Answer:
f(x) = 4x -9
Step-by-step explanation:
The slope-intercept form is f(x) = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope, m.
= [tex]\frac{-5-(-17)}{1-(-2)}[/tex]
= [tex]\frac{12}{3}[/tex]
= [tex]4[/tex]
m = 4, and now we plug it into the equation, using any given point, (1,-5) in this case.
f(x) = 4x + b
(-5) = 4(1) + b
-5 = 4 + b
b = -9
Now we find the equation: f(x) = 4x -9, and if we plug (-2,-17) in, we should get the same number as if we plug in (1,-5).
The points (2,-20) and (r,-5) lie on a line with slope 5/4. Find the missing coordinate r.
Answer: 14
Step-by-step explanation:
The formula for slope in this problem is:
[tex]\frac{-5-(-20)}{r-2}=\frac{5}{4}[/tex]
[tex]\frac{15}{r-2} = \frac{5}{4}[/tex] (cross multiply)
60 = 5(r-2)
60 = 5r - 10
70 = 5r
14 = r
Check: (2, -20) (14, -5)
[tex]\frac{-5-(-20)}{14-2}[/tex]
[tex]\frac{15}{12}[/tex]
[tex]\frac{5}{4}[/tex]
I took a picture because it may be a little difficult to understand if I wrote it in text. Hope this helps.
Solve the system by substitution. y=2x x+y=6 with solution
Answer:
The solution is x=2, y=4
Step-by-step explanation:
y = 2x
x+y = 6
Using substitution, we can substitute the first equation into the second equation
x + (2x) = 6
3x = 6
Divide by 3
3x/3 = 6/3
x = 2
Now we can find y
y = 2(2)
y = 4
The solution is x=2, y=4
Mitchell buys a bag of cookies that contains 7 chocolate chip cookies, 8 peanut butter cookies, 4 sugar
cookies and 7 oatmeal cookies.
What is the probability that Mitchell reaches in the bag and randomly selects a sugar cookie from the bag,
eats it, then reaches back in the bag and randomly selects an oatmeal cookie? Round your answer to four
decimal places.
The Probability of cookie is 0.0492
Describe probability.
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. The formula for computing probabilities in equiprobable sample spaces, the probability of the complementary event, etc., as well as the likelihood of two events joining together, are essential to understand in order to properly appreciate this branch of mathematics.
Given That:
chocolate chip cookies = 7
peanut butter cookies = 8
sugar cookies = 4
oatmeal cookies = 7
selecting a sugar cookie from the bag = [tex]\frac{4}{7+8+4+7}=\frac{4}{26}=\frac{2}{13}[/tex]
selecting a oatmeal cookie from the bag = [tex]\frac{8}{7+8+3+7} =\frac{8}{25}[/tex]
Over all probability = [tex]\frac{2}{13} *\frac{8}{25} = \frac{16}{325} =0.0492[/tex]
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a parallelogram has a 5-inch side and an 8-inch side that make a 50-degree angle. find the area of the parallelogram and the lengths of its diagonals.
For the given parallelogram of 5-inch side and an 8-inch side with an angle of 50-degree , the area of the parallelogram is equal to 30.64 square inches and the lengths of its diagonals are 11.85inches and 6.13 inches.
As given in the question,
Side lengths of the parallelogram are :
From the attached diagram we have,
Side AC = 5 inches
Side CD = 8 inches
Angle ACD = 50°
Draw altitude 'h' from vertex A to the base CD at point E.
Length of CE = x inches
In ΔACE,
sin 50° = h / 5
⇒ h = 5 sin 50°
⇒ h = 5 (0.766)
⇒ h = 3.83 inches
cos 50° = x/ 5
⇒ x = 5 cos 50°
⇒ x = 5 ( 0.6428)
⇒ x = 3.214 inches
Length of diagonal BC
BC = √ h² + ( 8 + x )²
= √(3.83)² + ( 8 + 3.214)²
= √140.422696
≈ 11.85 inches
Length of diagonal AD
AD = √ h² + ( 8 -x )²
= √(3.83)² + ( 8 - 3.214)²
=√37.574696
≈ 6.13 inches
Area of a parallelogram ABCD
= height × corresponding base
= 3.83 × 8
= 30.64 square inches
Therefore, for the given parallelogram of 5-inch side and an 8-inch side with an angle of 50-degree , the area of the parallelogram is equal to 30.64 square inches and the lengths of its diagonals are 11.85inch and 6.13 inch.
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what is the value of 2/10 divided by 5/4
Arlin takes out a mortgage of $160,000 from the bank for 20 years at 4.75%. Determine her monthly mortgage payment.
Answer:
Step-by-step explanation:
Hello, the solution to your problem can be found by using the PMT function in Excel.
The function would read: =PMT(.0475/12, 20*12, -160,000)
With this formula the monthly mortgage payment is: $1,033.96.
I have attached a screenshot file containing the correct answer as well; the formula in the bar also shows how to use the function for any other similar problems. I hope this helps. : )
Which triangle congruence postulate or theorem proves that these triangles are congruent?
Answer:
a squares + b squared = c squared
When 5 is added to 1/2 of a number, the result is 6 less than the number. Find the number.
Answer:
5 - 1/2x = x - 6
Step-by-step explanation:
hope this answer helps you please mark me as the brainliest.
A survey was conducted in a classroom of 40 students. On the survey, 10 stated they were
fond of pineapple juice, 15 were fond of orange juice, and 7 liked to have both pineapple and
orange juice. Find how many students were neither fond of pineapple nor orange juice?
Answer: 8
Step-by-step explanation: Add 15, 10, and 7 together to get 32 students fond of OJ or Pineapple juice. then do 40-32 to get 8.
Caitlin had $385 in her bank account. She withdrew $14 each week to pay for a swimming lesson. She now has $245. How many swimming lessons did she pay for
The answer is 10 weeks of lessons she paid for using arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Caitlin had $385 in her bank account. She withdrew $14 each week to pay for a swimming lesson.
She now has $245.
Total money spent 385-245 = 140
For 140 will pay 140/14 = 10 weeks
Hence total 10 weeks lessons she paid for.
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The equation 4/5d - 5 = 3/5d - 2 Represents the number of dimes, d, in a stack how many dimes are in the stack?
Answer:
d=10
Step-by-step explanation:
i hoped this helps
Answer:
15 dimes
Step-by-step explanation:
The equation 4/5d - 5 = 3/5d - 2 Represents the number of dimes, d, in a stack how many dimes are in the stack?
You are asked to solve for d:
4/5d - 5 = 3/5d - 2
subtract 3/5d from both sides:
4/5d - 5 - 3/5d = 3/5d - 2 - 3/5d
1/5d - 5 = -2
add 5 to both sides:
1/5d - 5 + 5 = -2 + 5
1/5d = 3
multiply both sides by 5:
5(1/5d) = 3(5)
d = 15
is chicken good yes or no
Answer:
Chicken is highly nutritious and a good source of protein. Adding chicken to your diet may help support weight loss, muscle growth, and bone health.
5
Riley is saving up to buy a new television. She needs a total of $1,028.25. Riley has saved $200.39 already and earns $75.26 per
week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
OA. 10
OB. 12
OC. 9
OD.
11
Answer:
D. 11 weeksStep-by-step explanation:
Let the number of weeks Riley need to work is x.
She has $200.39 and will save $75.26 for x weeks to get $1028.25 total.
Set this as equation:
75.26x + 200.39 = 1028.25Solve it for x:
75.26x = 1028.25 - 220.3975.26x = 807.86x = 807.86/75.26x = 10.73 ≈ 11 (rounded to whole number)Correct choice is D
Answer:
d) 11
Step-by-step explanation:
Forming the equation,
→ 75.26w + 220.39 = 1028.25
Now the value of w will be,
→ 75.26w + 220.39 = 1028.25
→ 75.26w = 1028.25 - 220.39
→ 75.26w = 807.86
→ w = 807.86/75.26
→ w = 10.73425
→ [ w = 11 weeks ]
Hence, the answer is 11 weeks.
In the triangle shown, what is the measure of QR?
Answer:
= (5sin(50°)) / sin(70°)
2/5 of what number is 44
Answer:
110
Step-by-step explanation:
2/5=44/x
Cross multiply
2x=44(5)
2x=220
/2. /2
x=110
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A student simplified (cube root of 125 − 12 ÷ 2)(4 − 6)2 using the following steps:
(cube root of 125 − 12 ÷ 2)(4 − 6)2
Step 1: (5 − 12 ÷ 2)(4 − 6)2 Simplify the cube root.
Step 2: (−13 ÷ 2) (4 − 6)2 Subtract within first parentheses.
Step 3: −6.5(4 − 6)2 Divide within the first parentheses.
Step 4: −6.5(4 − 36) Simplify the exponent.
Step 5: −6.5(−32) Subtract within the parentheses.
Step 6: 208 Multiply.
Part A: The student made a mistake in Step 2. Describe the mistake and explain how to correct it. (3 points)
Part B: The student made a mistake in Step 4. Describe the mistake and explain how to correct it. (3 points)
Part C: Show every step of your work to simplify (cube root of 125 − 12 ÷ 2)(4 − 6)2.
In both the steps student has done wrong simplification of the equation.
In step 2, student has done the wrong subtraction of 5 and 12.
Correct subtraction would be 5 - 12 = -7, not -13 so the equation will be (-7/2)(4-6)2.
In step 4, student has wrong multiplication in the parentheses with 4 and 6.
Correct multiplication would be -6.5(4-6)2 :
-6.5(8-12).
The correct solution of this equation is :
(cube root of 125 − 12 ÷ 2)(4 − 6)2
(5 − 12 ÷ 2)(4 − 6)2,
(5-6)(4 − 6)2, Dividing according to the BODMAS.
-1(-2)2, subtracting
4. multiplying
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If the figure on the left is the base of a right prism that is 8 feet high, how many
sugar cubes that measure 1 foot on a side will the solid hold? What is the
surface area of the prism? Dimensions are in feet. All angles are right angles.
Number of sugar cubes hold the sugar cube = 768÷1 = 768 unit
Surface area of the prism = 8×8 + 6×8 + 4×8 + 4×8 + 4×8 + 4×8 + 8×8+ 14×8 + 8×8 + 4×4 + 4×8 = 512 sqft
Divide the base area of figure into three parts
Area of the 1st part = 8×6 = 48 sqft
Area of the 2nd part = 4×4 = 16 sqft
Area of the 3rd part = 4×8 = 32 sqft
Height of the prism is 8 ft
So the total volume of the prism ,
Volume = 8×( 6×8 + 4×4 + 4×8 )
= 8×( 48 + 16 + 32 )
= 8×96 = 768 cubic feet
1 feet side sugar cube solid holds a volume = 1×1×1 = 1 cubic feet
Number of sugar cubes hold the solid prism = volume of prism / volume of sugar cube
Number of sugar cubes hold the sugar cube = 768÷1 = 768 unit.
Surface area of the prism =( lateral surface area) + (top surface area)
Lateral surface area = 8×8 + 6×8 + 4×8 + 4×8 + 4×8 + 4×8 + 8×8+ 14×8 = 416 sqft
Top surface area = 8×8 + 4×4 + 4×8 = 96 sqft
Surface area of the prism = 8×8 + 6×8 + 4×8 + 4×8 + 4×8 + 4×8 + 8×8+ 14×8 + 8×8 + 4×4 + 4×8 = 512 sqft
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no contestant received the same score on two different days. if a contestant is selected at random, what is the probability that the selected contestant received a score of 555 on day 222 or day 333, given that the contestant received a score of 555 on one of the three days?
The probability that the selected contestant received a score of 555 on day 222 or day 333 is 5/7.
If it is given that on day 222 the no of contestants received a score of 555 is 2 and no of contestants received a score of 555 on day 222 is 3.
Given:
It is given that no contestant received the same score on two different days. So, we have 7 days in a week which means there are 7 contestants only who could be chosen and have a score of 555.
So, the contestants who received a score of 555 on any day = 7.
Now, the contestant received a score of 555 on day 222 is 2 and on day 333 is 3.
Probability = No of favorable outcomes/Total no. of outcomes
Probability = (2 + 3)/7 = 5/7
The probability that the selected contestant received a score of 555 on day 222 or day 333 is 5/7.
If it is given that on day 222 the no of contestants received a score of 555 is 2 and no of contestants received a score of 555 on day 222 is 3.
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53=y−47.4 pls help sssssssssss
Answer:
5.6
Step-by-step explanation:
y = 53- 47.4=?
a triangle has 2 vertices at (1,10), (-5,2), and (7,2)
What is the circumcenter
The circumcenter of the triangle that has vertices at (1, 10), (-5, 2), and (7, 2) is (1, 3.75)
What is the circumcenter of a triangle?The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the three sides of the triangle.
The distance from the circumcenter to each of the three vertices are congruent.
The coordinates of the circumcenter can found using the as follows;
Let (x, y), represent the coordinates of the circumcenter, we get;
The distance of the circumcenter from the vertices of the triangle is the same for the three vertices, therefore;
The specified vertices of the triangle are; (1, 10), (-5, 2), and (7, 2)
The distance of the circumcenter, (x, y), from (1, 10), is therefore;
D₁ = √[(x - 1)² + (y - 10)²]
The distance of the circumcenter, (x, y), from (-5, 2), is therefore;
D₂ = √[(x - (-5))² + (y - 2)²]
The distance of the circumcenter, (x, y), from (7, 2), is therefore;
D₃ = √[(x - 7)² + (y - 2)²]
The properties of the circumcenter indicates that we get;
D₁ = D₂ = D₃
D₁ = √[(x - 1)² + (y - 10)²] = D₂ = √[(x - (-5))² + (y - 2)²] = D₃ = √[(x - 7)² + (y - 2)²]
D₁ = D₂ indicates;
√[(x - 1)² + (y - 10)²] = √[(x - (-5))² + (y - 2)²]
(x - 1)² + (y - 10)² = (x - (-5))² + (y - 2)² = (x + 5)² + (y - 2)²
(x - 1)² + (y - 10)² = (x + 5)² + (y - 2)²
x² - 2·x + y² - 20·y + 101 = x² + 10·x + y² - 4·y + 29
According to the addition and subtraction properties of equality, we get;
x² - 2·x + y² - 20·y + 101 - (x² + 10·x + y² - 4·y + 29) = 0
12·x + 16·y - 72 = 0...(1)D₁ = D₃ indicates√[(x - 1)² + (y - 10)²] = √[(x - 7)² + (y - 2)²]
(x - 1)² + (y - 10)² = (x - 7)² + (y - 2)²
x² - 2·x + y² - 20·y + 101 = x² - 14·x + y² - 4·y + 53
x² - 2·x + y² - 20·y + 101 - (x² - 14·x + y² - 4·y + 53) = 0
12·x - 16·y + 48 = 0...(2)Equation (1) and (2) indicates;
12·x + 16·y - 72 = 12·x - 16·y + 48
12·x - 12·x + 16·y - (-16·y) = 48 - (-72) = 48 + 72 = 120
16·y - (-16·y) = 16·y + 16·y = 32·y = 120
y = 120 ÷ 32 = 3.75
y = 3.75
12·x - 16·y + 48 = 0...(2)
12·x - 16 × 3.75 + 48 = 0
12·x - 12 = 0
12·x = 12
x = 12/12 = 1
x = 1
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Use the given arithmetic sequence to write an equation.
-3, -8, 13, -18,
-
Answer:
assuming 13 is supposed to be -13, the equation will be y=-5x+2
Step-by-step explanation:
common difference = -5
y=-5x+b
-3=-5(1)+b - plug in the first term of the sequence
b=2
start a penny (1 scent) on day one, and double it every day for one month (31 days) how much? will you have?
HELP ME PLEASEEE
Answer:2^(31-1)
Step-by-step explanation:
Width: X
Length: 3x
Determine the lengths of the
sides of the rectangle using the
given area. Give answers both
exactly and approximately (to
the nearest tenth).
The area of the rectangle is 45
cm squared.
Answer:
[tex]3x \times x = 45 \\ {3x}^{2} = 45 \\ {x}^{2} = \frac{45}{3} \\ {x}^{2} = 15 \\ x = \sqrt{15} \\ x = 3.872983346 \\ x = 3.9[/tex]
Step-by-step explanation:
area of a rectangle is width a length
area of length already given as 45cm²
find the unknown x using a normal equation
Solve the inequality.
6(4q − 8) > 8(3q + 2)
The inequality 6(4q − 8) > 8(3q + 2) have no solution.
How to solve inequalities?The inequality can be solved as follows:
An inequality is an expression that has <, >, ≤ and ≥ symbols.
Therefore,
6(4q − 8) > 8(3q + 2)
open the bracket on both sides of the inequality
6(4q − 8) > 8(3q + 2)
24q - 48 > 24q + 16
add 48 to both sides of the inequality
24q - 48 > 24q + 16
24q - 48 + 48 > 24q + 16 + 48
24q > 24q + 64
Subtract 24 q from both sides of the inequality
24q > 24q + 64
24q - 24q > 24q - 24q + 64
0 > 64
The inequality cannot be solved
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Consider the inequality x+36>x4+1. Which value of x is a solution to the inequality?.
The inequality x+36>x4+1. The inequality's solution is the value of x.
x+36>4+1
x+36>5
x>5-36
x>-31
-31 value of x is a solution to the inequality.
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campus residence office receives 120 applications for ra from students. assuming that these applicants can be viewed as a random sample of all such students, what is the probability that between 35% and 45% of them are women if 40% of all students are women? round your answer to 3 decimal places.
The probability to have women applications between 35% to 45% is 1.
Here we are given that the sample number of applications received was 120.
Also, 40% of total applications are of women.
Hence this is clearly a Binomial Distribution with,
n = 120
p= 0.4
We need to find the probability that the sample applications have women applicants between 35% to 45%. For this, we need to use the method of Normal Approximation
Now,
np = 120 X 0.4
= 48
Since np > 10,
We can use Normal approximation here, with
mean = np = 48
Variance = np(1 - p)
= 48 X 0.6
= 28.8
35% of applicants = 42
45% of applicants = 54
Hence we need to find
P(42<X<54)
P(a<X<b)
= P(X<b) - P(X<a)
Therefore we get
P(X < 54) - P(X<42)
Now subtracting it with its mean and dividing it by its standard deviation we get
P(X < (54 - 48)/5.3666) - P(X < (42- 48)/5.3666)
= P(X < 1.1180) - P(X < -1.1180)
= 0.86650 - 0.13350
= 1
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There are five times as many pink buttons as yellow buttons.
number of yellow buttons : number of blue buttons = 4 : 7
e button is selected at random.
ork out the probability that the button is either pink or blue.
ve your answer as a fraction in its simplest form.
Optional working
nswer:
Write your fraction in the form a/b
Answer:
please put the number of yellow buttons if you can
thank you.
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The complete table of values is:
x -2 -1 0 1 2
y 1/9 1/3 1 3 9
How to complete the table of values?From the question, we have the following equation:
f(x) = 3ˣ
From the table of values, we have the following x values
x = -2, -1, 0, 1 and 2
Substitute x = -2, -1, 0, 1 and 2 in the equation f(x) = 3ˣ
When x = -2
f(-2) = 3⁻² = 1/9
When x = -1
f(-1) = 3⁻¹ = 1/3
When x = 0
f(-1) = 3⁰ = 1
When x = 1
f(1) = 3¹ = 3
When x = 2
f(2) = 3² = 9
Hence, the complete table of values is:
x -2 -1 0 1 2
y 1/9 1/3 1 3 9
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it is known that the population variance equals 484. with a 0.99 probability, what is the sample size that needs to be taken if the desired margin of error is 5 or less? round your answer up to an integer.
For a population variance of 484 with a probability of 0.99 the sample size needed if the desired margin of error is 5 or less is 129
Margin of error refers to a statistical measurement that represents the difference between actual and projected outcomes in a random survey sample. In other words, the margin of error enabled the researcher to measure the level of unpredictability in data and research outcomes. Margin of error is given by:
MOE = z x σ/√n
In order to determine the z score, the value is determined by the z table. As the table is set up for one tailed probability and the given confidence level uses a two tailed probability, the p value is determined by (1 + 0.99)/2 = 0.995. As the p value of 0.995 lies in the row containing 2.5 and column containing 0.08, the z = 2.5 + 0.08 = 2.58.
The standard deviation is the square root of the variance, hence σ = √484 = 22
As MOE = z x σ/√n
Substituting the values from the given data,
5 = 2.58 x 22/√n
5√n = 56.76
√n = 11.35
N = 128.8 ≈ 129
Hence, at least a sample size of 129 is required.
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consider the two jars below, which each contain 10 marbles. in jar a, 70% of the marbles are green and 30% of them are blue. in jar b, 30% of the marbles are green and 70% of them are blue. suppose a computer randomly chooses one of the jars, where there is a 15% chance it chooses jar a and a 85% chance it chooses jar b. the randomly chosen jar is shaken (shuffling its contents), and a marble is drawn out of it: the marble is green. what is the percent chance it came from jar a?
The likelihood that a green marble from jar A will be drawn out of it is 0.105.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
Here,
For jar A,
Total Marbles=10
Number of green marbles=7
Number of blue of marbles=3
For jar B,
Total Marbles=10
Number of green marbles=3
Number of blue of marbles=7
Probability of choosing jar A=15/100
Probability of choosing jar B=85/100
Probability that a marble is drawn out of it is the marble is green that came from jar a= 15/100*7/10
=105/1000
=0.105
Probability that a marble is drawn out of it is the marble is green that came from jar A is 0.105.
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