Answer:
r.a) (3) = r(a(3)) = r(3) = -2(3)² - 2 = -2(9) - 2 = -18 - 2 = -20
(q-r) (3) = q(3) - r(3) = -3 + 1 - (-18) = -2
So, (r.a) (3) = -20 and (q-r) (3) = -2
Step-by-step explanation:
If the simple interest on $6,000 for 7 years is 2,100, then what is the interest rate?
Answer:
5%
Step-by-step explanation:
First, you do:
$2100/7 = $300
Then you do:
r x 6000 = $300
r = 300/6000 = 0.05
Finally, you do:
0.05 x 100 = 5%
So the interest rate is: 5%
Compute Autin' total ocial ecurity and Medicare taxe for the fourth quarter, if he i elf-employed and earn $5,000. 00 on a emimonthly bai. (For elf-employed peron, ocial ecurity tax i 12. 4% of wage up to $128,400, and Medicare tax i 2. 9% of all wage. )
The total Social Security and Medicare taxes for the fourth quarter would be $728.00 ($600.00 for Social Security and $128.00 for Medicare). This is calculated by multiplying $5,000.00 by 12.4% for Social Security and 2.9% for Medicare.
The total Social Security and Medicare taxes for the fourth quarter would be $728.00. This is calculated by multiplying the total wages for the quarter ($5,000.00) by 12.4%, the Social Security tax rate for self-employed individuals, and then multiplying the same wages by 2.9%, the Medicare tax rate for self-employed individuals. This gives us $600.00 for Social Security taxes and $128.00 for Medicare taxes, for a total of $728.00. The Social Security tax rate is applied up to the wage base of $128,400 for the year.
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How do you find the median of a cumulative frequency graph class 10?.
To find the median of a cumulative frequency graph the median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.
When a set of numbers is arranged in ascending order of magnitude, the middle number is known as the median. A collection of n numbers has a median value of (n+1)/2. N is the cumulative frequency in the case of a cumulative frequency curve.
The median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.
Create the cumulative frequency curve using the numbers provided first. Mark the point with the highest cumulative frequency, then draw a line perpendicular to the Y-axis that precisely passes through it. The lowest cumulative frequency is then marked, and a line is drawn parallel to the X axis. Mark the place where these two lines intersect.
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What is the factor of 9x² 6x 1?.
The factored form of given equation 9x² - 12x + 4 is (3x - 2)(3x - 2).
The given expression is 9x² - 12x + 4
By splitting the middle term, let us factor this polynomial.
To identify the factors we have to consider factors of 36 as (9 × 4)
9x²- 6x - 6x + 4
=3x(3x - 2) - 2(3x - 2)
=(3x - 2)(3x - 2)
Another example of a quadratic polynomial can be taken to demonstrate similar factorization:
x² + 9x + 20
= x² + 5x + 4x + 20
= x × (x + 5) + 4 × (x + 5)
= (x + 5)(x + 4)
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Match a system of equations to each description.
System with one solution: (-1, 3)
System with no solutions
System with infinite number of solutions
2x + 2y = -8 and 3x + 3y = - 12
- 3x + 3y = 12 and 5x + 5y = 10
y +4 =-x and y = -x + 2
Answer:
Image result for System with one solution 1 3 System with no solutions System with infinite number of solutions 2x 2y 8 and 3x 3y 12 3x 3y 12 and 5x 5y 10 y 4 x and y x 2
You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.
Step-by-step explanation:
Answer:
1) 2x + 2y = -8 and 3x + 3y = - 12: Infinite: the lines are the same.
2) - 3x + 3y = 12 and 5x + 5y = 10: One solution (-3.10)
3) y +4 =-x and y = -x + 2: No solutions. Parallel
Step-by-step explanation:
See the attached worksheet. All three explanations are used to identify the three systems of equations. Some of the equations are equal to each other, apparent only when one rearranges the equations.
1.
(04.02 LC)
Which of the following is a common characteristic of a binomial distribution? (4 points)
There are more than two possible outcomes.
The probability of success is the same in all trials.
There are infinitely many observations.
You should perform x trials until you observe a success.
Each trial is dependent on the previous trial.
Answer: The probability of success is the same in all trials.
The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.
What is the independent probability?Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.
You should perform x trials until you observe a success.
We have given that,
There are exactly two possible outcomes success and failure.
We have to determine the following is NOT a common characteristic of a binomial distribution.
By process of elimination:-
A binomial experiment is a statistical experiment that must meet certain requirements
All trials are independent.
There are a fixed number of n trials.
The probability of success, p, is the same for each trial.
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What is the solution to this system of linear equations x − 3y − 2 x 3y 16 7 3 3 7 − 2 − 3 − 3 − 2?.
Solving the system of equations by the method of elimination we get
x = 7 and y = 7/3
Here we are given the system of equations:-
x - 3y = -2 [1]
x + 3y = 16 [2]
Since nothing is mentioned we will use the method of elimination for the question
Subtracting equation [2] rom [1] we get
-6y = -14
or, y = 14/6
or, y = 7/3
Now adding equation [1] and [2] gives us
2x = 14
or, x = 14/2
or, x = 7
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Complete Question
What is the solution to this system of linear equations
x - 3y = -2,
x + 3y = 16
You have a list of 600 random, normally distributed numbers with a mean of 10 and a standard deviation of 2. Which of these statements is true?.
About 285 numbers lie between the values 10 and 14. (option C).
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or a Gaussian distribution. In statistics and the natural and social sciences, normal distributions are crucial concepts.
There are 600 numbers and their mean is 10 where the standard deviation is 2.
47.5% of the numbers should fall between 10 and 14, as expected. In a normal distribution, 47.5% of the sample size will fall between the mean and two standard deviations on either side of it.
By doing calculation on option C, we got that = [tex]\frac{285}{600}*100=47.5[/tex]
Hence, option C is correct, i.e., about 285 numbers would lie between the values 10 and 14.
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How many perfect squares from 1 to 100?.
There are eight perfect squares from 1 to 100 (i.e., except 1 and 100). They are represented as 4, 9, 16, 25, 36, 49, 64 and 81.
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, we can say that a perfect square is a number that can be expressed as the product of an integer by itself or as the second power of an integer. Perfect Square Formula : Let us consider if N is a perfect square of a whole number x, then N can be represent as the product of x and x = x². So, the perfect square formula formula is , N = x². For example, If x = 3, and N = x². This means, N = 3× 3 = 3² = 9 . Here, 9 is a perfect square because it is equal to the square of a whole number, 3. We have to determine the number of perfect squares from 1 to 100.
1² = 1 ; 2² = 4 ; 3² = 9 ; 4² = 16 ; 5² = 25 ; 6² = 36 ; 7² = 49 ; 8² = 64 ; 9² = 81 ; 10² = 100
As we get, there are 10 perfect squares from 1 to 100. But, in actual manner they are only 8 perfect squares from 1 to 100 after excluding 1 and 100.
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A mall box hold 60 hat. A large box hold 180% a many hat a the mall box. How many hat doe the large box hold
From probability of occurence of events the large box holds 180 hats.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows
Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.
The probability is classified into theoretical probability and experimental probability.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Here we have 60 hats in the mall box.
And a large box holds 180% as many hats as the mall box is given.
So, 180/100 ×60 = 180
Therefore, from probability of occurence of events the large box holds 180 hats.
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6. Find m/ADB.
D
A
E
(13x-16) C
B
(9x+4)
The value of Angle ADB, which is the angle created while moving from A to D to B. Angle ABM is the angle created while moving from point A to point B to point M is [tex]41^{0}[/tex]
Finding the value of m∠ADB:Due to the fact that angle ADB is an inscribed angle, its measure is halved compared to the angle of the arc that it intercepts. In other words, the angle is 40 degrees in length, which is equal to half of an 80 degree angle.
By adding up all of your balances at the end of each day for each eligible month, you may get your average daily balances (ADB) by dividing that amount by the number of days in that qualifying month.
3x - 16 = 9x + 4
4x = 20 x = 5 m
with BCE: 9 (5) + 4 = 49°
m with ADB = 41°
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Juliette planted a sunflower that was 18 inches tall. Each week it grows ½ inches. How long will it take the flower to reach a height of 26 inches?
Answer:
Step-by-step explanation:
okay bc the inches is 26 so the answer is 88
bc if u subtract this 26 with this 1 its will. be 25 so add 50 to 25 it will be 88
15/20, 20/21 determine if the ratio are proportional
According to definition of proportional ratios, 15 / 20 is not a multiple of 20 / 21.
How to determine whether that two ratios are proportional
In this problem we find two ratios in fraction form, both are proportional if the numerator and denominator of one of them are multiple of the corresponding elements of the other. First, write the fraction with the lowest numerator:
15 / 20
Second, multiply numerator and denominator by 4 / 3:
[15 · (4 / 3)] / [20 · (4 / 3)]
20 / 26.667
Ratio 15 / 20 is not proportional to ratio 20 / 21.
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Write a conjecture for: the relationhip between the volume of a phere with a radiu that equal to y and the volume of a phere with a radiu equal to 2y
The conjecture for the relationship between the volume of the two spheres is "the volume of a sphere with radius 2y is 8 times greater than the volume of a sphere with radius y."
A conjecture is an educated guess or a hypothesis about a mathematical statement that has not yet been proven. It can be based on patterns or observations and can lead to further exploration and eventually a proof or disproof.
The formula for the volume of a sphere is given by (4/3)πr³, where r is the radius of the sphere. To compare the volumes of two spheres with different radii, we can substitute their respective radii into the formula.
If we let the radius of one sphere be y, then the volume of that sphere can be represented as (4/3)πy³. If we let the radius of the other sphere be 2y, then the volume of that sphere can be represented as (4/3)π(2y)³. Dividing the latter by the former, we get (4/3)π(2y)³ / (4/3)πy³ = (2y)³ / y³ = 8.
Thus, the volume of a sphere with a radius equal to 2y is 8 times greater than the volume of a sphere with a radius equal to y.
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For each transformation in the table below, indicate which properties are true and false by selecting true or false from the drop down menus in each box
Translation, rotation, and reflection are three of the fundamental transformations.
What properties do transformations have?Translation, rotation, and reflection are three of the fundamental transformations.The four main categories of transformations are as follows :Rotation.Translation.Dilation.ReflectionA metamorphosis is a significant alteration in appearance or form. The only change that might provide similarity is dilation.Non-rigid transformations are those that dilate when length and angle measurements are not preserved.Since they maintain length, translation, reflection, and rotation are isometries. Congruency transformations are hence translation, reflection, and rotation.An image that is congruent to the preimage is produced through stiff or isometric transformation.To learn more about transformation refer to:
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*URGENT*
Also have been stuck on this for the past two days
Rounded to the nearest foot, the height of the tree is 31 feet.
What is height?Height is a measurement of distance from the ground to the top of an object, such as a person, animal, or building. It is typically measured in centimeters (cm) or feet and inches. Height is an important measurement for medical professionals, as it can provide insight into a person's overall health and wellbeing.
Using the tangent formula in trigonometry, the height of the tree can be calculated as follows:
tan(angle of elevation) = Opposite/Adjacent
tan(angle of elevation) = 47/h
h = 47/tan(angle of elevation)
Therefore, the height of the tree is h = 47/tan(angle of elevation) = 47/tan(47°) = 47/1.53 = 30.78 feet
Rounded to the nearest foot, the height of the tree is 31 feet.
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Complete Question:
From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is : height of the tree to the nearest foot. The height of the tree is feet. Round your answer to the nearest foot. with explanation. (And photo in question)
Solve the equation 6z2-7z-5=0
Answer:
-1/2, 5/3
Step-by-Step Explanation:
6z^2 - 7z - 5 = 0
=> 6z^2 - 10z + 3z - 5 = 0
=> 2z(3z - 5) + 1(3z - 5) = 0
=> (2z + 1)(3z - 5) = 0
=> z = -1/2, 5/3
Hope it helps.
If you have any query, feel free to ask.
Can sine law be used on a right triangle?.
No, the Sine law cannot be used directly on right triangles.
What is right triangle?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). The angle that measures 90 degrees is formed by two sides of the triangle, called the legs, and the third side, called the hypotenuse, is the side opposite the right angle. The legs of the right triangle are perpendicular to each other, meaning they form a 90 degree angle.
What is law of sines?
The sine law, also known as the "law of sines," is a mathematical relationship that relates the lengths of the sides of a triangle to the sines of its angles. the law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
What is Pythagorean theorem ?
The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, can be used to solve for unknown side lengths in a right triangle. This theorem is particularly useful in trigonometry, geometry and navigation.
A right triangle is a special type of triangle that has one angle that measures exactly 90 degrees (a right angle). Since the sine law relates the lengths of the sides of a triangle to the angles, it can be used to solve for unknown side lengths or angles in a right triangle, as long as the other side lengths and angles are known.
However, it is important to note that the sine law is typically used to solve for unknowns in non-right triangles, where the angle measures are not known. In a right triangle, the Pythagorean theorem can be used instead, which relates the length of the hypotenuse to the lengths of the legs.
So, Sine law cannot be used directly on right triangles, but it can be used in solving triangles which includes right triangles as well.
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The Hall family and the Cox family each used their sprinklers last summer.
The water output rate for the Hall family's sprinkler was 25 L per hour.
The water output rate for the Cox family's sprinkler was 20 L per hour.
The families used their sprinklers for a combined total of 40 hours, resulting in a total water output of 875 L.
How long was each sprinkler used?
The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.
How long was each sprinkler used?The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.
Let h and n represent the amount of hours each household uses its sprinkler, the Halls and the Nguyens, respectively.
They use for a total of 50 hours, thus either h + n = 50 or h = 50 - n.
Additionally, their total water output is 1050 L, thus we may use the equation below.
35h + 15n = 1050
Replace h with h = 50 - n to get
35(50 - n) + 15n = 1050
1750 - 35n + 15n = 1050
35n - 15n = 1750 - 1050
20n = 700
34 hours, n
15 hours equal 50 h, 50 n, and 35 n.
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1/3x + 2y + 5/3x - 4y pls I have a 0 in math I need help with this
Answer:
2x-2y
Step-by-step explanation:
1/3x + 2y + 5/3x - 4y
= 1/3x + 5/3x - 4y + 2y
=6/3 x -2y
=2x-2y
An 8-foot-long board is leaning against a building. The angle formed by the ground and the board is 70 ∘ . How far up the side of the building does the board reach?
The height of the board up the side of the building is 7.5 feet.
How to find the side of a right triangle?An 8-foot-long board is leaning against a building. The angle formed by the ground and the board is 70 degrees.
The height of the board to the side of the building can be calculated as follows:
Therefore, the situation forms a right-angle triangle.
Using trigonometric ratios,
sin 70° = opposite / hypotenuse
sin 70° = x / 8
cross multiply
x = 8 sin 70°
x = 8 × 0.93969262078
x = 7.51754096629
Therefore,
distance of the board up the building = 7.5 feet
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Did Jas graph and find the solution correctly? If not, what was her mistake?
She did not find the correct solution. She graphed the bottom equation of the System incorrectly.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
According to the Problem
y = 3x - 3.....(1)
2x + 2y = 8........(2)
Substitute the value of y from equation 1 to equation 2
2x + 2(3x -3 ) = 8
2x + 6x -6 = 8
8x = 14
x = 1.75
Tus,
y = 3 * 1.75 - 3
y = 2.25
Therefore, she did not find the correct solution to the system of equations.
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I need help I’ll give BRAINLIEST
The team Seahawk has a larger mean value of about 23 inches.
What are mean, median, and mode?The three main methods for identifying the average value of a set of integers are mean, median, and mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.
The middle value in a list that is arranged from smallest to greatest is called the median.
The value that appears the most frequently on the list is the mode.
We know the mean of a data set is [tex]\frac{1}{n}\sum_{i=1}^{n} x_i[/tex].
So, The mean of Pelicans is, [tex]\frac{1}{15}\sum_{i=1}^{n} x_i[/tex].
= (1/15)×[20 + 20 + 22 + 21 + 22 + 23 + 22.5 + 24 + 21.5 + 22 + 23.5 + 22 + 23.5 + 22 + 24.5].
= (1/15)×[333.5].
= 22.23.
The mean of Seahawks is,
= (1/15)[21 + 23.5 + 23.5 + 22.5 + 23 + 21 + 23.5 + 23.5 + 22.5 + 23 + 21 + 23.5 + 23.5 + 22.5 + 23].
= 22.7.
So, Seahawks have a larger value of about 23 inches.
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make x the subject of the relation x/s-1+t/r+1=1
Answer:
s - 1 - t(s - 1)/(r + 1)
Step-by-step explanation:
x/(s - 1) + t/(r + 1) = 1
x/(s - 1) = 1 - t/(r + 1)
x = s - 1 - t(s - 1)/(r + 1)
do you have 8 cups of flour a recipe calls for 2/3 cup of flour of the recipe calls are 1/4 cup of flour how much flour do you have left after making the recipes
Answer: Total cup of flour=8 cups
One recipe calls for cup of flour=2/3
Cup of flour after making one recipe=8-2/3=(24-2)/3=22/3=7.33 cup of flour
Another recipe calls fro cup of flour=1/4
Cup of flour left after another recipe=22/3-1/4=(88-3)/12=85/12=7.08 cup of flour.
Amount of Floor left=7.08
Step-by-step explanation:
I really need help on this!
Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.
What is the product about?In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.
The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.
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For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that used to find a solution for the equation. Be sure to include at least two terms from the word bank. 1/4 x < -3
The inequality equation is x ≤ ( -12 )
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
( 1/4 )x ≤ -3 be equation (1)
On simplifying the equation , we get
x/4 ≤ -3
Multiply by 4 on both sides of the equation , we get
x ≤ ( -3 ) ( 4 )
x ≤ -12
Therefore , the value of x is less than or equal to -12
Hence , the inequality equation is x ≤ -12
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The city of Los Angeles wants to build a suspension bridge over Lake Casitas. The suspension
cables that are connected between the towers must have a parabolic curve. Let the y-axis
represent the axis of symmetry. The road/deck represents the directrix and sits 15 meters
above the water surface (which represents the x-axis). The vertex or minimum point of the
cable is 12 meters above the directrix. Write an equation to represent the parabolic shape of the
cables on the suspension bridge.
anchor
tower
cable
deck
foundations
hanger
approaches
A suspension bridge: a parabola represents the profile of the cable of a suspended-deck suspension bridge.
What is graph ?A graph is a topic which gives us the numerical facts into visual form.
That is, a graph gives the visual representation of the data collected.
The towers supporting the cable of suspension bridge are 15m apart and 12m above the bridge it supports.
Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.
lets have the bridged centered at the origin
Three points are needed on the parabola
x = 0, y = 20
x = -7.5, y = 12
x = +7.5, y = 12
using the form ax^2 + bx + c = y, we know that c=20
x=-7.5, y = 12 and x =+7.5, y = 12; write two equations
-7.5^2a - 7.5b + 20 = 12
+7.5^2a + 7.5 + 20 = 12
use elimination
56.25a - 7.5b + 20 = 12
56.25a + 7.5b + 20 = 12
addition eliminates b
112.5a + 40 = 24
112.5=16
a = 16/112.5
a = 0.1422
Now we can write the equation
y = 0.1422x^2 + 2
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The following table shows the life expectancy for women in the United States for selected years in the period 1975-2000.
Year
1975
1980
1985
1990
1995
2000
Women
76.6
77.4
78.2
78.8
78.9
80.0
Which graph makes the increase in life expectancy from 1975-2000 appear to be relatively small?
a.
A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 74 to 81 in increments of 0.7.
b.
A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 0 to 100 in increments of 10.
c.
A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 76 to 80, in increments of 0.4.
d.
A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 70 to 85 in increments of 0.5.
The graph that makes the increase in life expectancy from 1975-2000 appear to be relatively small is given by the following option:
b. A graph titled Life Expectancy of Women has Years after 1975 on the x-axis, from 0 to 25, and life expectancy (years) on the y-axis, from 0 to 100 in increments of 10.
What is the graph that makes the increase appear relatively small?The total increase is given as follows:
80 - 76.6 = 3.4 years.
Hence the higher the difference between the bounds of y, the smaller the difference will appear, meaning that the graph is given by option b.
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lution set.
-y-8<-3 ory+5>19
The solution set of the expression is y > -5
How to determine the solution set of the expression?From the question, we have the following parameters that can be used in our computation:
-y-8<-3 ory+5>19
Express the inequality properly
So, we have the following expression
-y - 8 < -3 or y + 5 > 19
Collect the like terms
This gives
-y < 8 - 3 or y > 19 - 5
Evaluate the like terms
This gives
-y < 5 or y > 14
Rewrite as
y > -5 or y > 14
When combined, we have:
y > -5
Hence, the solution set is y > -5
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Complete question
For the following inequality expression, determine the solution set
-y-8<-3 ory+5>19
