The minimum number of tables the store must sell is 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Using t and c as variables, we get
100c + 400t ≥ 3000
c+t≤16
The online furniture store must sell at least $3000 worth of chairs and tables each day, and can ship at most 16 pieces of furniture.
If the store sells 9 chairs for a total of $900, it needs to sell at least 5 tables to reach a total revenue of $3000.
Since the total number of pieces of furniture sold is 14 (9 chairs + 5 tables), which is less than the maximum of 16, the store meets the daily shipping requirement.
Therefore, the minimum number of tables the store must sell is 5.
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
-x+6y=9
-4x+24y=48
Answer:
no solution
Step-by-step explanation:
- x + 6y = 9 → (1)
- 4x + 24y = 48 → (2)
multiplying (1) by - 4 and adding to (2) will eliminate x and y
4x - 24y = - 36 → (3)
add (2) and (3) term by term
0 + 0 = 12
0 = 12 ← false statement
this false statement indicates the system has no solution
A Smoothie is mixed with strawberries and bananas in the ratio 7:3. Gill
makes a smoothie using 144g of bananas. How many grams of
Strawberry does she use?
Answer: et's call the amount of strawberries Gill uses "x" grams. We know that the ratio of strawberries to bananas is 7:3, so we can set up an equation:
x/144 = 7/3
To solve for x, we'll multiply both sides of the equation by 144:
x = 7/3 * 144
x = 7 * 48
x = 336
So Gill uses 336 grams of strawberries in the smoothie.
Step-by-step explanation:
Can someone help me please?
Answer:
JGK = 29 degrees
Step-by-step explanation:
i hope this helped :)
1. What is the area of triangle ABC? * 12 60° 60° A A. 6/3 square units B. 18 V3 square units A B C. 36 /3 square units D. 72 /3 square units
Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice
What is a formula of area of triangle?
To calculate the area of a triangle, use the formula area = 1/2 * base * height.
To find the area of triangle ABC, we can use the formula:
Area = (1/2) * base * height
where the base and height are the dimensions of the triangle that form a right angle.
In this case, we don't have the dimensions of the triangle that form a right angle, but we know that the triangle has two angles that are 60 degrees each. This tells us that the triangle is an equilateral triangle, and all three sides are equal.
Let's call the length of each side "s". Then, we can use the formula for the area of an equilateral triangle:
[tex]Area = (\sqrt(3)/4) * s^2[/tex]
Plugging in the given value of 12 for s, we get:
[tex]Area = (\sqrt{(3)/4) * 12^2}\\\\ Area \ = (\sqrt{(3)/4) * 144} \\\\Area = 36\sqrt{(3)}[/tex]
Therefore, the area of triangle ABC is [tex]36\sqrt(3)[/tex] square units.
Option C, 36/3 square units, is equivalent to this answer, so that is the correct choice.
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Please help with triangles
The value of x is given as follows:
x = 131º.
How to obtain the value of x?An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.
Considering the above text, the measure of the top angle of the bottom triangle is given as follows:
a = 180 - 98
a = 82.
The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence:
2b + 82 = 180
2b = 98
b = 49.
(the sum of the measures of the internal angles of a triangle is of 180º).
Considering the vertical angles, the base angles of the top triangle are given as follows:
b = 49.
Hence the value of x is given as follows:
x = 180 - 49
x = 131º.
(as the top triangle is also isosceles, and the angle measure x is the exterior angle of an interior angle with measure of 49º).
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Jan has a cookie jar that contains five peanut butter cookies, eight chocolate chip cookies, and twelve oatmeal raisin cookies. Jan reaches in and grabs a cookie, what is the probability that she will get a chocolate chip cookie?
Answer:
8/25
Step-by-step explanation:
5+8+12=25
8/25
Answer: 8/25
Step-by-step explanation:
Find probability with item/total.
total is 25
there are 8 chocolate chip cookies
8/25 is your answer
HOPE THIS HELPS _ MM
There are 800 students. Sixth grade has 226 and seventh grade had 275 how many eighth graders are there ?
We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade. So, there are 299 eighth graders in the school.
We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade. To find the number of eighth graders, we can use the fact that the total number of students is the sum of the number of students in each grade level:
Total number of students = Number of sixth graders + Number of seventh graders + Number of eighth graders
Substituting the given values, we get:
800 = 226 + 275 + Number of eighth graders
Simplifying and solving for the number of eighth graders, we get:
800 = 501 + Number of eighth graders
Number of eighth graders = 800 - 501
Number of eighth graders = 299
Therefore, there are 299 eighth graders in the school.
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Suppose you took a job walking the neighbor's dog because you had borrowed $50.00 from your parents, and you need to pay them back. For this job, you are paid $15 per week to walk the dog for 20 minutes each weekday. Suppose you took a job walking the neighbor's dog because you had borrowed $50.00 from your parents, and you need to pay them back. For this job, you are paid $15 per week to walk the dog for 20 minutes each weekday. Working on the Desmos Graphing Calculator, complete the table showing how many weeks it will take to pay your parents back the money you borrowed. Take a screenshot of your graph when you are finished to submit later in the assignment.
The graplh shows that it will take 3.33 weeks to pay up the money borrowed
How to find the equation to plotted on the graphA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The equation as described in the problem is represented using linear function as as follows
c = money borrowed from your parents = $50.00
m = you are paid $15 per week to walk the dog for 20 minutes each weekday = $15
x = number of weeks
y = amount remaining
The equation is
y = 15x - 50
From the graph the pay will be completed at x = 3.33 (3.33, 0)
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a college student organization wants to start a nightclub for students under the age of 21. to assess support for this proposal, they will select an srs of students and ask each respondent if he or she would patronize this type of establishment. what sample size is required to obtain a 90% confidence interval with a margin of error of at most 0.04?
A sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.
To determine the required sample size for a 90% confidence interval with a margin of error of at most 0.04, we can use the formula:
[tex]n = \left(\frac{z \cdot \sigma}{E}\right)^2[/tex]
where:
n is the sample size
z is the z-score associated with the desired confidence level (90% confidence level corresponds to z = 1.645)
σ is the standard deviation of the population (unknown, so we use 0.5 as a conservative estimate, since the proportion of students who would patronize the nightclub is unknown and assumed to be 0.5 for maximum variability)
E is the maximum desired margin of error (0.04)
Plugging in the values, we get:
n = (1.645 * 0.5 / 0.04)²
n ≈ 424
Therefore, a sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.
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which expressions are equivalent to minus -2X +3+ 7Y + 4X -5 
The expression equivalent to -2x +3+ 7y + 4x -5 is 2x+7y-2.
What exactly are expressions?
Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.
Now,
Given expression is -2x +3+ 7y + 4x -5
writing same terms together
=4x-2x+7y+3-5
=2x+7y-2
hence,
The expression equivalent to -2x +3+ 7y + 4x -5 is 2x+7y-2.
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Crayons are delivered to Miguel's Learning Center in boxes measuring 15.0 inches by 24.0 inches
by 8.5 inches. Miguel's ordered 17 boxes. How much storage space is needed for the crayons?
OA 3,060 cubic inches
OB 26,010 cubic inches
OC 39,015 cubic inches
OD 52,020 cubic inches
Answer:
OD 52020 cubic inches
Step-by-step explanation:
15.0×24.0=360
=360×8.5=3060
3060 inches×17 boxes=52020 inches
Therefore;52020 cubic inches storage space is needed for the crayons
PLS HELP ASAP geometry
Find x pls
Answer:
Step-by-step explanation:
i have no idea sorry
Answer:
Ac = 0.833334.
Step-by-step explanation:
SINCE THE QUESTION IS PYTHAGORAS THEOREM.
THE FORMULA IS
[tex] tan = \frac{ |bc| }{ac} [/tex]
From the question tan = 18°
bc = 15
ac= ?
making ac = x
therefore
[tex] tan = \frac{ |bc| }{ |ac| } \\ tan 18 = \frac{15}{x} \\ tan18(x) = x \times \frac{15}{x} \\ tan18x = 15 \\ = \frac{tan18x}{18} = \frac{15}{18} \\ x = 0.8333334[/tex]
therefore x = 0.8333334.
Graph the points, connect them in orden, find the perimeter of the polygon (-1,-1),(-1,1),(1,1),(3,-3)
Answer: the perimeter of the polygon is 29cm
Step-by-step explanation:
I desperately need help with this!!!!!!!!!!!!
Answer:
a. 54 = 2 * 3³
b. 108 = 2² * 3³
c. 360 = 2² * 3² * 5
etc.
Step-by-step explanation:
So, you need to have a list of primes handy:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, ...
Now, take your number and try to divide it by the first prime, 2.
54 = 27 * 2
That worked. Note down the 2 and repeat with the result. You find 27 cannot be divided by 2 again, but it can be divided by 3 (the next prime in the list):
27 = 9 * 3
Note down the 3 and repeat:
9 = 3 * 3
Note down a 3 again.
So you have
54 = 2*3*3*3 = 2 * 3³
You can continue this until the result is a prime number itself. Then you are done.
y at least inequality symbol 2/3x + 2 y<-1/3x+1
After solving the given inequality question, we will get x < -9.
What is an inequality symbol?A mathematical sign for comparing two values or expressions is an inequality symbol. Inequality symbols include: (less than), > (greater than), (less than or equal to), and (greater than or equal to). Inequalities can be used to represent connections between two or more variables, for as 5 10 indicating that 5 is less than 10. Inequalities can also be used to define mathematical equations or to describe connections between variables. The equation x + 2 7 can, for example, be used to represent the relationship between x and 7, or to communicate that the value of x must be less than 5 for the equation to be true.
In the given question,
2/3x + 2y < -1/3x + 1
⇒ 2/3x + 2y - (-1/3x + 1) < 0
⇒ 5/3x + 3 < 0
⇒ 5/3x < -3
⇒ x < -9
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Area of this figure?
Answer:
213 ft^2
Step-by-step explanation:
In this problem, we can create a larger rectangle that engulfs this image with a few missing pieces on the corners. The area of that rectangle would be 18ft * 17 ft = 306 ft^2. The sum of the missing pieces is 2ft * 7ft + 5ft * 6 ft + 7ft * 7ft = (14 + 30 + 49)ft^2 = 93 ft^2. So, the area of this figure is 306 - 93 = 213 ft^2
ANSWER: S=173ft^2
_._._._._._._._._._._._.
X over 2 linear or nonlinear
Answer:
linear
Step-by-step explanation:
when you graph x/2 it is a straight line, therefore it is linear
Pls, answer! Lots of points! Question down below!
The polynomial (x-a)(x-b)(x-c)....(x-z) has a coefficient of -351 for the x²⁵ term. Since there are 26 variables, the sum of all coefficients is 2²⁵, or 33554432.
The polynomial (x-a)(x-b)(x-c)....(x-z) can be written as
x²⁶ - (a+b+c+...+z)x²⁶ + (sum of products of pairs)x²⁴ - ... - abc...xyz
The coefficient of x²⁵ is the negative sum of the constants, which is -(a+b+c+...+z). Since there are 26 variables in total, the sum of the constants is just the sum of the first 26 letters of the alphabet, which is
(a+b+c+...+z) = 1 + 2 + 3 + ... + 26 = 351
So the coefficient of x²⁵ is -351.
To find the sum of all the coefficients, we can simply evaluate the polynomial when x = 1. At x = 1, each term in the polynomial is just the product of some combination of (1-a), (1-b), (1-c), ..., and (1-z). Since each variable is a letter from the alphabet, each term is either 0 or 1, depending on whether the corresponding letter is equal to 1 or not.
The sum of all the coefficients is therefore just the number of terms in the polynomial that are equal to 1.
Since there are 26 variables, there are 2²⁶ possible combinations of (1-a), (1-b), (1-c), ..., and (1-z), and exactly half of them are equal to 1 (since each variable is either 0 or 1 with equal probability). Therefore, the sum of all the coefficients is
2²⁵ = 33554432
So the sum of the coefficients of the polynomial (x-a)(x-b)(x-c)....(x-z) is 33554432.
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Select the reason that best supports statement 5 in the given proof.
Given: m
Prove: x=7
Answer:
C. Addition Property of Equality
Step-by-step explanation:
From step 4 to step 5, 20 is added to both sides.
Answer: Addition Property of Equality
A moving company charges $400 plus $0.04 per kg to move a family from Toronto to
Windsor.
a) Define the independent variable and the dependent variable.
b) Write an equation.
c) Use your equation to calculate a table of values with four sets of values to show the
moving costs for 0 – 25,000 kg.
a) Number of kgs independent variable, the amount charged by the company is the dependent variable.
b) The equation is y= 400+ 0.04x.
c) The equation is used to calculate a table of values with four sets of values to show the moving costs for 0 – 25,000 kg.
What is an equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
It is given that a moving company charges $400 plus 0.04 per kg to move a family from Toronto to Windsor.
a) The number of kgs is the independent variable and the amount charged by the company is the dependent variable because it depends on the number of kgs the family is willing to move.
b) The equation that represents the given data is y= 400+ 0.04x
where y is the total amount charged by the company, and x is the number of kgs.
c) For 4 different values of x between 0 - 25,000 we will find values of y.
x y= 400+ 0.04x
6250 650
12500 900
18750 1150
25000 1400
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explain how to solve the equation and how to check the solution.
40 = 8y
plse help me
Answer:
y=5
divide 40 by 8
times 5 by 8 to check your solution
Answer:
see explanation
Step-by-step explanation:
40 = 8y ( isolate y by dividing both sides by 8 )
5 = y
As a check
substitute y into the right side of the equation and if both sides are equal then it is the solution.
right side = 8y = 8 × 5 = 40 = left side
since both sides are equal then y = 5 is the solution to the equation
a person in a lighthouse 22m above sea level sights a buoy in the water. if the angle of depression to the buoy is 25o, how far from the base of the lighthouse is the buoy?
If the angle of depression to the buoy is 250, then the buoy is approximately 47.2 meters from the base of the lighthouse.
What is angle of depression ?
The angle of depression is the angle between a horizontal line of sight and the line of sight from an observer to a point or object that is lower than the observer. It is commonly used in trigonometry and geometry problems that involve the height or depth of an object relative to an observer or the ground.
We can start by drawing a diagram to visualize the situation.
In the diagram, A represents the location of the lighthouse, B represents the location of the buoy, and x represents the distance from the base of the lighthouse to the buoy that we want to find.
Since the angle of depression from the lighthouse to the buoy is 25 degrees, we know that angle ABx is also 25 degrees. We also know that the height of the lighthouse above sea level is 22 meters.
We can use the tangent function to find the value of x:
tan(25°) = opposite / adjacent
tan(25°) = 22 / x
Solving for x, we get:
x = 22 / tan(25°)
x ≈ 47.2 meters
Therefore, the buoy is approximately 47.2 meters from the base of the lighthouse.
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Time spent listening to music a sample of 200 college freshman was asked how many hours per week they spent listening to music the following distribution presents the results
Answer:
Step-by-step explanation:
200 rimwjh hdwqheywgygwuivug
4)
Slope:
2
y
(0, 1)
1
Y-Intercept:
Equa
Goal is to reach 14.4 km. Track is 720 m long. Ran 16 laps already. How many more to reach goal?
Answer:
4 more laps to reach the goal of 14.4 km.
Step-by-step explanation:
First, let's find the total distance covered so far: 720 m x 16 laps = 11,520 m.
Next, let's convert the goal distance to meters: 14.4 km x 1000 m/km = 14,400 m.
Finally, let's subtract the total distance covered from the goal distance to find the remaining distance: 14,400 m - 11,520 m = 2,880 m.
Since a lap is 720 m long, the remaining distance can be divided by 720 m to find the number of laps left: 2,880 m ÷ 720 m = 4 laps.
Therefore, the runner needs to run 4 more laps to reach the goal of 14.4 km.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
twenty five people, consisting of women and men are lined up in a random order. find the probability that the ninth woman to appear is in position 17. that is, find the probability there are women in positions thru and a woman in position 17
The probability that the ninth woman to appear is in position 17 is about 5.59%
We can approach this problem by using the binomial probability distribution. Let X be the number of women among the first 16 people in the line. Then X follows a binomial distribution with parameters n = 16 and p, the probability that any given person among the first 16 is a woman. We want to find the probability that X = 8, since this means that the ninth woman to appear is in position 17.
The probability of any given person being a woman is not specified in the problem, but we can assume that it is 0.5 for simplicity. Therefore, p = 0.5, and we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items. In this case, it gives the number of ways to choose k women from the first 16 people in the line.
Using this formula with n = 16 and k = 8, we get:
P(X = 8) = (16 choose 8) * 0.5^8 * 0.5^8
= 12870 * 0.00390625
= 50.27
This means that the probability of exactly 8 women appearing among the first 16 people in the line is about 50.27%.
Given that there are 8 women among the first 16 people, the probability that the ninth woman appears in position 17 is 1/9, since there are 9 possible positions for the ninth woman to appear, and they are all equally likely.
Therefore, the overall probability that the ninth woman to appear is in position 17 is:
P(X = 8) * (1/9) = 50.27% * (1/9) = 5.59%
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Interpret the meaning of the vertex with the maximum profit in context of John's baking
In the context of John's baking, the vertex with the maximum profit represents the point where John can maximize his profit. The vertex of a parabola represents the point at which the function reaches its maximum or minimum value.
The profit function is often modeled as a quadratic equation, where the vertex represents the maximum point of the parabola. In this case, the profit function may be a function of the number of cakes or pastries sold, the price at which they are sold, and the cost of producing them. When the profit is maximized at the vertex, it means that John is producing and selling the optimal number of cakes and pastries at the optimal price to maximize his profit. The vertex represents the sweet spot for John's baking business, where he can earn the most profit with the least amount of costs. Therefore, understanding the meaning of the vertex with the maximum profit is important for John to make informed decisions about his business, including the optimal number of cakes and pastries to produce, the price to sell them, and how to allocate his resources to maximize his profits.
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The graph of function f is shown.
The graph of exponential function passes through (minus 0.5, minus 8) and (5, 1) also intercepts the x-axis at the point 1 unit and y-axis at point minus 3
Function g is represented by the table.
x -1 0 1 2 3
g(x) -24 -4 0
Which statement correctly compares the two functions?
A.
They have the same y-intercept and the same end behavior as x approaches ∞.
B.
They have the same end behavior as x approaches ∞, but they have different x- and y-intercepts.
C.
They have the same x-intercept and the same y-intercept.
D.
They have the same x-intercept and the same end behavior as x approaches ∞.
The statement that correctly compares the two functions is
They have the same x-intercept and the same end behavior as x approaches ∞.
What is the end behavior of a function?A function's final behaviour is represented by the value of f(x) as x approaches infinity. Both functions in this scenario have the same final behaviour because they both have unbounded growth, or they both go to positive infinity.
To find y-intercept of a function we have to put x= 0
So, The y-intercept of f(x) is y = -3.
and, The y-intercept of g(x) is y = -4.
To find x -intercept of a function put y = 0
So, The x-intercept of f(x) is x = 1.
and, The x-intercept of g(x) is x = 1.
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Which statements describe the graph of 2 8/9>x
There is an open circle on ²9.
21909.
The graph contains the point 0
,8
There is a closed circle on ²ğ.
The arrow points to the left.
The arrow points to the right.
2x on a number line? Select three options.
The inequality 26/9 > x represents a line with an open circle at 26/9 going toward positive infinity represented by an arrow.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality [tex]2\frac{8}{9} > x[/tex].
26/9 > x.
Now, As the inequality is strictly greater than 26/9 it would be represented by a line open circled at 26/9 and going towards +∞.
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measures of variability are used to group of answer choices describe the extent to which scores in a distribution differ from one another. describe the extent to which scores in a distribution differ from the mode. make appropriate decisions regarding graph size, shape, and style. describe measures of central tendency.
Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.
Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.
Measures of variability include the range, variance, and standard deviation, and they give us a sense of how spread out the scores in a distribution are. These measures help us understand the variability or dispersion of the data and how far the individual scores in a distribution deviate from the mean or other measures of central tendency.
Measures of central tendency, such as the mean, median, and mode, describe the central or typical value of a set of scores. They provide a summary of the data and a single value that represents the center of the distribution.
The decisions regarding graph size, shape, and style are usually based on the type of data being presented and the message being conveyed. A histogram, for example, may be used to visually display the distribution of a set of scores, and the size, shape, and style of the graph can be adjusted to highlight important features of the data.
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