The smallest possible number of students in the algebra class is 13.
What is meant by the word inequality?Inequalities define the connection between two non-equal values. Inequality means being unequal. If two values really aren't equal, we use the "not equal symbol (≠)".Let n≥5 be the number of students.
The sum of their scores must be at least 5×100 + (n - 5).
Simultaneously, we must achieve the mean 76, which is equivalent to achieving the mean sum 76n.
As a result, we have a sufficient precondition on n: we should have 5×100 + (n - 5) ≤ 76n.
This can be reduced to 200 ≤ 16n. This is true for the smallest integer n = 13.
To complete our solution, we must now determine how 13 students might have scored just on test.
We have 13×76 = 988 points to distribute to them. Because five 100s equal 500, we must distribute the remaining 488 points as among remaining eight students.
This can be accomplished, for example, by awarding each of them 61 points.
Thus, the smallest possible number of students in the class is 13.
To know more about the inequality, here
https://brainly.com/question/25799000
#SPJ4
PLEASE HELP I LITERALLY HAVE 10 MINUTES!! 40 POINTSSS
The graph that matches the data on the table, representing the altitude and time of a hawk is the straight line graph in the second option.
What is a straight line graph?A straight line graph is the graph of a linear function or relationship
From the he values in the given, we have;
The difference between the consecutive altitude values (the first difference) = 70 - 80 = 60 - 70 = 50 - 60 = -10 is constant
The difference between consecutive time values = 1
Therefore;
The relationship is a linear relationship and the graph is a straight line.
Slope of the graph = -10/1 = -10
The equation in point and slope form is therefore;
(y - 80) = (-10) × (x - 1) = -10•x + 10
(y - 80) = -10•x + 10
y = 80 + 10 - 10•x = 90 - 10•x
y = 90 - 10•x
The y–intercept = 90
The slope = -10
The correct option is therefore the second graph that has the altitude (ft) on the the vertical axis and the time (s) on the horizontal axis, with a straight line decreasing from left to right starting at the point (0, 90) on the left
Learn more about the equation of a straight line graph here:
https://brainly.com/question/16934180
#SPJ1
a triangle with a base of 6cm has an area of 30cm squared. What is its perpendicular height?
The area of a triangle is 1/2bh. We know the area, a, the base, b, and we are attempting to find the height, h. So, we simplify the area formula with the value of b and solve for h, given a.
1/2(6)h = 30
3h = 30
Isolate h.
3h/3 = 30/3
h = 10
The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator. PLEASE HELP ASAP
Answer:
[tex]2\sqrt{2}[/tex]
Step-by-step explanation:
x^2+x^2=16
x^2=8
x= 2sqrt2
:]
I l over here and I have no idea
the table show the total cost to be a member of the gym for different numbers of months.number of months. total costs3. $53.976. $77.9412. $125.88create a function that gives the total cost C,in dollars to be a member of the gym given the number of months M of member ship.
The table shows the total cost to be a member of the gym for different numbers of months.
Number of months. total costs
3. $53.97
6. $77.94
12. $125.88
Create a function that gives the total cost C, in dollars to be a member of the gym given the number of months M of membership.
_____________________________________
Total cost = M* (factor per month ) + b
_____________________________________
The expression for a linear equation is
*The slope-intercept form.
y = mx + b
m= (y2-y1)/ (x2-x1) (I)
y-intercept is (0, b)
*and the point-slope form
y- y1 = m(x-x1) (II)
________________________
Point 1 (3, 53.97)
Point 2 (12, 125.88)
Replacing in (II)
The slope m = (y2- y1)/ (x2-x1) = (125.88- 53.97)/(12-3) = 7.99
y - 53.97 = 7.99* (x- 3)
y = 7.99 x - 7.99* 3 + 53.97
y = 7.99x + 30
____________________
Verifying
y = 7.99x + 30
x= 3
y = 7.99*3 + 30
y= 53.97
x= 6
y = 7.99*6 + 30
y= 77.94
x= 12
y = 7.99*12 + 30
y= 125.88
_________________________
Answer
The linear function is y = 7.99x + 30
Alex is fourteen years old and he is also nine years older than his sister Kristen. How old is Kristen?
Answer:
5
Step-by-step explanation:
If Alex is 14 and he's 9 years older than his sister Kristen,then Kristen is 5
14-9=5
Answer:
14-9 = 5, so Kristen is 5 years old
Juniper has a monthly budget that breaks down as follows 40% for rent 15% for food 18% free utilities 15% for savings for person for entertainment and 8% for personal items juniper has a net income of 3,250 each month calculate the amount of money that juniper has each month for rent
Juniper spends $1300 out of the monthly income of $3250 on rent
Total income of Juniper = 3250 each month
Income is the money that an individual or organization receives in return for their services or goods. Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.
Percentage of expenditure on rent = 40%
Percentage of expenditure on food = 15%
Percentage of expenditure on utilities = 18%
The percentage for savings = 15%
Percentage of expenditure for personal items = 8%
Money Juniper spends on rent each month out of total income:
= Income per month*40%
3250*40%
= $1300
Learn more about percentages:
https://brainly.com/question/24159063
#SPJ9
Please help. See picture attached.
The trapezoid's area can be understood as triangle a + triangle b. So, we write these triangles as an expression, and, since we cannot solve with no values, we simplify to prove the area of the trapezoid.
A triangle's area is 1/2bh. In their case, b is represented as b or a depending on the triangle.
t = 1/2ah + 1/2bh
Now, since both expressions use the terms 1/2 and h, distributed onto a second variable, it can be rewritten as a single expression where both are distributed onto both variables at the same time. This is because both terms being multiplied by something separately is the same as combining both terms and multiplying them both at the same time.
t = 1/2(a)h + 1/2(b)h
t = 1/2(a + b)h
7. A crate of soft drinks contains 9 bottles of coke, 6 bottles of pepsi and 4 bottles of limca. Ademola picks one bottle of soft drink and thereafter Adedeji picks another bottle. Find the probability that: (a) They both. picked limca (b) Ademola only picked pepsi (c) They both picked the same brand (d) They picked different brands.
The probability that the events (a) they both picked Limca = 0.04, (b) Ademola only picked Pepsi = 0.32, (c) They both picked the same brand = 0.33 (d) They picked different brand=0.67.
What is probability?Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.
Total possible outcome of the event of picking drinks contained in the crate = 19
Hence, we can compute the following as follows;
(a) The probability they both picked Limca = (4/19)×(3/18)
Limca = 12/342
Limca = 0.04
(b) The probability Ademola only picked pepsi = 6/19
pepsi = 0.32
(c) The probability they both picked the same brand = (9/19)×(8/18)+(6/19)×(5/18)+(4/19)×(3/18)
=(72+29+12)/342
= 114/342
= 0.33
(d) The probability they picked different brand = (9/19)×(6/18)+(9/19)×(4/18)+(6/19)×(9/18)+(6/19)×(4/18)+(4/19)×(9/18)+(4/19)×(6/18)
The probability they picked different brand = (54+36+54+24+36+24)/342
The probability they picked different brand = 228/332
The probability they picked different brand = 0.67
Therefore, the probability for events (a) is 0.04, (b) is 0.32, (c) is 0.33 and (d) is 0.67.
Know more about probability here: https://brainly.com/question/24830485
#SPJ1
solve. 2-6: MathXL for School: Practice & Problem Solving (Grade 8 Pre-Algebra)
The area of the rectangle is [tex]b^2[/tex] +9b square feet
The rectangle is the quadrilateral whose opposite sides are parallel and equal. The rectangle is a four sided shape that all the angles are 90 degrees
The area is defined as the total space occupied by the two dimensional shape like rectangle, triangle, circle etc..
The length of the rectangle = (5/3)b+15 feet
The width of the rectangle = (3/5)b feet
The area of the rectangle = The length of the rectangle × The width of the rectangle
Substitute the values in the equation
The area of the rectangle = [(5/3)b+15] ×(3/5)b
Apply the distributive property in the equation
[(5/3)b+15] ×(3/5)b = [tex]b^2[/tex] +9b square feet
Hence, the area of the rectangle is [tex]b^2[/tex] +9b square feet
Learn more about area of the rectangle here
brainly.com/question/20693059
#SPJ1
Elena received a $25 gift card to a fun center. She drives a race car which costs $4.75. She also wants to use the gift card to play video games. Each game costs $0.75 which of these inequalities describe this situation, where n is the number of games Elena wants to play.
A. 4.75 + 0.75. ≤ 25
B. 4.75 + 0.75. ≥ 25
C. 4.75 - 0.75. ≥ 25
D. 4.75 - 0.75. ≤ 25
Answer: B - 4.75 + 0.75 is greater than 25
Step-by-step explanation:
so, first you have 4.75 and she want to play video games that cost 0.75 each but we don't know how many video games she played.
so, n = how many video games played4.75 + 0.75n =? which is greater than 25divide 4.75 + 0.75n 0.75 0.75after dividing you will get 4,100 + 1n = which equals 4.101 is greater than 25Samuel was preparing for the triathlon. He did 3 activities every morning: ran for 30 minutes, covering 4.5 miles swam for 20 minutes, covering 2 3 mi biked for 45 minutes, covering 9 miles What was Samuel's average speed during his morning training?
Samuel's average speed during his morning training is 0.41 miles/minute.
Here we have to find the average speed of Samuel. We can solve this problem by following a few steps.
According to the problem, Samuel was preparing for the triathlon. He did 3 activities every morning; ran for 30 minutes, covered 4.5 miles; swam for 20 minutes, covered 2.3 miles biked for 45 minutes, and covered 9 miles.
We have to recall the formula of average speed as,
average speed = total covered distance/ total time
The total distance which has been covered is,
4.5 miles by running,2.3 miles by swimming,9 miles by biking.The total covered distance is, ( 4.5 + 2.3 + 9 ) = 36.5 miles.
The total time which has been spent is,
30 minutes for running,20 minutes for swimming,45 minutes for biking.The total spent time is, (30+ 20+ 40) = 90 minutes.
Now, we can easily calculate the average speed. Which is (36.5/90) = .41 miles/minute.
To know more about the average speed visit,
https://brainly.com/question/28123159?referrer=searchResults
#SPJ9
How many solutions does this equation have?
–4k − 13 = 19 − 8k + 20
Answer: k = 13
Step-by-step explanation:
Jennie drew a scale drawing of her family's game room. The pool table is 4 feet wide in real life. Using a scale of 1 inch: 2 feet, how wide is the pool table in her drawing?
Please answer ASAP.
(Will give brainliest)
When Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches
The width of the pool table in real life = 4 feet
The scale of width in drawing to real life = 1 inch : 2 feet
Therefore the equivalent ratio is
1 inch : 2 feet :: x inches : 4 feet
1 / 2 = x / 4
x = (1/2) × 4
= 2 inches
Hence, when Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches
Learn more about ratio here
brainly.com/question/13419413
#SPJ1
Write (9m) to the power of 4 without exponents.
6561m⁴ is the value of the expression (9m)⁴ without applying the exponent property.
What is an exponent?
The type of mathematical shorthand known as exponential notation enables us to write complex expressions more concisely. The base, which can be either a number or letter, is an exponent. It implies that the base is to be raised to a specific level of power. While n is the power, X is the base.
The expression is (9m)⁴.
The value of the expression (9m)⁴ without applying the property of the exponent will be
→ 9m × 9m × 9m × 9m
(we've simply expanded (9m)⁴ )
which on further simplifying gives,
→ 6561m⁴
to learn more about exponents visit:
https://brainly.com/question/5497425
#SPJ9
(02.05 MC)
Given f(x) and g(x) = f(kx), use the graph to determine the value of k.
-3
-1/3
1/3
3
Using the graph obtained value of k is 1/3. Option C is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that
f(x) and g(x) = f(k-x),
The standard equation of a line is,
y = mx + b
The slope of the line for the coordinate points are (1, 2) and (1.5, 5)
m = 5-2/1.5-1
m = 3/0.5
m = 6
The y-intercept of the line is,
2 = 6(1) + b
2 - 6 = b
b = -4
As a result the obtained equation is g(x) = 6x - 4
For the other coordinate point (3, 2) and (2, 0), the slope is
m = 0-2/2-3
m = -2/-1
m = 2
The y-intercept of the line is,
2 = 2(3) + b
2 - 6 = b
b = -4
As a result the obtained equation will be f(x) = 2x - 4.
Substitute xk at the place of x in the function as
f(xk) = 2(xk)- 4
If g(x) to f(k⋅x)
6x + 4 = 2(xk)- 4
6x = 2xk
6 = 2k
k = 1/3
Thus, using the graph obtained value of k is 1/3. Option C is correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
6. What is the constant of proportionality of the linear function?
Time, x 12 3 4
Cost ($), y 25 50 75 100
F. 2 G. 12 H. 25 I. 50
Pls help!!
The table has a constant of proportionality of 25
How to determine what is the constant of proportionality?The table represents the given parameter
On the table, we have the following points
(x, y) = (1, 25)
The constant of proportionality of the points is then calculated as
k = y/x
Substitute the known values in the above equation
So, we have
k = 25/1
Evaluate the quotient
So, we have
k = 25
Hence, the constant of proportionality of the table is 25
Read more about constant of proportionality at
brainly.com/question/28413384
#SPJ1
A ring is now reduced to £840.
This is a saving of 40% of the original price.
b) Work out the original price of the ring.
Answer:
The original price was $864
Step-by-step explanation:
if the ring is now $840 $40 u do $40 - %40 = %24
$24 + $840 = $864
I messed up and didn’t show this for my last question, so sorry on my part.
Evaluate the function for the following values
f(-2)=
f(0)=
f(3)=
Answer:
1 , 7 , 7
Step-by-step explanation:
to evaluate f(- 2) means what is the value of y when x = - 2
locate x = - 2 on the x- axis , go vertically up to meet the graph at (- 2, 1)
f(- 2) = 1
similarly
f(0)
locate x = 0 , at the origin, go vertically up to meet the graph at (0, 7 )
f(0) = 7
f(3)
locate x = 3 on the x- axis , go vertically up to meet the graph at (3, 7 )
f(3) = 7
the number of messages that arrive at a web site is a possion distirbuted random variable with a mean of 5 messages per hour. round your asnwers to four decimal places. what is the probaiblity taht 5 messages are received in 1 hour
17.54% is the probability that 5 messages are received in 1 hour.
The chance that X reflects the number of successes of a random variable in a Poisson distribution is provided by the following formula:
P(X = x) = ([tex]e^{-u}[/tex] × [tex]u^{x}[/tex]) ÷ x!
In where x is the number of successes, e is the Euler number, and u is the mean in the specified time frame.
In this case, the average message rate is 5 messages per hour.
The probability of receiving 5 texts in one hour.
Determine the value of P for x = 5 and u = 6.
P(X = x) = ([tex]e^{-5}[/tex] × [tex](5)^{5}[/tex]) ÷ 5!
P(X = x) = 21.0560 ÷ 5!
P(X = x) = 0.1754
There is a 17.54% chance that 5 messages will be received in 1 hour.
Learn more about the probability at
https://brainly.com/question/13416734?referrer=searchResults
#SPJ4
About 30% of people age 50 to 60 suffer from mild depression. A researcher is interested in determining if a vitamin d supplement will increase or decrease the proportion of people that have mild depression. The researcher randomly selects 500 people between the ages of 50 and 60 and ask them to take a vitamin d supplement for 6 months. At the end of the six months, the participants are asked to complete a survey. A psychologist then classifies each participant as either depressed or not. The psychologist classifies 158 people as depressed. Is the proportion of people that are classified as depressed different from 0. 30? what is the null and alternative hypothesis?.
The null and alternative hypothesis is H₀ : p = 0.30 and Hₐ : p ≠ 0.30 respectively.
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis.
Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance.
One of the ideas put out in the hypothesis test is the alternate hypothesis.
Mild depression affects about 30% of adults in the 50 to 60 age range.
500 people between the ages of 50 and 60 are chosen at random by the researcher, and they are instructed to take a vitamin D pill for six months.
The psychologist classifies 158 people as depressed.
The null hypothesis will be:
H₀ : p = 0.30 and;
The alternative hypothesis is,
Hₐ : p ≠ 0.30
Learn more about hypothesis here:
brainly.com/question/606806
#SPJ4
PLEASE HELP ME THANK YOU
The area of half circle is 14.13 sq.unit
The total area of the figure is 86.13 sq.unit
Given,
The figure is combined by a triangle, rectangle and a half circle.
The area of triangle = 18 sq.units
The area of rectangle = 54 sq.units
We have to find the area of half circle to get the total area of the figure;
Here,
Area of circle = π r²
Then,
Area of half circle = π r² / 2
Here,
r = 6/2 = 3 units
Now,
Area = π r² / 2 = π × 3² / 2 = 28.27/2 = 14.13 sq.units
That is,
The area of half circle is 14.13 sq.unit
Then,
The total area of figure = Area of [triangle + rectangle + half circle]
The total area of figure = 18 + 54 + 14.13 = 86.13 sq.units
Therefore,
The total area of the figure is 86.13 sq.unit
Learn more about area of half circle here;
https://brainly.com/question/16734739
#SPJ1
12. Triangle ABC has vertices A(-4, 0), B(-4, 5) and C(1, 5) along line AC. Which are the
coordinates of another slope triangle along the same line?
A. D(-2,-2), E(-2, 1) F(-1,0)
B₁6
B. D(-3, 0), E(-3, 1) F(-2, 1)
C. D(-5, -1), E(-5, 0) F(-4, -1)
D. D(-6, -2), E(-6, -1) F(-5, -1)
Please help will mark brainliest
Considering the given triangle ABC that has vertices A(-4, 0), B(-4, 5) and C(1, 5). The option that has same slope with similar interval is B. D(-3, 0), E(-3, 1) F(-2, 1)
What is slope?Slope refers to the gradient and is the ratio of the difference in the ordinate to the difference in the abscissa of in a given coordinate plane.
How to calculate slopeThe given information from the question include
A(-4, 0), B(-4, 5) and C(1, 5)
The slope of the given triangle is calculated as follows
slope = ( 0 - 5 ) / ( -4 - 1 )
slope = -5 / -5
slope = 1
The domain of the line is -4 ≤ x ≤ 1
The range of the line is 0 ≤ y ≤ 5
options C and D values do not satisfy the domain and range conditions
Options B and A satisfies the the domain and range conditions however the slope of option B is what is equal to the slope of the sloping part of the given triangle and hence the correct option.
Learn more on slope of line: https://brainly.com/question/24820338
#SPJ1
which of these expressions are equal to 3/5×6?Explain why the others aren't equal to this expression.3×(6÷5)3÷(5×6)(3×6)÷53×6/5
Answer:
(3×6)÷5
Step-by-step explanation:
We are given the following expression:
(3/5)*6
The 6 can also be written as a fraction(6/1).
So we have a multiplication of fractions, is which we multiply the numerators and denominators.
So
(3*6)/5
The fraction sign means division
So the answer is:
(3×6)÷5
Orlando makes a trail mix for his hiking trip. He uses 1 \frac{5}{6}1 6 5 pounds of cashews, 1.6 pounds of sunflower seeds, 1 \frac{1}{8}1 8 1 pounds of raisins, and 1.625 pounds of pecans. Which answer choice shows these weights in order from least to greatest ? DUE TODAY NEED NOW WILL GIVE BRAINLIEST PART OF TEST REALLY NEED
An answer choice shows these weights in order from least to greatest is:
1 1/8 pounds of raisins.1.6 pounds of sunflower seeds.1.625 pounds of pecans.1 5/6 pounds of cashews.What is a numerical data?A numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.
In order to arrange the given numerical data (weights) in order from least to greatest, we would convert the fractions into a decimal number as follows:
1 5/6 pounds of cashews = 11/6 = 1.8333 pounds.1.6 pounds of sunflower seeds = 1.6 pounds.1 1/8 pounds of raisins = 9/8 = 1.125 pounds.1.625 pounds of pecans = 1.625 pounds.Now, we can arrange the numerical data in order from least to greatest based on the weight of each item:
1.125 pounds = 1 1/8 pounds of raisins.1.6 pounds = 1.6 pounds of sunflower seeds.1.625 pounds = 1.625 pounds of pecans.1.8333 pounds = 1 5/6 pounds of cashews.Read more on greatest numbers here: brainly.com/question/24654699
#SPJ1
Find x 109° x 31° 35°
No need to help anymore. I figured out the answer.
The value of x is 43.
As per the property of exterior angles, the exterior angle is equal to sum of opposite interior angles. Also, the rightmost interior angle of triangle will be 35°. This will be according to the property that opposite angles are equal. Now, forming the equation for sum of exterior angles.
109 = x + 31 + 35
Performing addition on Right Hand Side of the equation
109 = x + 66
Rearranging the equation
x = 109 - 66
Performing subtraction on Right Hand Side of the equation
x = 43
Therefore, as per the angles of triangle, the value of x is 43.
Learn more about triangle -
https://brainly.com/question/17335144
#SPJ1
Answer the questions below to find the total surface area of the can..
The total surface area of the cylinder is equal to 117.8 in^2
Total Surface Area of Cylinder
The total surface area of a cylinder can be calculated using the formula
[tex]TSA = 2\pi rh + 2\pi r^2[/tex]
h = height of cylinderr = radius of cylinderLet's substitute the values and proceed to solve.
[tex]TSA = 2\pi rh + 2\pi r^2\\TSA = 2\pi * 2.5 * 5 + 2\pi * 2.5^2\\TSA = 117.8in^2[/tex]
The total surface area of the cylinder is 117.8 squared inch.
The area of each circle is
[tex]A = \pi r^2 \\A = 19.6in^2[/tex]
And there are two identical circle in the diagram and this will have a total area of
[tex]A = 2 * 19.6\\A = 39.2in^2[/tex]
The area of the sum of the two circles is 39.2in^2 and the total surface area of the cylinder is 117.8in^2
Learn more on total surface area here;
https://brainly.com/question/22982196
#SPJ1
Antonio draws a spuare that has 13 centimeters what the perimeter of his spuare
Answer:
52 centimeters
Step-by-step explanation:
A square has 4 sides
Side of square = 13 cm
Perimeter of square = sum of all sides of square
Perimeter of square = 4 x 13 = 52 cm
ANSWER FAST I WILL GIVE BRAINLIEST
Which graph represents the solution to one seventhm ≤ −1 over 22? number line with closed circle on point negative 14 over 11 and arrow shaded to the right number line with closed circle on point negative 7 over 22 and arrow shaded to the right number line with closed circle on point negative 14 over 11 and arrow shaded to the left number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Answer: arrow shaded to the left number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Step-by-step explanation:
Answer:
for easier explanation.... it's D
Step-by-step explanation:
Don’t ignore help pls I think i know it but I’m not sure
Answer:
The y intercept is 0
Step-by-step explanation:
Where the line crosses the y axis that is your y intercept
Check the picture below.
Name a pair or vertical angles.
Answer:
There are two pairs:
1 and 3
2 and 4
Step-by-step explanation:
Verticle angles are angles opposite to each other when two lines intersect.