-43x < 79 - 16
How can the inequality −43x + 16 < 79 be solved?To solve the inequality −43x + 16 < 79, we need to isolate the variable x.
Let's begin by subtracting 16 from both sides of the inequality:
−43x + 16 - 16 < 79 - 16
Simplifying the equation, we have:
−43x < 63
Next, we divide both sides of the inequality by -43. However, when we divide by a negative number, the direction of the inequality sign will be flipped:
x > 63 / -43
Simplifying further, we have:
x > -1.465
Therefore, the solution to the inequality is x > -1.465.
In interval notation, we can represent the solution as (-1.465, ∞), indicating that x is greater than -1.465 and extends indefinitely towards positive infinity.
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a pet store has 115 fish and each tank can hold six fish how many tanks do you nedd
Answer:
20 tanks
Step-by-step explanation:
if each tank holds 6 fish and there are 115 fish, you need to divide the amount of fish total by amount that go in 1 tank:
115/6 = 19.1666666667
Now we round up bc we cant leave any fish out right?
So your answer is 20 tanks will be needed to hold 115 fish if it’s 6 fish per tank.
Check this by multiplying the tanks and fish in every tank:
20 x 6 = 120
Meaning that 115 fish go into 20 tanks, one of the tanks just having 1 fish :D
Answer: 20 is the correct option.
Step-by-step explanation:Given that a pet store has 115 fish that need to be placed into fish tanks and each tank hold 6 fish.
We are to find the number of tanks that the store need.
We will be using the UNITARY method to solve the given problem.
Number of tanks needed to store 6 fishes = 1.
So, number of tanks needed to store 1 fish will be [tex]\frac{1}{6}[/tex]
Therefore, number of tanks needed to store 115 fishes is given by
[tex]\frac{1}{6}[/tex] × 155 =[tex]\frac{115}{6}[/tex]= 19 [tex]\frac{1}{6}[/tex] = 19.16.
Since we cannot have 0.16 tank, so we need one tank more than 19 to store all fishes.
Thus, the store needs 20 tanks for 115 fishes.
Hope this helps :)
Jen is filling bags with M&Ms. She has 5 1/2 cups of M&Ms. She needs 1 1/4 cups of M&Ms to fill each bag. How many bags can Jen fill completely?
Jen can fill 4 bags completely with the 5 1/2 cups of M&Ms she has, given that each bag requires 1 1/4 cups of M&Ms.
First, we need to find the total number of cups of M&Ms Jen has
5 1/2 cups = 11/2 cups
Then, we divide the total number of cups by the number of cups needed to fill each bag
(11/2 cups) ÷ (1 1/4 cups/bag)
To divide by a fraction, we can multiply by its reciprocal
(11/2 cups) x (4/5 cups/bag)
= 44/10 cups
Simplifying, we get
= 4 2/10 cups
= 4 1/5 cups
So, Jen can fill 4 bags completely.
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x An investor puts $4,500 into a life insurance policy that pays 8.0% simple annual interest. If no additional investment is made into the policy, how much accumulated interest should the investor expect at the end of 8 years? HELP PLEASE
The amount of accumulated interest the investor can expect in 8 years is $2,880.
How to find the accumulated interest ?To calculate the accumulated interest on the life insurance policy, we can use the simple interest formula:
I = P x r x t
In this case, the principal amount invested is $4,500, the annual interest rate is 8.0% (or 0.08 as a decimal), and the time period is 8 years. Therefore:
I = 4,500 x 0.08 x 8
I = $2,880
Therefore, the investor can expect to earn $2,880 in accumulated interest at the end of 8 years.
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Sofia owns a small business selling ice cream. She knows that in the last week 56 customers paid cash, 6 customers used a debit card, and 18 customers used a credit card.
Based on these results, express the probability that the next customer will pay with a credit card as a fraction in simplest form
The probability that the next customer will pay with a credit card is 9/40.
To find the probability that the next customer will pay with a credit card, we need to determine the total number of customers and then calculate the fraction of those who used a credit card.
Step 1: Find the total number of customers.
56 customers paid cash, 6 customers used a debit card, and 18 customers used a credit card.
Total customers = 56 + 6 + 18 = 80 customers
Step 2: Calculate the probability of a customer using a credit card.
Number of customers who used a credit card = 18
Total number of customers = 80
Probability = (Number of customers who used a credit card) / (Total number of customers)
Probability = 18 / 80
Step 3: Simplify the fraction.
Divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 18 and 80 is 2.
18 ÷ 2 = 9
80 ÷ 2 = 40
Simplified fraction: 9/40
So, the probability that the next customer will pay with a credit card is 9/40.
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made bracelets with string and beads. she used xx centimeters of string to make 77 bracelets. she used 17.817.8 centimeters of string for each bracelet. how much string did she use in all? write an equation and use it to solve this problem.enter the correct answers in the boxes.show hints
Total string used = Number of bracelets × String used per bracelet
Total string used = 77 × 17.8 = 1370.6 cm
How much string did she use in total?Let's denote the total amount of string used as "T". We know that the girl used xx centimeters of string to make 77 bracelets, and each bracelet required 17.8 centimeters of string.
To find the total string used, we can set up the following equation:
T = 77 * 17.8
Simplifying the equation, we have:
T = 1369.6
Therefore, the girl used a total of 1369.6 centimeters of string to make all the bracelets.
In conclusion, the equation T = 77 * 17.8 can be used to determine the total amount of string used, and the solution to the equation is T = 1369.6 centimeters.
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I’m confused as to what the solution is if I follow the first step
Answer:
x = 4, y = 1, z = 5
Step-by-step explanation:
z + x =9....(3) we can say it's x + z = 9
x - z = - 1
x + z = 9
______ -
- 2z= - 10
z = 10/2
z = 5
if z + x = 9
5 + x = 9
x = 9 - 5
x = 4
if x + y = 5
4 + y = 5
y = 5 - 4
y = 1
#CMIIW10-2 skills practice simplifying radical expressions square root of 5 over 3
Step-by-step explanation:
sqrt (5/3) = sqrt 5 / sqrt 3
multiply by ONE in the form sqrt (3) / sqrt 3
sqrt 5 / sqrt 3 * sqrt 3 / sqrt 3
= sqrt 15 / 3
Or maybe you meant
sqrt (5) / 3 = .745
Frank needs to find the area enclosed by the figure. The figure is made by
attaching semicircles to each side of a 54-m-by-54-m square. Frank says the area
is 1,662. 12 m2. Find the area enclosed by the figure. Use 3. 14 for it. What error
might Frank have made?
The area enclosed by the figure is
m2
(Round to the nearest hundredth as needed. )
To find the area enclosed by the figure, we first need to find the area of the square and the area of each semicircle.
The area of the square is simply the length of one of its sides squared, which is:
54 m x 54 m = 2,916 m²
The area of each semicircle is half the area of a full circle with the same radius as the side of the square. The radius of each semicircle is 54 m/2 = 27 m.
The area of each semicircle is:
1/2 x π x 27 m² = 1/2 x 3.14 x 27 m x 27 m ≈ 1,442.31 m²
Since there are four semicircles, the total area of the semicircles is:
4 x 1,442.31 m² = 5,769.24 m²
Therefore, the total area enclosed by the figure is:
2,916 m² + 5,769.24 m² ≈ 8,685.24 m²
Frank's answer of 1,662.12 m² is significantly less than the actual area. He may have made the mistake of only calculating the area of one of the semicircles instead of all four, or he may have forgotten to include the area of the square.
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If f(x) = 3x² - 3, find x = 2
Answer:
The answer is 9
Step-by-step explanation:
When x = 2,
f(2) = 3×2^2-3
f(2) = 3×4-3
f(2) = 12-3
f(2)= 9
If KN = 3 cm, MN = 7 cm, RS = 14 cm, and PS = 6 cm, what is the scale factor of figure KLMN to figure PQRS?
The scale factor of figure KLMN to figure PQRS is 6 cm / 3 cm = 2.
To find the scale factor of figure KLMN to figure PQRS, given KN = 3 cm, MN = 7 cm, RS = 14 cm, and PS = 6 cm, follow these steps:
1. First, find the length of a side in figure KLMN. We can use KN since it's given: KN = 3 cm.
2. Next, find the corresponding side length in figure PQRS. Since KN corresponds to PS, we have: PS = 6 cm.
3. Now, find the scale factor by dividing the length of the side in figure PQRS by the length of the corresponding side in figure KLMN: scale factor = PS/KN = 6 cm / 3 cm.
The scale factor of figure KLMN to figure PQRS is 6 cm / 3 cm = 2.
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The answer to this math problem please.
Answer:
C) 6
Step-by-step explanation:
n=6
6( 6 + 1) + 3 =45
36 + 6 + 3 = 45
36 + 9 = 45
Solve for w.
65=170-w
The table below shows the number of students in Mr. Jang's class that are taking 1, 2, 3, or 4 AP classes. After a new student joined the class (not shown in the table), the average (arithmetic mean) number of AP classes per student became equal to the median. How many AP classes is the new student taking?
A) 2
B) 3
C) 4
D) 5
Answer:
2
Step-by-step explanation:
To solve this problem, we need to first find the current average and median number of AP classes per student, and then use that information to determine the number of AP classes the new student is taking.
To find the current average number of AP classes per student, we can use the information in the table:
(1 AP class) x 6 students = 6 AP classes
(2 AP classes) x 9 students = 18 AP classes
(3 AP classes) x 5 students = 15 AP classes
(4 AP classes) x 4 students = 16 AP classes
Total number of AP classes = 6 + 18 + 15 + 16 = 55
Total number of students = 6 + 9 + 5 + 4 = 24
Average number of AP classes per student = Total number of AP classes / Total number of students
= 55 / 24
= 2.29 (rounded to two decimal places)
To find the current median number of AP classes per student, we need to order the number of AP classes per student from least to greatest:
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4
The median is the middle value when the data is ordered in this way. Since there are 24 students, the median is the average of the 12th and 13th values:
Median = (2 + 2) / 2
= 2
Since we know that the current average and median are not equal, the new student must be taking a number of AP classes that will bring the average up to 2. We can set up an equation to represent this:
(55 + x) / (24 + 1) = 2
where x is the number of AP classes the new student is taking. Solving for x, we get:
55 + x = 50
x = -5
This is a nonsensical answer, as the number of AP classes taken by the new student cannot be negative. Therefore, our assumption that the new student is taking a number of AP classes greater than the current average is incorrect. Instead, the new student must be taking a number of AP classes less than the current average, which will bring the average down to 2.
Let y be the number of AP classes the new student is taking. We can set up a new equation to represent this:
(55 + y) / (24 + 1) = 2 - ((2.29 - 2) / 2)
where the term on the right-hand side represents the amount by which the average needs to decrease in order to reach 2. Solving for y, we get:
55 + y = 46.5
y = 46.5 - 55
y = 8.5
So the new student is taking 8.5 AP classes. However, since the number of AP classes must be a whole number, we need to round this value to the nearest integer. Since 8.5 is closer to 9 than to 8, we round up to 9. Therefore, the answer is:
The new student is taking 9 AP classes. Answer: None of the above (not given as an option).
Use the rules to find derivatives of the functions at the specified values.
f(x) = 4x^3 at x = 2
f(2) = _____
The value of the function f(x) at x = 2 is 48.
The question asks us to find the value of the function f(x) = 4[tex]x^3[/tex] at x = 2 and its derivative f'(x) at x = 2.
The value of the function f(x) at x = 2, we simply plug in x = 2 into the function and evaluate:
f(2) = 4[tex](2)^3[/tex] = 4(8) = 32
Therefore,
The value of the function f(x) at x = 2 is 32, which we can write as f(2) = 32.
To find the derivative of the function f(x) at x = 2, we first need to find the general formula for the derivative of f(x), which we can do using the power rule for derivatives.
The power rule states that
To find the derivative of f(x) at x = 2, we simply plug in x = 2 into the formula for f'(x) that we just found:
f'(2) = [tex]12(2)^2[/tex] = 48
Therefore,
The derivative of the function f(x) at x = 2 is 48, which we can write as f'(2) = 48To find the derivative of the function
f'(x) = 12[tex]x^2[/tex]
To find the value of f(2), we can simply plug in x = 2 into the original function:
f(2) = 4[tex](2)^3[/tex] = 32
To find the value of f'(2), we can plug in x = 2 into the derivative we just found:
f'(2) = 12[tex](2)^2[/tex] = 48
Therefore,
f(2) = 32 and f'(2) = 48.
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1. A company is testing a new energy drink. Volunteers are asked to rate their energy one hour
after consuming a beverage. Unknown to them, some volunteers are given the real energy
drink and some are given a placebo-a drink that looks and tastes the same, but does not have
the energy-producing ingredients. Show your work using the following list of random digits to
assign each participant listed either the real drink or the placebo.
69429 86140 11625 87049 23167
Volunteer
Abby
Barry
87524 24575 87254 97801 82231
Callie
Dion
Ernie
Falco
Garrett
Hallie
Indigo
Jaylene
Real or Placebo
2. The local water authority has received complaints of high levels of iron in the drinking water.
They decide to randomly select 20 houses from each subdivision of 100 houses to visit and test
their water. Describe how to use random numbers to select the 20 houses in each division.
3. A couple is willing to have as many children as necessary to have two girls.
a) Describe a simulation that can be performed to estimate the average number of children
required to have two girls.
8 pound of peanuts cost 24 dollars. 6 pounds of walnuts cost half as much. Which is more expensive and by how much.
Answer:
Step-by-step explanation:
The cost of 1 pound of peanuts can be found by dividing the total cost of 8 pounds by 8:
Cost of 1 pound of peanuts = $24 / 8 pounds = $3 per pound
The cost of 1 pound of walnuts can be found by dividing the total cost of 6 pounds by 6 and then multiplying by 2 (since the cost of 6 pounds is half that of the peanuts for the same weight):
Cost of 1 pound of walnuts = ($24 / 6 pounds) x 2 = $8 per pound
Therefore, we see that walnuts are more expensive than peanuts by $5 per pound ($8 - $3).
In other words, 1 pound of walnuts costs $5 more than 1 pound of peanuts.
Farmer jones raises only pigs and geese. he wants to raise at most 16 animals. he wants no more
than 12 geese. he spends $5 to raise a pig and $2 to raise a goose and has 550 available to spend. if he
makes a profit of s4 per pig and s8 per goose, how many of each does he need to raise in order to
maximize his profits?
write the objective function. let a represent the number of pigs and y represent the number of geese.
The profit per pig is $4 and the profit per goose is $8.
How can the farmer raise at most 16 animals in order to maximize his profits?Let's start by defining the variables:
a = number of pigs Farmer Jones raises
y = number of geese Farmer Jones raises
The problem tells us that he wants to raise at most 16 animals, so we can write:
a + y ≤ 16
It also tells us that he wants no more than 12 geese, so we can write:
y ≤ 12
We know that it costs $5 to raise a pig and $2 to raise a goose, and he has $550 available to spend. So the cost of raising the animals can be expressed as:
5a + 2y ≤ 550
Finally, we want to maximize his profits. The profit per pig is $4 and the profit per goose is $8. So the objective function for Farmer Jones' profits is:
Profit = 4a + 8y
To summarize, the linear programming model for this problem is:
Maximize: Profit = 4a + 8y
Subject to:
a + y ≤ 16
y ≤ 12
5a + 2y ≤ 550
where a and y are non-negative integers.
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A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 112 seconds at a speed of 0.8 feet per second.
She then travels directly up for 120 seconds at a speed of 0.6 feet per second.
After this 232-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at 3.5 feet per second? If necessary, round your answer to the nearest tenth of a second.
The length of time, in seconds, that it will take for the scientist to travel back to sea level at 3.5 feet per second will be 5.0 seconds.
How to calculate the amount of timeTo calculate the amount of time, we will begin by calculating the distance traveled from sea level in all of the instances.
1. 112 seconds × 0.8 feet per second = 89.6 feet
2. 120 seconds × 0.6 feet per second = 72 feet
The distance from sea level is now: 89.6 feet - 72 feet
= 17.6 feet
The time, in seconds, that it will take for the scientist to travel back to sea level at 3.5 feet per second will be:
17.6 feet ÷ 3.5 feet per second
5.0 seconds to the nearest tenth.
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21. if you have the raw scores of two individuals on a norm-referenced test, which of the following is important in terms of making meaning of those scores? a. measures of central tendency (mean, median, mode) b. the relative positions of the scores to the rest of the group c. whether higher scores are better than lower scores d. how an individual feels about his or her score e. all of these are important.\
The term which is important in terms of making meaning of those scores is measures of central tendency (mean, median, mode), option A.
A single number that seeks to characterise a set of data by pinpointing the centre location within that set of data is referred to as a measure of central tendency. As a result, measurements of central location are occasionally used to refer to measures of central tendency.
These also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.
The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, certain indicators are more useful than others.
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[tex]\frac{4}{-2} -\frac{3}{-6}[/tex]
The value of the fraction is 3/-2
What is a fraction?A fraction can simply be described as the part of a whole variable, a whole number or a whole element.
The different types of fractions in mathematics are;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
4/-2 - 3/-6
find the lowest common factor
12 - 3/-6
subtract the value, we get;
9/-6
Divide the values into simpler forms
3/-2
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the line is parallel to the graph of y=-1/2x-1 and contains the point (-4, 5)
The equation of the line parallel to the graph of y = (-1/2)x - 1 and containing the point (-4, 5) is y = (-1/2)x + 3.
What is the equation of the parallel line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the graph
y = (-1/2)x - 1
The equation of a line parallel to the graph of y = (-1/2)x - 1 will have the same slope as the given line, which is -1/2.
Now. using the point-slope form, we can find the equation of the line that passes through the point (-4, 5) with slope -1/2:
y - y1 = m(x - x1)
y - 5 = (-1/2)(x - (-4))
y - 5 = (-1/2)x - 2
y = (-1/2)x + 3
Therefore, the equation of the parallel line is y = (-1/2)x + 3.
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Zachary says that the equation 0 = (x – 4)(x – c) has one unique real number solution. What must be the value of c for his statement to be true?
c = 4
Answer:
c=4
Step-by-step explanation:
as there is only one solution for this quadratic equation which is supposedly have 2 or more answers, c can only be 4 in order to be the same equation as the the first one x-4=0
Let AX = B be a consistent linear system with 12 equations and 8 variables. If the solution of the system contains 3 free variables, then what is the rank of the coefficient matrix A?
The rank of the coefficient matrix A is 5.
How to determined the matrix?Since the system AX = B is consistent and has 12 equations and 8 variables, the rank of the coefficient matrix A must be less than or equal to 8 (the number of variables).
If the solution of the system contains 3 free variables, it means that the dimension of the null-space of A is 3. By the rank-nullity theorem,
we know that the dimension of the null-space of A plus the rank of A is equal to the number of columns of A (which is 8 in this case).
Therefore, we have:
rank(A) + dim(null(A)) = 8
rank(A) + 3 = 8
rank(A) = 5
So, the rank of the coefficient matrix A is 5.
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Y’all pls help this is due
Answer: 4.7KL
Step-by-step explanation:
KL=DAL/100
KL=470/100
KL=4.7
Max has eight circular chips that are all the same size and shape in a bag.
(3 chips are square, and 5 are stars)
Max reaches into the bag and removes one circular chip. What is the theoretical probability that the circular chip has a star on it? Write your answer as a fraction, decimal, and percent
The probability of drawing a star-shaped chip is 5/8.
The theoretical probability of drawing a star-shaped circular chip from the bag is 5/8 or 0.625 or 62.5%. Out of the total of eight circular chips, five are stars, and three are squares.
Therefore, the probability of drawing a star-shaped chip is the ratio of the number of star-shaped chips to the total number of chips in the bag, which is 5/8.
To understand this conceptually, we can think of probability as a fraction where the numerator is the number of favorable outcomes (in this case, drawing a star-shaped chip) and the denominator is the total number of possible outcomes (all the circular chips in the bag).
Thus, the theoretical probability of drawing a star-shaped chip is 5/8 because there are five star-shaped chips out of the total eight circular chips in the bag.
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100 points Please help asap!
The solution of the system of equations is given by the ordered pair (-2, 2).
Based on the table, a x-value that is a solution to the equation is -2.
The solution to the equations are (-6, 3) and (-4, -5).
An ordered pair which is the best estimate for the solution of the system is: A. (-0.5, -1.75).
How to graphically solve this system of equations?In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
8x - 4y = -24 ......equation 1.
4x - 12y = -32 ......equation 2.
Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-2, 2).
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The total cost C(x) (in dollars) incurred by Aloha Company in manufacturing x surfboards a day is given by the following function.
C(x) = −10x2 + 500x + 110 where (0 ≤ x ≤ 15)
(a)
Find C '(x).
C '(x) = (b)
What is the rate of change of the total cost (in dollars) when the level of production is 7 surfboards a day?
$ per surfboard
(a) First, we need to find the derivative of the cost function, C'(x), with respect to x.
The given function is: C(x) = -10x^2 + 500x + 110
To find the derivative, we will apply the power rule:
C'(x) = d/dx (-10x^2) + d/dx (500x) + d/dx (110)
For each term: d/dx (-10x^2) = -20x d/dx (500x) = 500 d/dx (110) = 0 So, C'(x) = -20x + 500
(b) Now, we need to find the rate of change of the total cost when the level of production is 7 surfboards a day.
To do this, we will substitute x=7 into the derivative function C'(x): C'(7) = -20(7) + 500 C'(7) = -140 + 500 C'(7) = 360
The rate of change of the total cost when the level of production is 7 surfboards a day is $360 per surfboard.
Your answer: a) C'(x) = -20x + 500 b) $360 per surfboard
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What is the max/min of the quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7)? Is it a maximum or a minimum? Show your workor explain your reasoning.
The quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7) have a minimum point. The minimum value of the function is -11.
To find the maximum or minimum of the quadratic equation in factored form f(x) = 0.5(x+3)(x-7), we need to convert it to standard form by expanding the terms:
f(x) = 0.5(x² - 4x - 21)
f(x) = 0.5x² - 2x - 10.5
The coefficient of x² is positive, so the parabola opens upwards and we have a minimum point.
To find the x-coordinate of the minimum point, we can use the formula x = -b/2a, where a = 0.5 and b = -2:
x = -(-2)/2(0.5) = 2
So the minimum point is at x = 2. To find the y-coordinate, we can substitute x = 2 into the equation:
f(2) = 0.5(2)^2 - 2(2) - 10.5 = -11
Therefore, the minimum value of the function is -11.
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It takes an apprentice four times as long as the experienced plumber to replace the pipes under an old house. If it takes them 15 hours when they work together, how long would it take the apprentice alone?
Find the measure of Tu in the photo
The value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12
What are circle theoremsCircle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.
For the tangent TU and the secant through U which intersect the circle at points V and W;
TU² = UV × VW {secant tangent segments}
(5x)² = 9 × 16
(5x)² = 144
5x = √144 {take square root of both sides}
5x = 12
x = 12/5
so;
TU = 5(12/5)
TU = 12
Therefore, the value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12
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