The answer of the given question based on the plotting graph , the steps are given below .
What is Inequality?An inequality is a statement that compares two values or expressions and indicates that one is greater than, less than, or equal to the other. Inequalities can be solved or simplified using various algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides by the same quantity, or factoring and finding the roots of the expressions
To plot the inequality 4x - 5y ≤ -15, you can follow these steps:
First, rearrange the inequality to solve for y:4x - 5y ≤ -15
-5y ≤ -4x - 15
y ≥ (4/5)x + 3
This gives you the equation of the boundary line. Plot this line on a graph by plotting two points and drawing a straight line through them. To plot the line, you can choose any two values of x and find the corresponding values of y using the equation.Let's choose x = 0 and x = 5.
When x = 0: y = (4/5)(0) + 3 = 3, so one point is (0, 3).
When x = 5: y = (4/5)(5) + 3 = 7, so another point is (5, 7).
Plot these two points and draw straight line through them.
Now, to shade the region that satisfies the inequality, choose a point that is not on the boundary line. The easiest point to choose is (0,0). Substitute x and y values of this point into inequality.4x - 5y ≤ -15
4(0) - 5(0) ≤ -15
0 ≤ -15
Since this is not true, the point (0,0) is not in the region that satisfies the inequality. Shade the region above the boundary line to show the region that satisfies the inequality.
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This is untrue since the point (0,0) is not located in the area where the inequality is satisfied. To highlight the area that satisfies the inequality, shade the area above the boundary line.
What is Inequality?An inequality is a comparison that shows that one value or expression is larger than, less than, or equal to another. Different algebraic methods, such as adding, subtracting, multiplying, or dividing both sides by the same amount, or factoring and determining the roots of the equations, can be used to resolve or simplify inequalities.
Plotting the inequality 4x - 5y ≤-15 can be done by doing the following:
To solve for y, rearrange the inequality first:
4x - 5y ≤ -15
-5y ≤ -4x - 15
y ≥ (4/5)x + 3
You are then provided with the boundary line's equation. Plot two points on a graph, then draw a straight line through them to represent this line. You can use the equation to determine the values of y that correspond to any two x values to plot the line.
Let's choose x = 0 and x = 5.
When x = 0: y = (4/5)(0) + 3 = 3, so one point is (0, 3).
When x = 5: y = (4/5)(5) + 3 = 7, so another point is (5, 7).
Plot these two spots and a line should be drawn directly between them.
Now select a point that is not on the border line to shade the area that satisfies the inequality. (0, 0) is the simplest position to select. In the inequality, replace the x and y values of this point.
4x - 5y ≤ -15
4(0) - 5(0) ≤ -15
0 ≤ -15
Since this is untrue, the point (0,0) is not located in the area where the inequality is satisfied. To highlight the area that satisfies the inequality, shade the area above the boundary line.
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Real-life Problems Question 9
The Results:
a) Cost of the bouncy castle for 20 children = £149
b) Number of children who went to the party = 14.
How to find the cost of the bouncy castle for 20 children?a) To find the cost of the bouncy castle for 20 children, we can substitute the number of children, which is 20, into the formula provided:
Cost = £3.65 * number of children + £76
Cost = £3.65 * 20 + £76
Now we can estimate the cost:
Cost = £73 + £76
Cost = £149
Thus, the cost of the bouncy castle for 20 children = £149.
b) To find the number of children who went to the party based on the given cost of £127.10, we can rearrange the formula to solve for the number of children:
Cost = £3.65 * number of children + £76
£127.10 = £3.65 * number of children + £76
Subtracting £76 from both sides of the equation:
£127.10 - £76 = £3.65 * number of children
£51.10 = £3.65 * number of children
Now we can divide both sides of the equation by £3.65 to isolate the variable:
£51.10 / £3.65 = number of children
14 = number of children
Therefore, the number of children who went to the party = 14.
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Consider the following set of equations:
Equation R: -3y = -3X-9
Equation S: y=x+3
Which of the following best describes the solution to the given set of equations? (4 points
No solution
One solution
Infinite solutions
OTwo solutions
HI THIS IS DREAM AND TO
what is the binary notation for the decimal number 12?
Answer:
1100
Step-by-step explanation:
8 = 1000
9 = 1001
10 = 1010
11 = 1011
12 = 1100
hope this helps :)
sum
one help pretty pleasededeeee
The function N for d days of both rumors are N(d) = 2 + 5d and N(d) = 2(3)^d
How many students know the rumor on day 0Here, the number of students are the students that start the rumor i.e. Susanna and Liz
So, we have
JB = 2 studentsRihanna = 2 studentsHow many students know the rumor on day 2For the Justin Beiber rumor, the rumor spreads at a linear rate of 5 per day
So, we have
JB day 2 = 2 + 5(2) = 7
For the Rihanna rumor, the rumor spreads at an exponential rate of 3
So, we have
Rihanna day 2 = 2 * (3)^2 = 18
Days for students to knowUsing the functions, we have
JB
2 + 5x = 32 students
5x = 30
x = 6 days
Rihanna
2(3)^x = 162 students
3^x = 81
x = ln(81)/ln(3)
x = 4 days
The function N for d daysJB
N(d) = 2 + 5d
Rihanna
N(d) = 2(3)^d
So, we have
d JB Rihanna
0 2 2
1 7 6
2 12 18
3 17 54
4 22 162
5 27 486
6 32 1458
7 37 4374
8 42 13122
9 47 39366
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You are applying fertilizer to the football field field is 360 feet long is 160 feet why do you use 8 pounds of fertilizer per thousand square feet the fertilizer comes and 50 pound bags how many bags of fertilizer what you need to co
To cover the full football pitch, you will want 10 bags of fertiliser, rounded up to the nearest whole number.
What is area?The term "area" refers to the volume of space occupied by a two-dimensional (2D) form or surface.
It's represented by squares.
You must multiply the length by the breadth of the football pitch to determine its total area:
field size for football = length x width
field size for football = 360 feet x 160 feet
field size for football = 57,600 square feet
You must now calculate how many thousands of square feet the football pitch has in order to get the total amount of fertiliser required:
the size of a football pitch in square feet = the size of the football pitch overall / 1,000
the size of a football pitch in square feet = 57,600 / 1,000
the size of a football pitch in square feet = 57.6
You must spread 8 pounds of fertiliser per 1,000 square feet of the football pitch because it is 57.6 thousand square feet in size.
Total required fertiliser quantity = 8 pounds per 1,000 square feet x 57.6 thousand square feet
Total required fertiliser quantity = 460.8 pounds
Given that the fertiliser is sold in 50-pound bags, you will require:
number of fertiliser bags = Total amount of fertilizer needed / Weight of each bag
number of fertiliser bags = 460.8 pounds / 50 pounds/bag
number of fertiliser bags = 9.216 bags
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Can someone help/explain me with numbers 1-3 would really appreciate it
The payment due is given as Rs 875.94
Interest rate Rs 730.50
The principal is Rs 145.44
The balance is Rs 145954.56
How to solveGiven:
P = principal, the initial amount of the loan
I = the annual interest rate (from 1 to 100 percent)
L = length, the length (in years) of the loan, or at least the length over which the loan is amortized.
J = monthly interest in decimal form = I / (12 x 100)
N = number of months over which loan is amortized = L x 12
Okay now for the big monthly payment (M) formula, it is:
J
M = P x ------------------------
1 - ( 1 + J ) ^ -N
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2+8- x=-24 sole for x and show work
There are 60 children in a club.
In the club, the ratio of the number of girls to the number of boys is 3:1
3/5 of the girls play a musical instrument.
4/5 of the boys play a musical instrument.
What fraction of the 60 children play a musical instrument?
(4 marks)
Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. sin(u) = 5/13, pi/2 < u < pi.
According to the information, the exact values of sin(2u), cos(2u) and tan(2u) are sin(2u) = -120/169, cos(2u) = -1, and tan(2u) = -120/119.
How to calculate the exact values of sin(2u), cos(2u) and tan(2u)?We can use the double-angle formulas to find the values of sin(2u), cos(2u), and tan(2u) in terms of sin(u) and cos(u).
sin(2u) = 2 sin(u) cos(u)cos(2u) = cos²(u) - sin²(u)tan(2u) = (2 tan(u)) / (1 - tan²(u))First, we need to find cos(u) using the Pythagorean identity:
cos²(u) + sin²(u) = 1cos²(u) = 1 - sin²(u)cos(u) = ±sqrt(1 - sin²(u))Since pi/2 < u < pi, we know that sin(u) is positive and cos(u) is negative. Therefore:
cos(u) = -sqrt(1 - (5/13)²) = -12/13Now we can substitute sin(u) and cos(u) into the double-angle formulas:
sin(2u) = 2 sin(u) cos(u) = 2 (5/13) (-12/13) = -120/169cos(2u) = cos²(u) - sin²(u) = (-12/13)² - (5/13)² = -144/169 - 25/169 = -169/169 = -1tan(2u) = (2 tan(u)) / (1 - tan²(u)) = (2 (5/12)) / (1 - (5/12)²) = (10/12) / (119/144) = -120/119Therefore, sin(2u) = -120/169, cos(2u) = -1, and tan(2u) = -120/119.
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At a large high school, 20% of the students prefer to have a salad for lunch. If you take a random sample of 10 students from this population, the probability that exactly 2 students prefer salad is
The probability that exactly 2 students prefer salad is 0.302
Calculating the probability that exactly 2 students prefer saladFrom the question, we have the following parameters that can be used in our computation:
n = 10
r = 2
p = 20%
The probability is then calculated as
P(x = 2) = nCr * p^x * (1 - p)^(n - x)
substitute the known values in the above equation, so, we have the following representation
P(x = 2) = 10C2 * (20%)^2 * (1 - 20%)^8
Evaluate
P(x = 2) = 0.302
Hence, the probability is 0.302
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Which ordered pairs represent points on the graph of this equation? Select all that apply. y = 2x - 3 a)3-3 b) 0,-3 c) 5,7 d) -2,-7 e) 2,1 or f) 4,5
The ordered pairs that represent points on the graph of y = 2x - 3 are (0,-3), (5,7), (-2,-7), (2,1), and (4,5).
What is equation?An ordered pair is a pair of numbers written in a specific order (x,y) that represents a point in the coordinate plane.
What is graph?A graph is a visual representation of data or a mathematical function that is plotted on a coordinate plane, usually with an x and y-axis. It is used to analyze trends and relationships between variables.
According to the given information:
To determine whether a given ordered pair represents a point on the graph of the equation y = 2x - 3, we need to substitute the values of x and y into the equation and see if the equation is true.
a) (3,-3):
y = 2x - 3
-3 = 2(3) - 3
-3 = 3
This is not true, so (3,-3) is not on the graph.
b) (0,-3):
y = 2x - 3
-3 = 2(0) - 3
-3 = -3
This is true, so (0,-3) is on the graph.
c) (5,7):
y = 2x - 3
7 = 2(5) - 3
7 = 7
This is true, so (5,7) is on the graph.
d) (-2,-7):
y = 2x - 3
-7 = 2(-2) - 3
-7 = -7
This is true, so (-2,-7) is on the graph.
e) (2,1):
y = 2x - 3
1 = 2(2) - 3
1 = 1
This is true, so (2,1) is on the graph.
f) (4,5):
y = 2x - 3
5 = 2(4) - 3
5 = 5
This is true, so (4,5) is on the graph.
Therefore, the ordered pairs that represent points on the graph of the equation y = 2x - 3 are: (0,-3), (5,7), (-2,-7), (2,1), and (4,5). Answer: b), c), d), e) and f).
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QUICK I’LL MARK YOU BRAINLIEST! Equations with fractions and/ or decimals can be rewritten as ______ _______ without fractions and/ or decimals and then solve in the ________ manner.
We can fill in the blanks as "Equations with fractions and/or decimals can be rewritten as equivalent equations without fractions and/or decimals, and then solve in the usual manner."
How to solve equationsThe process described above is called clearing the equation of fractions and/or decimals. To clear fractions, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators. To clear decimals, you can multiply both sides of the equation by a power of ten that will shift the decimal point to the right until there are no more decimals.
After clearing the equation of fractions and/or decimals, you can simplify and solve the equation using algebraic techniques, such as combining like terms, distributing, and isolating the variable.
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A triangle is 11 in tall and 22 in wide. If it is enlarged to a height of 198 in, then how wide will it be?
Answer: 12 inches
Step-by-step explanation:
If the dilation is uniform, both height and width will be multiplied by 4.
So the new height = (1 in) × 4 = 4 in
and the new width = (3 in) × 4 = 12 in
Hope it helps!
PLEASE HELP ASAP
Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1). Determine the image coordinates of M′ if the preimage is translated 4 units up.
M′(−4, −1)
M′(4, −1)
M′(0, −5)
M′(0, 3)
The image coordinates of M′ are M′(0, 3).
What is translation?
A translation is a geometric transformation when each point in a figure, shape, or space is moved in a specific direction by the same amount. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Here, we have
Given: Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1).
When the shape is moved up by k units, then replace y with y + k.
The translation is as follows:
Here, J(-2, -5) → (-2, -5+4) → J'(-2, -1)
K(-4, 0) → (-4, 0+4) → K'(-4, 4)
L(-1, 2) → (-1, 2+4) → (-1, 6)
M(0, -1) → (0, -1+4) → (0, 3)
Hence, the image coordinates of M′ are M′(0, 3).
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The numbered disks shown are placed in a box and one disk is selected at random. Find the probability of selecting an number, given that a disk is selected.
The probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
How did we arrive at the conclusion above?1. Let's calculate the probability of selecting a blue disk
We can select a blue disk with number 2, 6 or 8 out of a total of 8 disks, it means that the probability of selecting a blue disk is
3/8
2. Let's calculate the probability of selecting the blue disk labeled with number 2:
We can select the blue disk labeled with number 2 out of three blue disks, it means that the probability of selecting the blue disk labeled with number 2 is 1/3
3. These are dependent events because the fact that we select the disk labeled with number 2, depends on selecting a blue disk before, thus:
Probability of selecting a 2 given that a blue disk is selected =
3/8 * 1/3 = 3/24 = 1/8
So we can state that the probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.
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Full Question:
See the attached image.
Write the slope-intercept form of the equation of the line through the given points.
5) through: (4, 2) and (2,-5)
Answer:
[tex]m = \frac{ - 5 - 2}{2 - 4} = \frac{ - 7}{ - 2} = \frac{7}{2} [/tex]
[tex]2 = \frac{7}{2} (4) + b[/tex]
[tex]2 = 14 + b[/tex]
[tex]b = - 12[/tex]
[tex]y = \frac{7}{2} x - 12[/tex]
Use a net to find the surface area of the prism.
A. 469 in.2
B. 315 in.2
C. 539 in.2
D. 784 in.2
The surface area of the triangular prism is 511 in²
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
The surface area of the prism is gotten by summing the individual area of each surface of the prism.
The surface area = (0.5 * 11 in * 7 in) + (0.5 * 11 in * 7 in) + (11 in * 14 in) + (9 in * 14 in) + (8 in * 14 in) = 511 in²
The surface area is 511 in²
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3. What two assumptions must be met when you are using
the z test to test differences between two means? Can the
sample standard deviations s, and so be used in place of
the population standard deviations o, and o₂?
Brainiest please.
During the first couple weeks of a new flu outbreak, the disease spreads according to the equation I(t) = 3900e^0.0514, where I(t) is the number of infected people t days after the outbreak was first identified. Find the rate at which the infected population is growing after 8 days and select the appropriate units.
The rate at which the infected population is growing after 8 days of the outbreak is approximately 1096.57 people per day, as determined by the derivative of the given function with respect to time.
To find the rate at which the infected population is growing after 8 days, we need to take the derivative of the given function I(t) with respect to t:
[tex]dI/dt = 3900(0.0514)e^(0.0514t)[/tex]
At t=8, the rate at which the infected population is growing is:
[tex]dI/dt = 3900(0.0514)e^(0.0514*8) = 1096.57[/tex]
Therefore, the rate at which the infected population is growing after 8 days is approximately 1096.57 people per day.
It is important to note that this rate of growth is an instantaneous rate at t=8, and it will likely change as time passes and the outbreak progresses. Furthermore, the rate of growth of the infected population depends on various factors such as the transmission rate of the virus, the effectiveness of preventive measures, and the availability of healthcare resources.
In conclusion, the rate at which the infected population is growing after 8 days of the outbreak is approximately 1096.57 people per day, as determined by the derivative of the given function with respect to time. This result provides insight into the early stages of a flu outbreak, but further analysis is required to understand the longer-term dynamics of the outbreak and the factors that affect the spread of the disease.
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The lengths of two sides of a triangle are 4 inches and 7 inches. What is a possible length, in inches, of the third side? Select all that apply.
2
3
4
5
6
8
11
Pls tell me the ones that are right! It’s select all that apply
The right answers outoff these options are: 3,5,6,8
Define length?Length is a measure of the size or distance of an object or space in one dimension, usually referring to the longest dimension of an object. It is typically measured in units such as inches, meters, or feet.
What is triangle?In geometry, a triangle is a closed two-dimensional shape that is formed by connecting three non-collinear points with straight line segments. The line segments are called sides, and the points where they meet are called vertices. A triangle has three angles, which are formed by the intersection of its sides.
To determine the possible length of the third side of a triangle, we need to apply the triangle inequality theorem which states that the sum of the lengths of any two sides is always greater than the third side.
Using this theorem, we can see that the possible lengths for the third side are:
- 3 inches
- 5 inches
- 6 inches
- 8 inches
Therefore, the correct answers are:
3,5,6,8.
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Color can be used to highlight parts of a painting, but it cannot work to bring together parts of a painting.
OA. True
OB. False
The statement "color cannot work to bring together parts of a painting" is false. OB. False
what is proportionality ?
The interaction of two variables that changes as a single ratio or proportion is referred to as proportionality.
The use of a cohesive color palette can help to create a sense of unity throughout the painting, tying together disparate elements and creating a harmonious whole. Color can also be used to create visual connections between different parts of the painting, leading the viewer's eye from one area to another and creating a sense of flow and movement within the composition.
So, the statement "color cannot work to bring together parts of a painting" is false.
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Need help will give brainliest and 5 stars! :)
To write the given equation in logarithmic form, we can use the definition of logarithms. The equation 10^m = w can be rewritten as a logarithm with base 10: log10(w) = m
How to write in log formThe general relationship between exponents and logarithms is as follows:
base^(exponent) = result
In logarithmic form, it's written as:
log_base(result) = exponent
For our given equation, 10^m = w, we have:
base = 10
exponent = m
result = w
Applying the general logarithmic relationship, we write:
log10(w) = m
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which of the following points (A, B, C or D) correctly represents 5/2 on the number line?
Answer:
C
Step-by-step explanation:
if we have a number line that has fractions listed, it should be C, because if 6/2 makes 3, which would be D, 5/2 should be C.
whats angle A pls help
Answer:
x = 19.6
Step-by-step explanation:
The sum of the angles of a triangle is 180.
<A + <B+ < C = 180
x + 5x + 4x - 16 = 180
Combine like terms.
10x-16=180
Add 16 to each side.
10x-16+16 = 180+16
10x = 196
Divide each side by 10.
10x/10 = 196/10
x = 19.6
Answer :
Angle A = 19.6°Step-by-step explanation :
According to the question It is given that,
Angle A = x Angle B = 5x Angle C = 4x - 16We will apply angle sum property in the question.
Angle sum property states that sum of all the angles of triangle is 180°
[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180
[tex]\: :\implies [/tex] x + 5x + 4x - 16 = 180
[tex]\: :\implies [/tex] 10x - 16 = 180
[tex]\: :\implies [/tex] 10x = 180 + 16
[tex]\: :\implies [/tex] 10x = 196
[tex]\: :\implies [/tex] x = 196/10
[tex]\: :\implies [/tex] x = 19.6
Therefore, The Measure of Angle A is 19.6°
Evaluate the expression for the given values. If x=−5 and y=29, find y−x2.
Answer:
We have,
y - x^2 = 29 - (-5)^2
= 29 - 25
= 4
Therefore, y - x^2 = 4 when x = -5 and y = 29.
A vegetable has six carrot sticks four celery sticks five tomatoes and three pieces of cauliflower. in how many different orders could we eat all the vegetables?
Answer:
There are 18 total pieces of vegetables, so there are 18 possible choices for the first piece, 17 possible choices for the second piece, 16 possible choices for the third piece, and so on, until there is only 1 possible choice for the last piece. Therefore, the total number of different orders we could eat all the vegetables is:
18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
which simplifies to:
18! / 0! = 6,402,373,705,728
Therefore, there are 6,402,373,705,728 different orders in which we could eat all the vegetables.
Answer:
There are 6,402,373,705,728 different orders in which we could eat all the vegetables.
Step-by-step explanation:
To find the total number of different orders in which we could eat all the vegetables, we can use the formula for permutations of n objects:
[tex]\sf\qquad\dashrightarrow P(n) = n![/tex]
where:
n is the total number of objectsIn this case, we have a total of 18 vegetables (6 carrot sticks + 4 celery sticks + 5 tomatoes + 3 pieces of cauliflower). So we can calculate the permutation of 18 objects:
[tex]\begin{aligned}\sf:\implies P(18)& =\sf 18! \\&=\sf 18 \times 17 \times 16 \times ... \times 3 \times 2 \times 1 \\ &= \boxed{\bold{\:\:6,402,373,705,728\:\:}}\:\:\:\green{\checkmark}\end{aligned}[/tex]
Therefore, there are 6,402,373,705,728 different orders in which we could eat all the vegetables.
Mark Chase and Beatrice are running at 100 m race which list represents the sample space of all the possible ways in which the three runners can win first second and third place is if there were four runners and three positions to be one where else would the sample size be
We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).
Where else would the sample size be?For the 100 m race with Mark Chase and Beatrice, the sample space of all the possible ways in which the three runners can win first, second, and third place is:
{M-C-B, M-B-C, C-M-B, C-B-M, B-M-C, B-C-M}
where M stands for Mark, C stands for Chase, and B stands for Beatrice. We have six possible permutations because there are three choices for the first place, two choices for the second place (as one person has already won first place), and one choice left for the third place.
If there were four runners and three positions to be won, the sample space would be:
{A-B-C-D, A-B-D-C, A-C-B-D, A-C-D-B, A-D-B-C, A-D-C-B, B-A-C-D, B-A-D-C, B-C-A-D, B-C-D-A, B-D-A-C, B-D-C-A, C-A-B-D, C-A-D-B, C-B-A-D, C-B-D-A, C-D-A-B, C-D-B-A, D-A-B-C, D-A-C-B, D-B-A-C, D-B-C-A, D-C-A-B, D-C-B-A}
where A, B, C, and D represent the four runners. We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).
Note that in both cases, we assume that all runners are equally skilled and have an equal chance of winning each position. In reality, there may be differences in skill levels, which would affect the probabilities of each possible outcome.
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Each side of a square classroom is 20 feet long. What is the room's area?
Answer:
Area = length * width
Step-by-step explanation:
If all the sides of the room are equal, all you have to do is 20*20 = area
Can someone solve this?
An equation of the regression line is y = 5.98 + 0.39x.
The data has a pattern that is not a straight line.
How to write the regression equation and determine the correlation coefficient?In this scenario, the x-values (x) would be plotted on the x-axis of the scatter plot while the y-values (y) would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the relationship between the x-values (x) and y-values (y), the linear regression equation and the correlation coefficient are given by:
y = 5.98 + 0.39x
Correlation coefficient, r = 0.6021345002 ≈ 0.60
In conclusion, we can logically deduce that there is a moderate correlation between the data because the correlation coefficient (r) is is greater than 0.4 but less than 0.7;
0.4＜|r| ≤ 0.7 (strong correlation)
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Amy is planning an event for her company where at least 1,640 guests are expected to attend. She is reserving rooms at a large hotel-convention center. Each ballroom (x) can hold 139 people and each conference room (y) can hold 30 people. Select the inequality that Amy could use to determine how many of each type of room she will need to reserve. a. 30x + 139y<1640 b. 30x + 139y>1640 c. 30y + 139x<1640 d. 30y + 139x>1640
The inequality states that the sum of the number of conference rooms and ballrooms should be greater than the number of guests, so that all the guests can be accommodated. The correct answer is d. 30y + 139x>1640.
What is inequality?It is usually written using symbols such as “<”, “>”, “≤”, and “≥”, where one side of the expression is greater than, less than, or equal to the other side.
This is the appropriate inequality to determine how many of each type of room Amy will need to reserve because it expresses the total number of guests (1,640) that must be accounted for in the total number of conference rooms (30y) and ballrooms (139x).
To solve the inequality, Amy can start by assuming the number of conference rooms (y) she will need to reserve.
If she decides to reserve 10 conference rooms, the inequality will become 30(10) + 139x > 1640.
This can be simplified to 1390x > 1640 - 300, which reduces to x > 7.64. This means that Amy will need to reserve at least 8 ballrooms to accommodate all 1,640 guests.
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