The sum of two numbers is 10. The larger number is 4 times the smaller number. What are the two numbers?
Original system: x + y = 10,
y = 4x
Slope-intercept form:
y = –x + 10,
y = 4x
Use the work shown to complete the statement.
The slopes and y-intercepts of the two equations are
, so this system has
.
Answers
Answer: different (b)
exactly one solution (b)
Step-by-step explanation:
correct on edge 2020
Related Questions
Ms. Baker has a class of 15 students. She can spend $21 on each student to buy math supplies for the year. She first buys all of her students calculators, which
costs a total of $67.65, After buying the calculators, how much does she have left to spend on each student?
Answers
Find the value of x.
Answers
Answer:
I think the answer is x=120
Has anyone done the inverse functions mastery text on edmentum it’s super hard stuck on this question and the pictures wont help
Answers
The amount of time to complete a physical activity in a PE class is approximately normally normally distributed with a mean of 32.9 seconds and a standard deviation of 6.4 seconds.
A) What is the probability that a randomly chosen student completes the activity in less than 33.2 seconds?
B) What is the probability that a randomly chosen student completes the activity in more than 46.6 seconds?
C) What proportion of students take between 35.5 and 42.8 seconds to complete the activity?
D) 75% of all students finish the activity in less than____seconds.
Answers
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) of 32.9 seconds and a standard deviation (σ) of 6.4 seconds.
The z score is used to measure by how many standard deviation the raw score is above or below the mean. It is given by:
\(z=\frac{x-\mu}{\sigma}\\\)
a) For x < 33.2 seconds
\(z=\frac{x-\mu}{\sigma}\\\\z=\frac{33.2-32.9}{6.4} =0.05\)
From the normal distribution table, the probability that a randomly chosen student completes the activity in less than 33.2 seconds = P(x < 33.2) = P(z < 0.05) = 0.5199 = 51.99%
b) For x > 46.6 seconds
\(z=\frac{x-\mu}{\sigma}\\\\z=\frac{46.6-32.9}{6.4} =2.14\)
From the normal distribution table, the probability that a randomly chosen student completes the activity in more than 46.6 seconds = P(x > 46.6) = P(z > 2.14) = 1 - P(z < 2.14) = 1 - 0.9927 = 0.0073 = 0.73%
c) For x = 35.5 seconds
\(z=\frac{x-\mu}{\sigma}\\\\z=\frac{35.5-32.9}{6.4} =0.41\)
For x = 42.8 seconds
\(z=\frac{x-\mu}{\sigma}\\\\z=\frac{42.8-32.9}{6.4} =1.55\)
From the normal distribution table, the proportion of students take between 35.5 and 42.8 seconds to complete the activity = P(35.5 < x < 42.8) = P(0.41< z< 1.55) = P(z < 1.55) - P(z < 0.41) = 0.9332 - 0.6591 = 0.2741 = 27.41%
d) A probability of 75% = 0.75 corresponds to a z score of 0.68
\(z=\frac{x-\mu}{\sigma}\\\\0.68=\frac{x-32.9}{6.4} \\\\x-32.9=4.4\\x=4.4+32.9\\x=37.3\)
75% of all students finish the activity in less than 37.3 seconds
1. A target is divided into 100 squares colored in dark blue, white, and light blue. Amber throws a beanbag that lands on the target.
co
9 25
dark blue
What is the probability that it will land on a dark blue square?
26
white
light blue
Answers
The probability of landing on the dark blue target is 2/5.
Finding probabilityProbability is the ratio of required to the total possible outcomes of an event.
The required outcome = dark blue= 25Total possible outcomes= entire sample Space = 100P(dark blue ) = 40/100
divide through by 20
P(dark blue ) = 2/5
Therefore, the probability of landing on target is 2/5
Learn more on probability:https://brainly.com/question/24756209
#SPJ1
HELP PLEASE I’m having troubles!!!
Answers
1. The velocity at time t , v(t) = (18t² + 3 ) m/s
2. The velocity at time t = 3 seconds = 165 m/s
3. The acceleration at time t, a(t) =( 36t )m/s²
4. The acceleration at time t = 3 seconds = 108 m/s²
What is instateanou velocity and acceleration?The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.
Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.
1. s(t) = 6t³ + 3t +9
to find the velocity at time t, we differentiate s(t)
= 18t² + 3
2. at t = 3s
= 18(3)² +3
= 165 m/s²
3. v(t) = 18t² + 3
to get the acceleration at time t, we differentiate v(t)
= 36t
4. when t = 3
a = 36 × 3
= 108 m/s²
learn more about instantaneous velocity and acceleration from
https://brainly.com/question/2234298
#SPJ1
Elizabeth and James went to the school picnic to eat lasagna. The teachers cut the pan of lasagna into 12 equal portions. Elizabeth took 2 pieces and James took 4 pieces from the whole square pan. What fraction of lasagna did Elizabeth take? What fraction did james take?
4th Grade Math (Fractions)
Answers
James took 4/12
Find the volume.
pls help!!
Answers
Answer:
the answer to the problem is 48 km
Step-by-step explanation:
8*2*3
Answer: 48 sq km
Step-by-step explanation:
The length of the rectangular prism is 8 kilometers. The width is 3 kilometers. Lastly, the height is 2 kilometers. The formula for a rectangular prism is lwh, or length x width x height. 8 x 3 x 2 = 48 sq km.
What is the equation of the line of best fit for these data? Round the slopeand y-intercept of the line to three decimal places.хy12031451096164
Answers
The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X = 0).
We can use the least-squares method to find the line of best fit for a set of paired data, allowing you to estimate the value of a dependent variable (Y) from a given independent variable (X).
To do this we would require the following parameters.
Sum of X
Sum of Y
Mean X
Mean Y
Sum of squares (SSX)
Sum of products (SP)
STEP 1: We compute the mean of the x and y values
STEP 2: we compute the difference of each variable from their respective mean and sum the values the find the sum of squares (SSX) and Sum of products (SP)
The regression equation is given as
\(RegressionEquation=ŷ=bX+a\)Where b is
\(b=\frac{SP}{SS_X}=\frac{-137.2}{140.8}=-0.97443\)and a is
\(a=M_Y-bM_X=10.8-(-0.97\times6.8)=17.42614\)Therefore the line of best fit
\(ŷ=-0.974x+17.426\)ANSWER= OPTION B
actor 14x+7y using the GCF.
Answers
Answer:
so to factor out you find the greatest common factor of 14 and 7
if you have 2x-2 then you can factor out the 2 and get 2(x-1)
7=7*1
14=2*7
the greatest common factor is 7
14x-7=7(2x-1)
Is it a function (2,4) (4,9) (6,6) (2,6)
Answers
Repeats
Is this relation a function?*
{(5, 1),(-1,5),(-5, 1), (1,-5), (5,3)}
A. Function
B. Not a function
Answers
Answer:
B. Not a function
Step-by-step explanation:
Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X:(a) f(x) = c(x2 + 4), for x = 0, 1, 2, 3;(b) f(x) = c (2x) (33-x) , for x = 0, 1, 2. 2.^^(2 is supposed to be directly above x, but not in fraction form, same for 3 and 3-x)
Answers
The value of c is 1/17.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2
We have to find the value of c
Since f(x) represents the probability distribution x = 0, 1 ,2
So we have f(0)+f(1)+f(2)=1
c(0²+4)+c(1²+4)+c(2²+4)=1
4c+5c+8c=1
17c=1
Divide both sides by 17
c=1/17
Hence, the value of c is 1/17.
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ1
Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?
a.
1/3
b.
1/17
c.
1/2
d.
1/13
3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
Answers
The conditional probability that the person has the disease given that the test result is positive is of 0.4750 = 47.50%.
What is Conditional Probability?
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
In which:
P(B|A) is the probability of event B happening, given that A happened.\(P(A \cap B)\) is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, the events are:
Event A: Positive test.Event B: Has the disease.The percentages associated with a positive test is:
93.9% of 3.8%(has the disease).4.1% of 100 - 3.8 = 96.2%(does not have the disease).Hence:
\(P(A) = 0.939(0.038) + 0.041(0.962) = 0.075124\)
The probability of both a positive test and having the disease is given by:
\(P(A \cap B) = 0.939(0.038) = 0.035682\)
Hence the conditional probability is given by:
\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.035682}{0.075124} = 0.4750\)
More can be learned about conditional probability at https://brainly.com/question/14398287
#SPJ1
Julie has $80 to spend on clothes. If she buys a pair of jeans for $24.75, how many shirts can she buy for $12.50?
Answers
Answer:
4
Step-by-step explanation:
$80.00 - $24.75 = $55.25
$55.25 ÷ $12.50 = 4 Shirts!
Before you add fractions, they must have the same:
Answers
−4y−4+(−3) .........................................................
Answers
Let
P be a polynomial function, and
P(x) = 23 – dx2 - 4x – 20. If
(2 – 2) is a factor of the polynomial, what is the value of
d?
Answers
Answer:
The value of d = -5
The polynomial function x³ +5 x² - 4x -20 =0
Step-by-step explanation:
Explanation
Given that the equation is third degree polynomial
p(x) = x³ - d x² - 4x -20
Given factors x= 2 and x=-2
Substitute 'x' = 2 in given polynomial
8 -d(2²)-4(2) - 20 =0
⇒ 8 - 4 d - 8 -20=0
⇒ - 4 d-20 = 0
⇒ - 4 d = 20
⇒ d = - 5
The value of d = -5
Verification:-
After substitution d =-5 in given polynomial
x³ - (-5) x² - 4x -20 =0
put x=2
8 +5(4)-8-20 =0
20 =20
The factors are x= 2 and x=-2 of the given polynomial
the perimeter of a semicircle protractor is 14.8cm,find it's radius
Answers
The radius of the semicircle protractor is approximately 4.693 cm.
Given,Perimeter of a semicircle protractor = 14.8 cm.
To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.
Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.
for more questions on semicircle protractor
https://brainly.com/question/30188078
#SPJ8
What are the factors of 2a³ + a² + 2a + 1?
O 2(a² + 1)(a + 1)
O(a + 1)(a - 1)(2a + 1)
O (a² + 1)(2a + 1)
O 2(a + 1)2 (a - 1)
Answers
Answer:
The answer is (a²+1)(2a+1)
Here are some summary statistics for the durations for which candles from a certain company burn.
Candle type
Jar candle
Pillar candle
Mean duration
u=25 hours
u=95 hours
Standard deviation
o=2.5 hours
o=7.5 hours
Andrei had cinnamon-scented jar candle that burned for 30 hours and a berry-scented pillar candle that
burned for 88 hours,
Relative to its type, which candle burned faster?
Choose 1 answer:
The cinnamon-scented jar candle
The berry-scented pillar candle
The two candles burned equally fast relative to their types
It’s impossible to say without seeing all of the individual burning times
It’s impossible to say since we don’t know the shape of either distribution
Answers
Answer:
the berry-scented pillar candle
Step-by-step explanation:
khan academy
Mary purchased 4 tires by mail order. She paid $50.30 per tire plus $4.90 per tire for shipping and handling. There is no sales tax, because the tires were purchased out of state. She also had to pay $8.81 per tire for mounting and balancing. At a local store, Mary's total for the 4 tires with mounting and balancing would be $296 plus 6% sales tax. How much did Mary save by purchasing the tires through the mail?
Answers
The money saved by Mary if she purchased tires through mail order is equal to $57.72.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
It is given that Mary has purchased 4 tires by mail order.
Cost Mary paid for shipping and handling will be :
= ($50.30 + $4.90) × 4
= $220.8
Cost for mounting and balancing will be :
= $8.81 × 4
= $35.24
Total cost of 4 tires by mail order will be :
= $220.80 + $35.24
= $256.04
At the local store , cost Mary need to pay 4 tires with mounting and balancing would be $296 plus 6% sales tax :
= 296 + [(296 ×6) / 100]
= $313.76
Savings of Mary if she purchased tires through mail order will be :
= $316.76 - $256.04
= $57.72
Therefore , the money saved by Mary if she purchased tires through mail order is equal to $57.72.
Learn more about algebra here :
brainly.com/question/12377332
#SPJ1
dog is congruent to GED?
Answers
Answer:
Yes
Step-by-step explanation:
The Angles are the exact same.
Hope I helped! Please leave a review or rating!
Find the domain of the function
Answers
Answer:
Here you go :)
Step-by-step explanation:
Select the correct answer.
The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30
pages, what can you conclude?
OA About 60% of the books have fewer than 150 pages.
O B.
About 16% of the books have fewer than 150 pages.
OC.
About 95% of the books have more than 150 pages.
OD. About 16% of the books have more than 150 pages.
Answers
Answer:
B
About 16% of the books have fewer than 150 pages.
Step-by-step explanation:
Quizlet also said so
2.2 2.1.4 a Given that A and B are complementary angles and 7 cos A-3 = 0. Determine WITHOUT the use of a calculator, the value of: 7 cos B-3 tan A. (4)
Answers
88 1
2
3
81°
4
5
64%
m/1 =
m/2 =
m23 =
m/4 =
m25 =
Answers
Answer:
m<1 = 92°
m<2 = 24°
m<3 = 64°
m<4 = 35°
m<5 = 81°
Step-by-step explanation:
10+10
What is this...
Answers
Answer:
20
Step-by-step explanation:
By the end of the first week a movie had grossed $2.3million. By the end of is six week, it had grossed $6.8million. Graph the data with the week on the vertical axis, and draw a line through the points.Then find and interpret the slope of the line.
Answers
Answer:
The first step is to label the points being (1,2.3),(6,6.8) in which the first ordered pairs is the number of weeks, and the second one is the dollars in millions.
Hence, the slope is: m=(6.8-2.3)/(6-1) = 4.5/5 = 9/10 = 0.9
The slope represents the dollar rate in the millions per week. In this case, the movie grossed $0.9 million per week from week one to the sixth week.
If two negative integers are multiplied together, the product will be
F
negative
G
positive
H
both positive and negative
J
neither positive or negative
Answers
Answer: A
Step-by-step explanation:
Answer:
negative
Step-by-step explanation:
-x*-y=z