Answer: More than 40 students
Step-by-step explanation:
Let x be the number of students .
Given : Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student.
i.e. Total cost : [tex]80+5x[/tex] (1)
The Dino Discovery Museum simply charges $7 per student.
i.e. Total cost : [tex]7x[/tex] (2)
The inequality that shows Science Center charge less than the Dino Discovery Museum charges will be :-
[tex]80+5x<7x[/tex]
Subtract 5x on both sides , we get
[tex]80<2x[/tex]
Divide both sides by 2 , we get
[tex]40<x[/tex]
Hence, for more than 40 students the Science Center charge will less than the Dino Discovery Museum charges.
What is the area of the rectangle?
60 units²
66 units²
70 units²
74 units²
Which should be the first step in solving the equation 1.2 w -3.8= 12.4
1. Add 3.8 to both sides of the equation.
2. Subtract 1.2 from both sides of the equation.
3. Multiply both sides of the equation by 1.2.
4. Divide both sides of the equation by 3.8.
Answer:
Option 1 - Add 3.8 to both sides of the equation.
Step-by-step explanation:
Given : Equation [tex]1.2w-3.8=12.4[/tex]
To find : Which should be the first step in solving the equation?
Solution :
Equation [tex]1.2w-3.8=12.4[/tex]
Step 1 - Adding 3.8 both side,
[tex]1.2w-3.8+3.8=12.4+3.8[/tex]
[tex]1.2w= 16.2[/tex]
Step 2 - Divide 1.2 both side,
[tex]\frac{1.2w}{1.2}=\frac{16.2}{1.2}[/tex]
[tex]w=13.5[/tex]
Therefore, The first step in solving the equation is 'Add 3.8 to both sides of the equation.'
So, Option 1 is correct.
Dawn Lingua bought three yards of cloth to make some curtains. The cloth was on sale for $2.25 per yard. How much did Dawn pay for the cloth if the sales tax was 5%?
Answer:
Dawn paid $7.09.
Step-by-step explanation:
Dawn Lingua bought cloth to make curtains = 3 yards
Cost of the cloth = $2.25 per yard
Cost of 3 yard cloth = $2.25 × 3 = $6.75
Sales tax was = 5%
Sales tax on the total cost = 5% of 6.75
= (5/100) × 6.75 = 0.05 × 6.75 = $0.3375
Now we add sales tax to the total cost
= 6.75 + 0.3375 = $7.0875 rounded to $7.09
Dawn paid for the cloth with sales tax was $7.09
Ingrid is making a quilt using squares that measure 5in on each side. What is the length of a diagonal of one of the quilt squares?
Answer:
8.7 Maybe.
Step-by-step explanation:
Sort the sequences to whether they are arithmetic, geometric, or neither
1) 98.3 , 94.1 , 89.9 , 85.7
2) 1 ,0 , -1 ,0
3) 1.75 , 3.5 , 7 ,14
4) -1 ,1 , -1 ,1
5) -12, -10.8, -9.6, -8.4
her answer is right but you just have to switch 4 and 5 around 4 is geometric while 5 is arithmetic
Final Answer:
Each sequence is tested for a common difference or ratio to determine if it is arithmetic or geometric. The sequences 98.3, 94.1, 89.9, 85.7 and -12, -10.8, -9.6, -8.4 are arithmetic, 1.75, 3.5, 7, 14 is geometric, and 1, 0, -1, 0 as well as -1, 1, -1, 1 are neither.
Explanation:
To determine if a sequence is arithmetic, geometric, or neither, we look for a common difference or ratio between consecutive terms.
For the sequence 98.3, 94.1, 89.9, 85.7, we subtract consecutive terms: 94.1 - 98.3 = -4.2, 89.9 - 94.1 = -4.2, 85.7 - 89.9 = -4.2. The common difference is -4.2, so this sequence is arithmetic.The sequence 1, 0, -1, 0 does not have a common difference or ratio, so it is neither arithmetic nor geometric.For 1.75, 3.5, 7, 14, the ratios are 3.5/1.75 = 2, 7/3.5 = 2, and 14/7 = 2. The common ratio is 2, so this sequence is geometric.The sequence -1, 1, -1, 1 alternates signs without a common difference or ratio, so it is neither.For the sequence -12, -10.8, -9.6, -8.4, the difference is -10.8 - (-12) = 1.2, -9.6 - (-10.8) = 1.2, -8.4 - (-9.6) = 1.2. The common difference is 1.2, making it an arithmetic sequence.Mateo is draining a pool at a rate of 1/8 of a gallon every 1/2 hour. If he continues to drain the pool , how much waters will be drained in 1 hour?
Jacob held different part-time jobs during his summer holiday. The table below shows the total money he earned for different amounts of time, in hours: Hours Worked 1 2 3 4 5 6 7 8 9 Money Earned (dollars) 4 8 12 16 20 24 28 32 36 What type of association will the scatter plot for this data represent between the number of hours worked and the total money earned?
The type of association scatter plot for this data represents the number of hours worked and the total money earned is a positive correlation.
How to find the type of association that represent the data?The number of hours and the amount of money increases at an even rate, 4 dollars for each hour.
The given table;
Hours Worked 1 2 3 4 5 6 7 8 9
Money Earned (dollars) 4 8 12 16 20 24 28 32 36
We can see here as the number of hours increases the amount of money is increasing, so it indicates that there is a positive association.
Also, there is an unequal change in equal intervals of time, so it represents a positive nonlinear association.
Hence, the graph is a line, y=4x,
The type of association scatter plot for this data represents the number of hours worked and the total money earned is a positive correlation.
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What is the answer to 3n-5=7n+11 with work shown
Ms. Frazier chooses two students to come to the board from a class of 12 boys and 8 girls. What is the probability that she will select a girl student first and a boy student second?
The probability that Ms. Frazier selects a girl first and a boy second from her class is 24/95, calculated by multiplying the probability of selecting a girl (8/20) by the probability of selecting a boy thereafter (12/19).
Explanation:To calculate the probability that Ms. Frazier will select a girl student first and a boy student second from her class of 12 boys and 8 girls, we need to use the concept of conditional probability because the selection of the second student depends on the first.
The total number of students is 12 boys + 8 girls = 20 students. The probability of selecting a girl first is the number of girls divided by the total number of students, which is 8/20. Once a girl is selected, there are now 19 students left. The probability of selecting a boy next is the number of boys left (which is still 12) divided by the new total, which is 12/19. The joint probability of both events happening in succession (selecting a girl then a boy) is found by multiplying the probabilities of the two individual events.
So, the probability of selecting a girl first and a boy second is (8/20) × (12/19) = 96/380. This simplifies to 24/95 when we divide both numerator and denominator by 4.
Therefore, Ms. Frazier has a probability of 24/95 to choose a girl first and a boy student second.
The probability of selecting a girl student first and a boy student second is approximately 0.2526.
Explanation:To find the probability of selecting a girl student first and a boy student second, we need to calculate the probability of each event separately and then multiply them together.
Step 1: Probability of selecting a girl student first
Number of girls: 8Total number of students: 12 boys + 8 girls = 20Probability of selecting a girl student first = Number of girl students / Total number of students = 8/20 = 0.4Step 2: Probability of selecting a boy student second
Number of boy students: 12Total number of students after selecting a girl student: 20 - 1 = 19Probability of selecting a boy student second = Number of boy students / Total number of students after selecting a girl student = 12/19 ≈ 0.6316Step 3: Multiply the probabilities from Step 1 and Step 2:
Probability of selecting a girl student first and a boy student second = Probability of selecting a girl student first × Probability of selecting a boy student second = 0.4 × 0.6316 ≈ 0.2526Greg, marcia, peter, jan, bobby and cindy go to a movie and sit next to each other in 6 adjacent seats in the front row of the theater. if marcia and jan will not sit next to each other, in how many ways different arrangements can the 6 people sit?
What is a correct congruence statement for the triangles shown?
Suppose △AYH≅△ZRL.
What is the corresponding congruent part for each segment or angle?
ZR¯¯¯¯¯
RL¯¯¯¯¯
∠L
∠Z
ah_____ yh___ ay__
if x is 50 then what is x4+44+3.5
A translation of directed line segment from the origin to (0,-3) followed by a reflection around the line y=x
To translate a directed line segment from the origin to (0,-3), simply subtract 3 from the y-coordinate. To reflect a point across the line y=x, swap the x and y coordinates. The reflected point of (0,-3) would be (-3,0).
Explanation:To translate a directed line segment from the origin to (0,-3), we can simply subtract 3 from the y-coordinate. The new coordinate would be (0,-3).
To reflect a point across the line y=x, we swap the x and y coordinates. So the reflected point of (0,-3) would be (-3,0).
2x-1
Evaluate the algebraic expressions for the given values of the variable
Ann and betty shared the sum of money in the ratio 2:3, if ann received $60 less than betty, what was the total sum of money shared
simplify ( 1/2A + 1/2B )^2
joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries, 1/2 pound of grapes, 1 3/4 pounds of oranges, and 1 1/4 pounds of pears. How many pounds of fruit Joanna bought in all?
A coin is weighted so that the probability of obtaining a head in a single toss is 0.3. if the coin is tossed 35 times, what is the probability of obtaining between 9 and 14 heads, exclusive.
The probability of obtaining between 9 and 14 heads , exclusive is 0.510
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the probability of obtaining a head in a single toss be p = 0.3
Let the number of times the coin is tossed be n = 35
Now , the mean and the standard deviation is calculated by
Mean M = np
Substituting the values of n and p , we get
Mean M = 0.3 x 35
Mean M = 10.5
Now , the standard deviation S = √M ( 1- p )
Substituting the values in the equation , we get
Standard Deviation S = √10.5 ( 1 - 0.3 )
Standard Deviation S = √10.5 x 0.7
Standard Deviation S = 2.71
Now , the probability of obtaining between 9 and 14 heads , exclusive is represented as P ( 9 < x < 14 ) = P ( 8.5 < x < 14.5 )
And , the z - scores of 8.5 and 14.5 are
z ( 8.5 ) = ( x - M ) / S
= ( 8.5 - 10.5 ) / 2.71
= -0.3688
z ( 14.5 ) = ( x - M ) / S
= ( 14.5 - 10.5 ) / 2.71
= 1.1066
So , the probability of obtaining between 9 and 14 heads , exclusive is represented as P ( 9 < x < 14 ) = P ( -0.3688 < x < 1.1066 )
So , the equation can be written as
P ( 9 < x < 14 ) = P ( z < 1.1066 ) - P ( z < -0.3688 )
Using z-scores of probabilities, we have:
P ( 9 < x < 14 ) = 0.86577 - 0.3561
P ( 9 < x < 14 ) = 0.50967
P ( 9 < x < 14 ) = 0.510
Therefore , the value of P ( 9 < x < 14 ) is 0.510
Hence,
The probability of obtaining between 9 and 14 heads , exclusive is 0.510
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The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.
According to bmi, a woman who is 5 feet 6 inches tall and weighs 175 pounds is considered to be
A woman who is 5 feet 6 inches tall and weighs 175 pounds has a BMI of 28.2 and would be classified as overweight.
The Body Mass Index (BMI) is a tool commonly used to assess whether a person has a healthy weight relative to their height. To calculate BMI, you divide a person's weight in pounds by their height in inches squared and multiply by 703.
For a woman who is 5 feet 6 inches tall and weighs 175 pounds:
Height: 66 inchesWeight: 175 poundsThe calculation for BMI would be:
BMI = (175 / (66×66)) × 703
BMI = 28.2
According to the BMI weight status categories:
BMI between 25 and 29.9 is considered overweight, and a BMI of 30 or higher is considered obese.
Therefore, a woman who is 5 feet 6 inches tall and weighs 175 pounds would be classified as overweight.
Sand dollars are animals that live buried in the sand of shallow coastal waters. The thin circular body of a sand dollar is usually 2 to 4 inches wide. Find the area of a sand dollar that is 3 inches wide.
Answer:
The area of a sand dollar that is 3 inches wide is [tex]7.0686 inch^2[/tex]
Step-by-step explanation:
Width of sand dollar's circular body = d = 3 inches
Radius of the sand dollar's circular body = r
[tex]r=\frac{d}{2} = \frac{3 inch}{2}=1.5 inches[/tex]
Area of circle = [tex]\pi r^2[/tex]
So, the area of a sand dollar that is 3 inches wide:
[tex]A=3.14\times (1.5 inch)^2=7.0686 inch^2[/tex]
The area of a sand dollar that is 3 inches wide is [tex]7.0686 inch^2[/tex]
Suzanne works 25 hours a week for four weeks at $9.50 per hour. how much does she earn at the end of four weeks?
At the movie theatre, child admission is $5.10 and adult admission is $9.00 . On Monday, 163 tickets were sold for a total sales of $1088.70 . How many adult tickets were sold that day?
a = adult tickets
c = child
c + a = 163 tickets total
rewrite as c = 163-a
5.10c + 9.00a = 1088.70
5.10(163-a) + 9.00a = 1088.70
831.30-5.10a + 9.00a = 1088.70
831.30 +3.9a = 1088.70
3.9a = 1088.70-831.30
3.9a = 257.40
a = 257.40 / 3.9 = 66
66 adult tickets were sold
ROUND 4,719,429 TO THE NEAREST 10,000
A figure drawn in the coordinate plane has the coordinates J(‒1,5), K(6,5), L(9,1) and M(2,1).
1) Use what you have learned in this unit to prove that the figure is either a parallelogram, rectangle, square or a rhombus.
2) Use what you have learned in this lesson to find the area and perimeter of the figure.
whats the bisector of an obtuse angle forms
acute angles
right angles
obtuse angles
straight angles
Answer:
A.Acute angle
Step-by-step explanation:
We are given that an obtuse angle
We have to find that which type of angle of bisector of an obtuse angle.
Bisector of an obtuse angle means it is divided into two equal parts.
Obtuse angle is that angle whose measurement is greater than 90 degrees and less than 180 degrees.
Suppose, we have an obtuse angle =100 degrees
After bisection , it divides into two equal parts
Let x and x are two equal parts of given obtuse angle
[tex]x+x=100[/tex]
[tex]2x=100[/tex]
[tex]x=\frac{100}{2}=50[/tex]
Each angle measurement=50 degrees < 90 degrees
The angle which is less than 90 degrees and greater than zero degrees is called acute angle.
Hence, the bisector of an obtuse angle forms acute angles.
Answer:A.Acute angle
A1 Plumbing Service charges $35 per hour plus a $25 travel charge for a service call. Good Guys Plumbing Repair charges $40 per hour for a service call with no travel charge. How many hours must a service call be for it to be better for you to call A1 Plumbing Service?
A1 = 35x+25
Good guys = 40x
35x+25 = 40x
subtract 3x x from each side
25 = 5x
divide each side by 5
x = 25/5 = 5
so 5 hours they would be the same cost, anything over 5 hours and A1 would be better
so X>5 for A1 to be the better price
Can you guys please help me with math? (Pt 2.)
(I've attached the picture)
Elian is placing a rectangle in the coordinate plane. He knows that the shorter side of the rectangle is half the length of the longer side. He places the longer side on the x-axis.
What coordinates should he assign to the top-left vertex of the rectangle?
Enter your answer in the boxes.
Let
x--------> the length side of the rectangle
y-------> the width side of a rectangle
we know that
[tex]y=\frac{1}{2}x[/tex] ------> equation A
[tex]x=2a\ units[/tex] ---------> given problem (see the graph)
substitute the value of x in the equation A
[tex]y=\frac{1}{2}2a=a\ units[/tex]
therefore
the answer is
the top-left vertex of the rectangle is the point [tex](0,a)[/tex]
Solve for x. x−14=38 Enter your simplified answer in the box.
Answer:
52
Step-by-step explanation:
How to order decimals from least to greatest with different decimals places?