Answer:
−1≤x<3
Step-by-step explanation:
−4≤3x−1<8
−4≤3x−1and3x−1<8
3x−1≥−4and3x−1+1<8+1
3x≥−3and3x<9
x≥−1andx<3
−1≤x<3
Which of these equations describe a line that is parallel to the y-axis, and passes through (-2.3) A. y=-2x+3 B. Y=3 C. X= -2 D. x=3
The y-axis it's a vertical line, so is represented by x=0.
Then, a parallel line to this one has to be vertical too, and if it passes thorugh (-2, 3). The equation of the parallel line would be x=-2.
Let me explain with a graph:
The bottom row of the pile has 25 apples and the top row has 9. Each row has 4 less apples than the row below. How many apples are in the pile?
There are 90 apples in the pile and the row has 4 fewer apples than the row below.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The sum of an arithmetic sequence is the sum of the first n terms of the sequence as
Sₙ = n/2(2a+(n−1)d)
In arithmetic, here a₁ is the first term and sequence d represents the common difference.
Sum of the apples = 25 + 21 + 17 + 14 + 13 + 9
This series is in AP where a = 25 , d = - 4 and n = 6
As per the given data, the sum of apples would be as:
S₆ = 6/2(2×25+(6-1)×-4)
S₆ = 3(50 + 5×-4)
S₆ = 3(50 - 20)
S₆ = 3(30)
S₆ = 90
Therefore, there are 90 apples in the pile.
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pls help me solve this with steps
The solution of the given inequality for the value of x, x ≥ 1/2.
Define inequality.In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. Both mathematical phrases, equations, and inequalities are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >,<,≥,≤,≠ or indicate that the two expressions in inequality are not always equal.
Given Data
Equation
[tex]\frac{4x -7}{2}[/tex] ≥ 4.5
4x - 7 ≥ 9
4x≥2
x ≥ [tex]\frac{1}{2}[/tex]
For the value of x, x ≥ [tex]\frac{1}{2}[/tex]
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What is the answer
Three friends ate at a restaurant. They ordered nachos for $18.85 and jalapeno poppers. Each friend paid $9.98, not including sales tax or tip, which was one third of the total. Determine the cost of the jalapeno poppers.
The cost of the jalapeno poppers is $11.09 .
In the question ,
it is given that
Cost of the nachos = $18.85
amount paid by each friend = $9.98
amount paid by three friends = 9.98*3 = $29.94
let the cost of jalapeno poppers = $x
So according to the question
the total amount paid by three friends = cost of nachos + cost of jalapeno poppers
Substituting the values from above , in the equation we get
29.94 = 18.85 + x
simplifying further , we get
x = 29.94 - 18.85
x = 11.09
Therefore , the cost of the jalapeno poppers is $11.09 .
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A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 10 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 6 insects will die? Round your answer to four decimal places.
The required probability that exactly 6 insects will die is 60%.
Given that,
A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 10 insects is exposed to the insecticide in a particular experiment. The probability that exactly 6 insects will die is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
Total number of sample spaces = 10
Total number of favorable outcomes = 6
probability can be given as,
= 6 / 10
= 0.6 or 60%
Thus, the required probability that exactly 6 insects will die is 60%.
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Pat and Terry believe the color yellow attracts hummingbirds. They decided to test their hypothesis by doing an experiment in which they set up four hummingbird feeders with the same amount of food and placed them in locations only hummingbirds could reach. One feeder was yellow, one was red, one was blue, and one was clear. Each day for one week, Pat and Terry measured and recorded the amount of food left in each of the feeders. At the end of the experiment the red feeder had the least amount of food left in it. What conclusion should Pat and Terry reach?
Step-by-step explanation:
red feeder is smarter
Under her cell phone plan, Zendaya pays a flat cost of $42 per month and $4 per gigabyte. She wants to keep her bill under $50 per month. Write and solve an inequality which can be used to determine x, the number of gigabytes Zendaya can use while staying within her budget.
Answer: 4x + 42 < 50
Step-by-step explanation: $42 is the flat price so that is our constant; $4 per gigabyte is our variable. If she wants to keep her bill UNDER $50 dollars a month you would put a less than symbol.
Answer:
Step-by-step explanation:
i did the work and i got 4x + 42 < 50
Consider the equation 3x3 + 14x2 – 14x + 60 = 0. The real solution is –6. What are the nonreal solutions?
Negative 2 i StartRoot 26 EndRoot, 2 i StartRoot 26 EndRoot.
4 minus 2 i StartRoot 26 EndRoot, 4 + 2 i StartRoot 26 EndRoot.
StartFraction negative 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction negative 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
StartFraction 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
Using the polynomial expression, the non-real solutions are x = (2 + i√26)/3 and x = (2 - i√26)/3
What are polynomial expressions?Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x^3 + 14x^2 - 14x + 60 = 0
From the question, we have
Real solution = -6
Rewrite the above equation as
x = -6
Add 6 to both sides of the equation
So, we have
x + 6 = 0
The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0
This is represented as
3x^3 + 14x^2 - 14x + 60/x + 6
Using a graphing calculator, we have
3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10
Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3
So, we have
x = (4 ± √-104)/6
This gives
x = (4 ± 2√-26)/6
Divide
x = (2 ± √-26)/3
Rewrite as
x = (2 ± i√26)/3
Split
x = (2 + i√26)/3 and x = (2 - i√26)/3
Hence, the non-real solutions of the polynomial expression are x = (2 + i√26)/3 and x = (2 - i√26)/3
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Use the given information to answer the question. The distance s that an object falls varies directly with the square of the time, t , of the fall. If an object falls 16 feet in one second, how long will it take for it to fall 48 feet? Round your answer to two decimal places.
The time that it will take for it to fall 48 feet will be ✓3 seconds.
How to illustrate the information?From the information, the distance s that an object falls varies directly with the square of the time, t , of the fall and an object falls 16 feet in one second.
This will be:
s = kt²
s = distance
k = constant
t = time
s = kt²
16 = 1²k
k = 16
Therefore, the time that it will take for it to fall 48 feet will be:
s = kt²
48 = 16t²
t² = 48 / 16
t² = 3
t = ✓3
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The sample space S= [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]
Given A = [E1, E3, E6, E9], define Ȃ
Given A = [E1, E3, E7, E9] and B = [E2. E3, E, E9]
a) What is A intersection B?
b) What is the union of A & B?
c) Is the union of A & B collectively exhaustive?
A) The intersection of subsets A and B is; A ∩ B = {E3, E7, E9}
B) The union of subsets A and B is; A ∪ B = {E1, E2, E3, E7, E9}
C) No, the union of A & B is not collectively exhaustive
What is the Union and Intersection of the Sets?
We are given;
Sample space;
S = [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]
A = [E1, E3, E7, E9]
B = [E2. E3, E, E9]
A) Now, the intersection of subsets A and B would be the values that are common to both sets. This gives us;
A ∩ B = {E3, E7, E9}
B) The union of the subsets A and B with be the combination of all terms in both subsets and this gives us;
A ∪ B = {E1, E2, E3, E7, E9}
C) The union of A & B is not collectively exhaustive because it does not contain all the data available in the sample space.
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13. The table shows the number of each type of seed packet a
garden center had remaining at the end of summer. Bags were
created with 20 random seed packets in each bag. How many
complete bags of seeds can be created?
Seed Type
Aster
Daisy
Pansy
Sunflower
Wildflower
Number of Packets
95
160
70
Answer:24 bags
Step-by-step explanation:
Using the given information, the number of bags created with random seed packets is 16 complete bags of seeds and a remainder of 5 seed packets
How to find the number of bagsThe number of bags created achieved by division. This is a basic mathematical operator used in sharing items
Given information
Seed Type Number of Packets
Aster 95
Daisy 160
Pansy 70
Sunflower -
Wildflower -
Adding the number of packets available gives
95 + 160 + 70 = 325 seed packets
Sharing them in a bag containing 20 seed packets each we divider the total number of seed packets by 20
= 325 seed packets / 20
= 16.25
Therefore 16 bags will be created and 5 will be remaining
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What is the first 3 pairs of opposite integers
The first 3 pair of opposite integers are (-1,1),(-2,2) and (-3,3).
Given that,
We have to find the first 3 pairs of opposite integers.
Opposite integers means the "counting numbers" (sometimes known as integers), as well as zero, are integers. The pairs of integers known as opposite integers share the same absolute value, or, to put it another way, are equally spaced from zero. The numbers 10 and -10 are the opposites. The numbers 43 and -43 are the opposites.
So,
Keep in mind that our whole numbers are our integers. The negative and positive iterations of a number together are called a pair of opposite integers.
We get, the first 3 pair of opposite integers are (-1,1),(-2,2) and (-3,3).
Therefore, the first 3 pair of opposite integers are (-1,1),(-2,2) and (-3,3).
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Ms jones has a rain barrel shaped like a cylinder in her backyard the barrel is 42in high and it has a diameter of 30 which answer is closet to the number of cubic inches of rain that the barrel can hold
A 30,000
B 120,000
C 100,000
D 40,000
The answer closest to the number of cubic inches of rain that the barrel can hold is 30,000. Option A
How to determine the valueIt is important to note that the formula for determining the volume of a cylinder is expressed as;
Volume = πr²h
Where;
The value of pi = 3. 14r is the radius of the cylinderh is the height of the cylinderAlso note that the formula for diameter is given as;
Diameter = 2 radius
Now, substitute the value of diameter
30 = 2r
Make 'r' the subject of formula
r = 15in
Substitute the values into the formula
Volume = 3. 14(15)²(42)
expand the bracket
Volume = 29, 673 cubic inches
Volume = 30, 000 cubic inches
Hence, the value is 30, 000 cubic inches
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Graph the inequality
Pls and thank you not urgent
To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation.
Which four steps are involved in graphing an inequality? Steps1:Always begin by separating the variable y from the inequality's left side.Step 2: Replace the inequality symbol with the equality symbol.Step 3: In the X, Y, XY, XY plane, graph the boundary line from Step 4 :The final step is to shade a portion or one side of the border line.Uneven relationships between two expressions are demonstrated by inequalities. Here are a few instances of inequality: 9 > 7 9 > 7 9 > 7. 6 a + 2 6 underlined a+2 6 < a+2. x < 5 x<5 x<5.To represent an inequality on a number line, such as x>3, first draw a circle around the number (e.g., 3). Fill in the circle if the sign also says equal to (or ). Leave the circle blank if the sign doesn't include equal to (> or ).To more learn about graphing an inequality refers to :
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During training, an athlete ran 250 m/min. By then on the day of a race, he increased his average speed to 300 m/min and finish the race on minute faster than he had during training. What distance was the race
If he increased his average speed to 300 m/min and finish the race on minute faster than he had during training. The distance of the race is: 1500 meters.
DistanceSlower speed :
rate = 250 m/min
time = x minutes
distance = r×t = 250x meters
Faster speed :
rate = 300 m/min
time = x - 1 minutes
distance = 300x - 300 meters
Equate
distance = distance
250x = 300x - 300
Collect like terms
50x = 300
Divide both side by 50x
x = 300/50
x = 6 minutes
Hence,
Race distance = 250x where x =6
Race distance = 250×6
Race distance= 1500 meters
Therefore we can conclude that the distance is 1500 meters.
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Rational Numbers - Part 1
Which statements about the opposite of -12 are true?
Select each correct answer.
The opposite of the opposite of -12 is -12.
0-12 and its opposite are on located on the same side of zero on a number line.
The opposite of -12 is -1/2
0-12 and its opposite are located the same distance from zero on a number line
The correct statement for the rational number is the opposite of the opposite of -12 is -12.
What is rational number?
Rational numbers are those numbers which include natural numbers, whole numbers as well as integers. And it is written in the form of a/b where a and b are integers. Sometimes, the values of the denominator is one then the given number is not fraction.
According to the question, rational number are those numbers which takes positive integers, negative integers as well as zero.
Therefore, on a number line, the opposite of (-12) is 12. And again the opposite of 12 is (-12). Therefore the first statement is correct.
Hence, the correct statement for the rational number is the opposite of the opposite of -12 is -12.
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Manuel's younger brother Ricky loves hot
wheels. Ricky has 28 boxes of toy cars. Each
box holds 16 cars. Ricky gives his brother
Manuel 15 cars. How many cars does Ricky
have now?
Answer:
29
Step-by-step explanation:
Add 28 + 16=44
Subtract 44 - 15=29
Determine if the relation is a function. { ( − 2 , 4 ) , ( − 1 , 7 ) , ( 0 , − 6 ) , ( 5 , 3 ) , ( 7 , 5 ) } {(−2,4),(−1,7),(0,−6),(5,3),(7,5)} Determine if the relation is a function. { ( − 2 , 4 ) , ( − 1 , 7 ) , ( 0 , − 6 ) , ( 5 , 3 ) , ( 7 , 5 ) } {(−2,4),(−1,7),(0,−6),(5,3),(7,5)} The relation is not a function. The relation is a function
Based on the given ordered pairs, yes, the relation is a function.
What is a function?A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable to an output variable.
Based on the ordered pairs shown above, we can reasonably infer and logically deduce that these ordered pairs represent a function because the elements of the set of "x" are uniquely mapped to the elements of the set of "y" as shown below:
x y__
-2 ↔ 4
-1 ↔ 7
0 ↔ -6
5 ↔ 3
7 ↔ 5
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A local restaurant ordered 81 cans of tomato paste. Each can contains 18 ounces of paste. Write an
equation using compatible numbers to estimate the total number of ounces of paste ordered.
OA. 81 x 18 = 1,458
OB. 80 x 20 = 1,600
OC. 85 x 20 = 1,700
OD. 100 x 20 = 2,000
Answer:
It would be A because they ordered 81 cans and in each can there 18 ounces so if you multiply it you can get the Total amount.
You and a group of friends participate in a game where you must use clues to escape from a room. You have a limited amount of time to escape and are allowed 3 free clues. Additional clues may be requested, but each removes 5 minutes from your remaining time. Whatinteger represents the total change in the time when you use 5 clues?
Integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.
As given in the question,
Number of free clues =3
Total number of clues used to escape from a room = 5clues
Out of these 5 clues, 3 clues are free to use. Hence these 3 clues do not result in any time change.
Hence total time elapsed after usage of 3 clues = 0
Each removes 5 minutes from your remaining time
Integer represents the total change in the time for the usage of 4th and 5th clue = 10 minutes
So overall change in timeline after consuming 5 clues = 10 minutes since each of the 4th and 5th clue results in decrease of 5 minutes each; thus effecting 10 minutes total time change (reduction)
Therefore, integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.
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please help me graph
Answer:
A
Step-by-step explanation:
See that the slope of the parabola changes at x=4
And left of x=4, the slope is positive, meaning the value is increasing (you can also see it directly from the graph)
Right of x=4, the slope is negative, meaning the value of the graph is decreasing. Thus the answer is A
3. It takes a Ferris wheel 1.5 minutes to complete one full rotation. If a ride lasts for 6 minutes, how many full rotations does the Ferris wheel make? O O T= 9 rotations T= = 4 rotations O Or = 7.5 rotations T = 4.5 rotations
Answer:
Four.
Step-by-step explanation:
6 divided by 1.5 is 4. We do that because if it takes 1.5 mins to make a full rotation and it takes 6 minutes to do blank rotations, the answer is 4 bc we either ti.es 1.5 by 4 to get 6, or do 6 divided by 1.5 to get 4. Sorry if that was confusing.
show work for 758 x 93
The product of the numbers 758 and 93 is 70494
How to determine the product of the numbers?The numbers are given as
758 x 93
By using the standard algorithm i.e. the partial product method, we have the following equation
758 x 93 = 758 x (90 + 3)
Open the bracket
So, we have the following equation
758 x 93 = 758 x 90 + 758 x 3
Evaluate the products
758 x 93 = 68220 + 2274
Next, we evaluate the sum
758 x 93 = 70494
This means that the final product is 70494
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The function g is defined by the following rule.
g(x) = (1/2)x
Find g(x) for each x-value in the table.
-1
0
1
2
3
Answer:
g(-1)=2, g(0)=1, g(1)=1/2, g(2)=1/4, g(3)=1/8
Step-by-step explanation:
On Tuesday Jill bought eight posters. On
Wednesday half of all the posters that she
had were destroyed. On Thursday there
were only 22 left. How many did she
have on Monday? Write an equation using
"p" for posters. Then solve the equation
and check your answer.
The number of posters Jill had on Monday are 18.
The equation is p + 8 - 4 = 22.
Given that:-
Number of posters bought by Jill on Tuesday = 8
Number of posters left on Thursday = 22
We can write,
Number of posters destroyed on Wednesday = (1/2)*8 = 4
Let the number of posters Jill had on Monday be p.
Hence, the equation for the posters is given by:-
Posters on Monday + Posters bought on Tuesday - Posters destroyed on Wednesday = Total posters on Thursday
It can be written as:-
p + 8 - 4 = 22
Solving the equation, we get
p + 4 = 22
p = 22 - 4
p = 18
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PLEASE ANSWER QUICKLY WILL GIVE BRAINLIEST IF RIGHT
Answer:
Domain:
{−4,1,6,7}
Range:
{5,3,8,−4}
Step-by-step explanation:
When Bob runs at 4 miles an hour, it takes him 20 minutes to run the path around the
park. If he ran instead at 5 miles an hour, how long would it take him to run that path
around the park?
Time taken to cover path around the park if he runs at speed 5miles/hour is 15.96min
What is Speed ?
Speed indicates how quickly something or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance x time.
Given that,
Time taken when Bob runs 4miles/hour = 20min
Time taken when Bob runs 5miles/hour = ?
First we have to find the distance of the path around the circle
Distance = speed x time
= 4 x 20/60
= 4/3 miles
= 1.33 miles
Now to calculate the time when he ran 5 miles/hours:
Time = distance / speed
= 1.33 / 5
= 0.266hours
0r
= 0.266 x 60 min
= 15.96 min
Hence, its will take 15.96min to cover the path around the park
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Help
Albie is comparing the ratio of students in her class that are wearing the color green to the total number of students in her class. She finds out of 30 students in her class, 7 are wearing green. What kind of ratio relationship is she using?:
A: Part-to-part relationship
B: Whole relationship
C: Part-to-whole relationship
D: Part relationship
Answer:
C
Step-by-step explanation:
Beacuse part to whole means describing a specific part of a group to the whole group, in our case students wearing green : students
Which of the following is equivalent to sin 37°?Group of answer choicescos 37°cos 53°sin 53°sin 63°
Recall that:
[tex]sin\theta=cos(90^{\circ}-\theta).[/tex]Therefore:
[tex]sin37^{\circ}=cos(90^{\circ}-37^{\circ}).[/tex]Simplifying the above result, we get:
[tex]sin37^{\circ}=cos53^{\circ}.[/tex]Answer: [tex]\begin{equation*} cos53^{\circ}. \end{equation*}[/tex]The net of a rectangular prism with a square base is shown. Use the net to find the surface area of the prism. PLEASE HELP!!!
Answer:
B
Step-by-step explanation:
the surface area is the sum of all individual side areas.
a prism (like a cube that is a special prism) has 6 sides.
top-bottom
left-right
front-back
in our case top and bottom are 5×5 squares.
and the other 4 sides are equal 5×20 rectangles.
so, we get
top-bottom : 2× 5×5 = 50 cm²
left-right : 2× 20×5 = 200 cm²
front-back : 2× 20×5 = 200 cm²
in total we have
200 + 200 + 50 = 450 cm²