The number of students in the class after the changes here are 35.
What are ratios?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
The question tells us that 7 more juniors have joined this class, while 2 seniors have dropped the class. Then the ratio would be 5 : 2 from the question.
This would give us the ratios as
[tex]\frac{3x+7}{2x-2} = \frac{5}{2}[/tex]From here we would have to cross multiply
2(3x + 7) = 5(2x - 2)
6x + 14 = 10x - 10
6x - 10x = -10 - 14
- 4x = -24
x = 6
Put the value of x in both equations
3x + 7 = 3 x 6 + 7
= 25
2x - 2 = 2 x 6 - 2 = 10
25 + 10 = 35
The number of students that are in the class is given as 25
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Find the slope between the points
below. Simplify your answer.
(-10, 5) and (14,-3)
Slope between the points (-10, 5) and (14,-3) is -1/3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We need to find slope between points (-10, 5) and (14,-3)
m=-3-5/14+10
m=-8/24
m=-1/3
Hence, slope between the points (-10, 5) and (14,-3) is -1/3.
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6) There are 11 marbles in a bag. Two are yellow, five are pink and four are green. Suppose you pull out one
marble, record its color, put it back in the bag and then pull out another marble. Find the probability that
when selecting 3 marbles, you have selected a yellow first, green second and pink last.
The probability is 0.1.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.acc to our question-
total marbles= 11yellow marbles=2pink marbles=5green marbles=30.01 + 0.04 + 0.05Hence,The probability is 0.1.
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a group of 1,000 randomly selected adults is classified into 4 smoking groups: nonsmoker, light smoker, moderate smoker, and heavy smoker. at the end of a ten-year period, the proportion in each group who developed lung cancer was determined. the null hypothesis is that all 4 groups will have the same incidence rate of lung cancer. the p-value is found to be smaller than the level of significance (i.e. smaller than .05). what is the most appropriate conclusion?
The null hypothesis is rejected thus there is a significant difference in the incidence of lung cancer in all four groups.
When the p-value is less than 0.05, the null hypothesis that there is no difference between the means is rejected, and we come to the conclusion that there is a significant difference. The existence of a significant difference cannot be inferred if the p-value is higher than 0.05.
The null hypothesis in the given scenario was that all four groups will have the same incidence rate of lung cancer which is rejected.
An assertion that there is no correlation between two population measures is referred to as a null hypothesis. To prepare the ground for additional experimentation or study that explains the position of interest, researchers reject or refute the null hypothesis.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, -6) and (-8, 2)
The distance between the two points is 8.25 units
What is meant by the distance between two points?The distance between two points in a plane is the length of the line segment separating the two locations. Typically, the equation d=((x2 - x1)2 + (y2 - y1)2) is used to calculate the distance between two locations. You may use this formula to get the separation between any two points on an x-y plane or coordinate plane.
The following is the formula for the separation between two points:
d= √(x₁-x₂)²+(y₁-y₂)²
Points (x1, Y1) and (x2, Y2)
As given in the question, the points are (-6, -6) and (-8, 2)
The distance between the two points is,
d= √(-6+8)²+(-6-2)²
d=√4+64
d=√68 units= 8.25 units
Therefore, the distance between the two points is 8.25 units
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Please help me I WILL GIVE BRAINLY IF CORRECT!!<3 Question 2(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions LC)
Rewrite 30 - 6x³ using a common factor.
O2(15-3x³)
O 2x(15-3x²)
O6(5-6x³)
O6x(5-x²)
By factorizing algebraic expression 30 - [tex]6x^3[/tex] using a common factor, the result will be option (A) 2(15 - [tex]3x^3[/tex])
The expression is given,
30 - [tex]6x^3[/tex]
The expression is the mathematical sentence that consist of different types of variables, numbers and the mathematical operators. The mathematical operators will be addition, subtraction, division and multiplication. The expression does not contains a equal sign or inequality signs
The expression is given,
30 - [tex]6x^3[/tex]
Take a common term outside
Here the common term is 2
30 - [tex]6x^3[/tex] = 2((30/2) - [tex]6x^3[/tex] /2)
= 2(15 - [tex]3x^3[/tex])
Hence, by factorizing algebraic expression 30 - [tex]6x^3[/tex] using a common factor, the result will be option (A) 2(15 - [tex]3x^3[/tex])
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EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the slope intercept form of the equation of the line through the given point with the given slope
through (-1, 0) slope = -4
Answer:
y=-4x-4
Step-by-step explanation:
we know the slope so put it in the slope intercept form
y=-4x
Now fill it in to find y intercept with the coordinates
0=-4(-1)
0=4
We need to subtract 4 to make this equation true so the y intercept is -4
The equation will become
y=-4x-4
Hopes this helps please mark brainliest
What is at least one social issue associated with food deserts?
Answer:
Food desert census tracts typically have fewer populations than all other census tracts, a higher percentage of unoccupied or abandoned dwellings, and residents who are less likely to have a college degree, make less money, or be employed.
What is the slope of the line that passes through the points (-4,6) and (-4,18 Write your answer in the simplest form.
What is the slope of the line passing through the points A(−2,5) and B(1,10)
Answer:
Slope is equal to the change in y y over the change in x x, or rise over run. m = change in y change in x m = change in y change in x. The change in x x is equal to the difference in x-coordinates (also called run ), and the change in y y is equal to the difference in y-coordinates (also called rise ). m = y2 −y1 x2 −x1 m = y 2 - y 1 x 2 - x 1.
PLEASE HELP!
Find the y-intercept of the line on the graph.
Enter the correct answer.
008
Clear all
7
DONE
Answer: y intercept is -1
Step-by-step explanation:
23X-17 = 15X+7 give me the solution
Answer: x=3
Step-by-step explanation:
Simplify equation to get 8x=24. Divide 24 by 8 to get x=3. Please give brainliest :D
Answer:
Step-by-step explanation:
23X - 17 = 15X + 7First add 17 to both sides to isolate the variable (usually the one with the bigger coefficient is best)
23X = 15X + 24subtract 15x from both sides to combine 23X and 15X terms
8X = 24Divide by 8 to solve
X = 3Write a polynomial f (x) that satisfies the given conditions.
Degree 3 polynomial with integer coefficients with zeros 7i and 9/5
If the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]
The zeros of the polynomial = 7i and 9/5
Here the degree of polynomial is 3, therefore there will be three zeros in polynomial, here only 2 zeros are given. We have to find the third zero of the polynomial.
Here one of the polynomial is complex number, therefore another zero will be the conjugate of the complex zero
Therefore the equation will be
(x+7i)(x-7i)(5x-9) = 0
We have to solve the equation
([tex]x^2[/tex] -7ix+7ix+49)(5x-9) = 0
([tex]x^2[/tex] + 49)(5x - 9) = 0
[tex]5x^3-9x^2+245x-441 =0[/tex]
Therefore
f(x) = [tex]5x^3-9x^2+245x-441[/tex]
Hence, if the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]
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An uber charge a flat rate of $20 plu $2 per mile. Lyft charge a flat rate of $15 plu $4 per mile. Write an equation to find the number of mile m for which uber and lyft would cot the ame amount
The required equation is 20 + 2m = 15 + 4m. The number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.
Uber charges a flat rate of $20 plus $2 per mile. Lyft charges a flat rate of $15 plus $4 per mile. We need to find out the equation and the number of miles for which Uber and Lyft would charge the same amount for the ride.
Let the charge of Uber and Lyft be represented by the variables C1 and C2. We can write the equations given below.
C1 = 20 + 2m
C2 = 15 + 4m
We need the charge for both companies to be equal.
C1 = C2
20 + 2m = 15 + 4m
Hence, the required equation is 20 + 2m = 15 + 4m. Now we will solve this equation to find the number of miles.
2m = 5
m = 2.5
Hence, the number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.
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pythagorean theorem digital escape puzzle 2 HELPPPP
Answer:
EGFB
Step-by-step explanation:
PQ= (105)^2 + (208)^2
PQ=233
Area = b*h
Area = 21840
RS = (210)^2 + (120)^2
RS = 241.87
Area = 1/2bh
Area = 1/2 (210)(120)
Area = 12600
Dan spends
3
4
of his wages on rent and
1
8
on food. If he makes £240 per week, how much money does he have left?
The money left with Dan is £30 .
In the question ,
it is given that
the amount of money earned by Dan in a week is = £240 .
amount of money spent by Dan on rent is = 3/4 wage
amount of money spent by Dan on food is = 1/8 of wage
So ,
the total amount spent = amount spent on food + amount spent on rent
Substituting the values ,
we get ,
= 3/4 + 1/8 = 7/8 of his wage = (7/8)*240
= 210
so , total amount spent is £210 .
Amount left = amount earned - amount spent
= 240 - 210
= 30
Therefore ,The money left with Dan is £30 .
The given question is incomplete , the complete question is
Dan spends 3/4 of his wages on rent and 1/8 on food. If he makes £240 per week, how much money does he have left?
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snoopy brown is interested in the number of businesses that do not allow dogs in st. paul, mn. to conduct his study, he randomly selects 100 businesses listed in the st. paul phone book, calls them and asks their policy. what is the sample of this study?
The sample of study is 100 business.
Define sample.An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values. A sample is that precise value. The probability distribution of the random variable determines the possible values and the likelihood of each. A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.
Given,
Snoopy brown is interested in the number of businesses that do not allow dogs in st. paul, mn. to conduct his study, he randomly selects 100 businesses listed in the st. paul phone book, calls them and asks their policy.
The sample of study is 100 business.
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Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of ?1/3
Oy + 2 = (x+3)
Oy -2=(x-3)
Oy+ 3 = (x + 2)
Oy-3=(x-2)
The equation which passes through (3,2) and slope 1/3 is:
y - 2 = 1/3 (x - 3)
Given, we have:
slope (m) = 1/3
Point = (3,2) = (x₁,y₁)
we are asked to determine the point slope form :
we know that:
point slope form:
y-y₁ = m(x-x₁)
substitute the above values in the formula:
y - 2 = 1/3 (x - 3)
Hence the correct option is B.
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What is (-81.7)+346.2 Pls show ur work
Answer: 264.5
Step-by-step explanation:
(-81.7) + 346.2
346.2 - 81.7 = 264.5
a family has 5 natural children and has adopted 2 girls. each natural child has equal probability of being a girl or a boy, independent of the other children. find the pmf of the number of girls out of the 7 children.
PMF probability mass function:
2 - 0.03125, 3 - 0.15625, 4 - 0.3125, 5 -0.3125, 6 - 0.15625, 7 - 0.03125.
Define the term Probability?The probability of such a function is the degree to which an event will occur as a rational number.
A family has 2 adopted girls and 5 biological daughters.
Each naturally occurring child does have an equal chance of being a boy or a girl.
Out of the seven offspring, the probability mass function for girls is as follows:
B should stand for Boy, and G should stand for G.
Consequently, this is the probability mass function:
P(GGBBBBB) = ⁵C₀ x (0.5)⁰ x (0.5)⁵
= 0.03125
P(GGGBBBB) = ⁵C₁ x (0.5)¹ x (0.5)⁴
= 0.15625
P(GGGGBBB) = ⁵C₂ x (0.5)² x (0.5)³
= 0.3125
P(GGGGGBB) = ⁵C₃ x (0.5)³ x (0.5)²
= 0.3125
P(GGGGGGB) = ⁵C₄ x (0.5)⁴ x (0.5)¹
= 0.15625
P(GGGGGGG) = ⁵C₀ x (0.5)⁵ x (0.5)⁰
= 0.03125
Thus, the probability mass function for girls out of the 7 children is obtained.
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what is the slope intercept form of 4y+x=-1
Answer:
[tex]y=-\frac{1}{4}x-\frac{1}{4}[/tex]
Step-by-step explanation:
To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]4y+x=-1 \\ \\ 4y=-x-1 \\ \\ y=-\frac{1}{4}x-\frac{1}{4}[/tex]
im struggling fr help me
FIND THE SLOPE FROM THE GRAPH
a.
b.
c.
d.
Answer:
A
Step-by-step explanation: Rise/run. is important
it goes up 4 and then over 6 and so we have to simplify which is 2/3 and snice it is going down it is negitive.
I need help with this
Answer:
Yes.
Step-by-step explanation:
To decide if these triangles are similar, we need to check 2 criteria. The first is that the angles are all the same as their corresponding angles on the other triangle, which is true. The second is to check if the sides are all in the same proportional relationship. To do this, we need to put 40/50, 40/50, and 16/20 to see if they simplify to the same fraction (which is the proportion.) 40/50 and 40/50 simplify to the same fraction, 4/5. 16/20 also simplifies to 4/5, so the sides are all in the same proportion, which means the shapes are similar.
pens cost 20p each and pencils cost 12p each if i buy 6 pens and 5 pencils what will be the total cost
Answer:
$1.80
Step-by-step explanation:
someone please help me im begging u for points
The solution of the algebraic equation is x = -2. The proof is elaborated below.
The algebraic equation given to us is 14(x + 1) = -7(4 + x). An equation is a mathematical statement that proves the equality of two mathematical expressions. The first step is to simplify the brackets. The equation becomes 14x + 14 = -28 - 7x. Now, we will add 7x to both sides of the equation. The equation is modified as 21x + 14 = -28. Now, we will subtract 14 from both sides of the equation. The equation is modified as 21x = -42. Now, we will divide both sides of the equation by 21. The equation is modified as x = -2.
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Evaluate 2(x - 3) if x = 15
Answer:
24
Step-by-step explanation:
2(x-3)
2(15-3)
2(12)
24
Hopes this helps please mark brainliest
Answer:
24
Step-by-step explanation:
2(x - 3)
==> plug in x = 15
2(15 - 3)
==> subtract 3 from 15
2(12)
==> multiply 2 and 12
=24
Remember we evaluate using pemdas
Parenthesis
Exponents
Multiplication and Division (going left to right)
Addition and Subtraction (going left to right)
This is the order of operations we use to determine which operation we perform. Here we first used "parenthesis" and did all operations inside of the parenthesis. We then ended with multiplication
Given l||m and m∠1 = 60°, select all angles that are also equal to 60°. 8 2 6 7 5 4 3
Answer:
2 , 3 , 4
Step-by-step explanation:
Corresponding angles: When two parallel lines are intersected by a transversal, the angles on the same side and same position of the transversal are same.
∠3 = ∠1
Vertically opposite angles: When two lines intersect, the opposite angles are congruent.
∠2 = ∠1
∠4 = ∠3
So, ∠1 = ∠2 = ∠3 = ∠4 = 60°
What is the domain of the function?
A XER
B x≤5
C y≤ 5
D y≥5
Answer:
A
Step-by-step explanation:
Domain is the set of x values, so we can cross off C and D as answer choices as those would be possible answer choices for range. Looking at the graph, you can see the graph continues infinitely. The domain of the function is all real numbers, or A.
Please help thank u! I would appreciate it ASAP
Answer:
Step-by-step explanation:
can’t be determined
carrie draws 6 cards simultaneously from a well-shuffled deck of 52 playing cards. 12. what is the probability that she chooses 4 spades and 2 cards that are not spades? a. 0.0692 b. 0.0260 c. 0.2811 d. 0.1376 e. 0.0815 13. what is the probability that she chooses 2 red face cards? a. 0.7809 b. 0.3741 c. 0.2387 d. 0.1202 e. 0.6601
Using the theories of probability, we got that 0.0260 is the probability of choosing 4 spades and 2 cards that are not spades and 0.1202 is the probability of choosing 2 red face cards from a well shuffled deck of 52 playing cards..
We know a deck of 52 playing cards has 13 hearts, 13 clubs, 13 spades,
13 diamonds.
∴ The possibility that she chooses 4 spades and 2 cards that are not spades is,
= ([tex]^1^3C_4[/tex]×[tex]^3^9C_2[/tex])/([tex]^5^2C_6[/tex])
As from the 13 spade cards 4 are chosen, so now we are left with (52 - 4) = 48
and 2 cards that are not spades means out of 9 spades that are left after choosing 4 that is 9 will also be subtracted (48 - 9) = 39.
= (13!/(13 - 4)!×4!)×(39!/(39 - 2)!×2!)/52!/(52 - 6)!×6!
= (13!/9!×4!)×(39!/37!×2!)/(52!/46!×6!)
= (13×12×11×10)/(4×3×2)×(39×38)/2)/(52×51×50×49×48×47)/(6×5×4×3×2)
= (529815)/(20358520)
= 0.026.
Similarly, the probability of choosing 2 red face card is given by
=([tex]^6C_2[/tex]×[tex]^4^6C_4[/tex])/([tex]^5^2C_6[/tex])
=[ [(6! / (2!.4!)] × [46! / (4!.42!)] ]/ [52! / (6!.46!)]
=(15×163185)/20358520
=0.1202.
Hence, the probability of choosing 4 spades and 2 cards by carrie that are not spades is 0.026 and the probability of choosing 2 red face cards by carrie is 0.1202.
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