \text{Open the brackets:} \\ (10x^2+8x-7)-(6x^2+4x+5)=10x^2+8x-7-6x^2-4x-5 \\ \text{Arrange the like term together:} \\ (10x^2+8x-7)-(6x^2+4x+5)=10x^2-6x^2+8x-4x-7-5 \\ \text{Simplify the like terms together:} \\ (10x^2+8x-7)-(6x^2+4x+5)=4x^2+4x-12 \end{gathered}[/tex]The resulting polynomial be:
[tex](10x^2+8x-7)-(6x^2+4x+5)=4x^2+4x-12[/tex]The highest degree of the polynomial is 2 so, the polynomial is Quadratic polynomial
Answer: 4x^2 + 4x - 12, Quadratic polynomial
(f o g)(x) = x(g o f)(x) = xwrite both domains in interval notation
the fact that both functions are polynomial of degree 1 we get that the domain and range of both functions are the real numbers. In intervalo notation this is:
[tex]\begin{gathered} \text{domain:}(-\infty,\infty) \\ \text{range:}(-\infty,\infty) \end{gathered}[/tex]Braden goes to the store to buy earmuffs. The sign says they were originally $13.50 but they are on sale for 15% off. What is the cost of the earmuffs now
Answer:
$11.48
Step-by-step explanation:
Change 15% to 0.15. then you multiply 13.50 by 0.15
13.50 x 0.15 = 2.025
Then you round 2.025
by rounding 2.025 you should get 2.03
with that you should subtract $13.50 by 2.03
13.50 - 2.03 = 11.48
I hope this helps :)
At the fast food restaurant, an order of fries costs $0.94 and a drink costs $1.04. Howmuch would it cost to get 3 orders of fries and 2 drinks? How much would it cost toget f orders of fries and d drinks?
Determine the total cost for 3 order of fries and 2 drinks.
[tex]\begin{gathered} T=3\cdot0.94+2\cdot1.04 \\ =2.82+2.08 \\ =4.9 \end{gathered}[/tex]Determine the expression for f orders of fries and d drinks.
[tex]\begin{gathered} T=f\cdot0.94+d\cdot1.04 \\ =0.94f+1.04d \end{gathered}[/tex]So cost of 3 order of fries and 2 drinks is $4.9.
The cost order for f orders of fries and d drinks is 0.94f + 1.04d.
Express y in terms of x. Then find the value of y when x= -1-3 (x + 2) = 5yY in terms of x:Y=
LEt's express y in term of x:
[tex]\begin{gathered} -3(x+2)=5y \\ y=\frac{-3(x+2)}{5} \end{gathered}[/tex]Therefore:
[tex]y=-\frac{3}{5}x-\frac{6}{5}[/tex]Now, if x=-1, then we have:
[tex]\begin{gathered} y=-\frac{3}{5}(-1)-\frac{6}{5} \\ =\frac{3}{5}-\frac{6}{5} \\ =-\frac{1}{5} \end{gathered}[/tex]Therefore, if x=-1 then y=-1/5
A herd of 23 white-tailed deer is introduced to a coastal island where there had been no deer before. Their population is predicted to increase according to A=276/1+11e^(- .35t)where A is the number of deer expected in the herd after t years.(a) How many deer will be present after 3 years? Round your answer to the nearest whole number.(b) How many years will it take for the herd to grow to 50 deer? Round your answer to the nearest whole number.
Given:
[tex]A=\frac{276}{1+11e^{-0.35t}}[/tex]Where A is the number of deer expected in the herd after t years.
We will find the following:
(a) How many deer will be present after 3 years?
So, substitute t = 3 into the given equation:
[tex]A=\frac{276}{1+11e^{-.35*3}}\approx56.9152[/tex]Rounding to the nearest whole number
So, the answer will be A = 57
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(b) How many years will it take for the herd to grow to 50 deer?
substitute A = 50 then solve for t
[tex]\begin{gathered} 50=\frac{276}{1+11e^{-.35t}} \\ 1+11e^{-.35t}=\frac{276}{50} \\ \\ 11e^{-.35t}=\frac{276}{50}-1=4.52 \\ e^{-.35t}=\frac{4.52}{11} \\ -0.35t=ln(\frac{4.52}{11}) \\ \\ t=\frac{ln(\frac{4.52}{11}_)}{-0.35}=2.54 \end{gathered}[/tex]Round your answer to the nearest whole number.
So, the answer will be t = 3
Suppose that an airline uses a seat width of 16.2 in. Assume men have hip breadths that are normally distributed with a mean of 14 in. and a standard deviation of 1 in. Complete parts (a) through (c) below.
Given:
population mean (μ) = 14 inches
population standard deviation (σ) = 1 inch
sample size (n) = 126
Find: the probability that a sample mean > 16.2 inches
Solution:
To determine the probability, first, let's convert x = 16.2 to a z-value using the formula below.
[tex]x=\frac{\bar{x}-\mu}{\sigma\div\sqrt{n}}[/tex]Let's plug into the formula above the given information.
[tex]z=\frac{16.2-14}{1\div\sqrt{126}}[/tex]Then, solve.
[tex]z=\frac{2.2}{0.089087}[/tex][tex]z=24.6949[/tex]The equivalent z-value of x = 16.2 is z = 24.6949
Since we are looking for the probability of greater than 16.2 inches, let's find the area under the normal curve to the right of z = 24.6949.
Based on the standard normal distribution table, the area from the center to z = 24.6949 is 0.5
Since we want the area to the right, let's subtract 0.5 from 0.5.
[tex]0.5-0.5=0[/tex]Therefore, the probability that a sample mean of 126 men is greater than 16.2 inches is 0.
One-third of a number b multiplied by -11 is more than 3 2
