Answer:
[tex]a = 1[/tex]
Step-by-step explanation:
Given
[tex]4x - 3(x + a) = 2[/tex]
[tex]x = 5[/tex]
Required
Determine the value of a
[tex]4x - 3(x + a) = 2[/tex]
Substitute 5 for x
[tex]4(5) - 3(5 + a) = 2[/tex]
Open all brackets
[tex]20 - 15 - 3a = 2[/tex]
[tex]5 - 3a = 2[/tex]
Collect Like Terms
[tex]-3a = 2 - 5[/tex]
[tex]-3a = -3[/tex]
Solve for a
[tex]a = -3/-3[/tex]
[tex]a = 1[/tex]
what is the slope of the line that passes through (37, -9) and (36, 81)
Answer:
m= -90 is your answer
Step-by-step explanation:
For future reference, you should try using Symbolab, it works really well and I use it ALL the time!
what is the measure of each angle
Answer:
60 degrees
Step-by-step explanation:
60 degrees because all sides are equal and 180/3 is 60.
In 1980, the number of high school dropouts in a country was 5217 thousand. By 2008, this number had decreased to 3120 thousand. Find and interpret the average rate of change
per year in the number of high school dropouts.
Answer:
74893 students per year
Step-by-step explanation:
The Average rate of change is calculated as
= Difference in number of students / Difference in years
= 3120 thousand - 5217 thousands/ 2008 - 1980
= (3120000 - 5217000)/(2008 - 1980)
= -2097000/28
= -74892.857143 per year
Therefore, the average rate of change
per year in the number of high school dropouts is approximately 74893 students per year
When three numbers are added two at a time, the sums are 29, 46, 53. What is the sum of all three numbers?
Answer:
[tex]Sum = 64[/tex]
Step-by-step explanation:
Let the three numbers be a, b and c; such that:
[tex]a + b = 29[/tex] ---- (1)
[tex]b + c = 46[/tex] --- (2)
[tex]a + c = 53[/tex] --- (3)
Subtract equation 2 from 3
[tex]a - b + c - c = 53 - 46[/tex]
[tex]a - b = 7[/tex] --- (4)
Add this equation to the (1)
[tex]a + a + b - b = 29 + 7[/tex]
[tex]2a= 36[/tex]
Solve for a
[tex]a = 36/2[/tex]
[tex]a = 18[/tex]
Substitute 18 for a in (1)
[tex]a + b = 29[/tex]
[tex]18 + b = 29[/tex]
Solve for b
[tex]b = 29 - 18[/tex]
[tex]b = 11[/tex]
Substitute 11 for b in (2)
[tex]b + c = 46[/tex]
[tex]11 + c = 46[/tex]
Solve for c
[tex]c = 46 - 11[/tex]
[tex]c = 35[/tex]
[tex]Sum = a + b +c[/tex]
[tex]Sum = 18 + 11 + 35[/tex]
[tex]Sum = 64[/tex]
Eight less than a number is negative eighteen. What is the number?
Answer:
-10
Step-by-step explanation:
n - 8 = -18
n = -10
Negative 10
Or -10
Eight more than -18 is -10
A ball is thrown with an initial velocity of 32 ft/s from a height of 4.5 feet. It’s height as a function of time is given by the equation h(t)=-16t2+32t+4.5. How long will the ball be in the air, and how high does the ball go?
Answer:
the ball will be in the air for possibly 2.5 seconds and it max hieght was 10 ft
Step-by-step explanation:
no clue
Suppose that the scores on a reading ability test are normally distributed with a mean of and a standard deviation of . What proportion of individuals score more than points on this test? Round your answer to at least four decimal places.
Answer:
The proportion of individuals score at most 74 points on this test is 70%.
Step-by-step explanation:
The complete question is:
Suppose that the scores on a reading ability test are normally distributed with a mean of 70 and a standard deviation of 8. What proportion of individuals score at most 74 points on this test? Round your answer to at least four decimal places.
Solution:
Let X represent the scores on a reading ability test.
It is provided that [tex]X\sim N(70,8^{2})[/tex].
Compute the probability that an individuals score is at most 74 points on this test as follows:
[tex]P(X\leq 74)=P(\frac{X-\mu}{\sigma}\leq \frac{74-70}{8})[/tex]
[tex]=P(Z<0.50)\\=0.69146\\\approx 0.70[/tex]
Thus, the proportion of individuals score at most 74 points on this test is 70%.
Toby works at an amusement park. He loads 10 new passengers onto the roller coaster every
3/4
of a minute. At what rate does Toby load passengers?
Pleaseeee
Answer:
13 1/3
Step-by-step explanation:
im sure this is right btw
Barkery’s Bakery sold 20 dog cakes during Week 1 of operation, 27 dog cakes during Week 2, and 34 dog cakes
during Week 3.
a. If this pattern continues, represent the first five
terms of the sequence using a table of values.
Answer:
Week 1 - 20
Week 2 - 27
Week 3- 34
Week 4 - 41
Week 5 - 48
Etc, etc,...
Step-by-step explanation:
The values increase by 7 each week.
The soccer field at Mario’s school has an area of 6000 square meters how can Mario show the area has a whole number multiplied by a power of 10
Answer:
[tex]Area = 6 * 10^3\ m^2[/tex]
Step-by-step explanation:
Given
[tex]Area = 6000m^2[/tex]
Required
Write as a number by power of 10
[tex]Area = 6000m^2[/tex]
Split 6000 as 6 * 1000
[tex]Area = 6 * 1000m^2[/tex]
Express 1000 as 10^3 --- Law of indices
[tex]Area = 6 * 10^3\ m^2[/tex]
What is 5x + 4y = 10
Answer:
x=2 - 4y/5
y = 5/2 − 5x/4
Step-by-step explanation:
I don't know what you are asking for specifically, but here is both!!
United Airlines' flights from Boston to Dallas are on time 80 % of the time. Suppose 7 flights are randomly selected, and the number on-time flights is recorded. 1.The probability that at least 3 flights are on time is
Answer: 14.5
Step-by-step explanation:
Given data:
Success rate = 80% = 0.8
No of flights = 7
No of failures = 1 – 0.8 = 0.2
Solution
at least 3 flights are on time is
= 7C3 * (0.80)^3 * (0.80)^1 + 7C7 * (0.80)^7 * (0.80)^1
= 35 * 0.512 * 0.8 + 1 * 0.21 * 0.8
= 14.336 + 0.168
= 14.5
How many units is -9 from zero on the number line?
Select one:
A. 9
B. - 9
C. 0
D. 18
Answer:
A
it is asking for its absolute value
Step-by-step explanation:
Solve −3x=2x2−4
using the Quadratic Formula.
Answer:
-3x= 2×2-4
Step-by-step explanation:
-3x= 4-4
-3x= 0
divide both sides by the co-efficient of x
-3x/-3= 0÷-3
x= 0/-3x = 0
The solution of the quadratic equation 2x² + 3x − 4 = 0 will be 2.35 and negative 0.85.
What are the roots of the equation?Let the equation be ax² + bx + c = 0. Then the roots of the equation will be given as,
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]
The equation is given below.
−3x = 2x² − 4
Simplify the equation, then we have
2x² − 4 = −3x
2x² + 3x − 4 = 0
Then the roots of the equation are given as,
x = [3 ± √(3² - 4 · 2 · (-4))] / (2 · 2)
x = (3 ± 6.403) / 4
x = 2.35, -0.85
The solution of the quadratic equation 2x² + 3x − 4 = 0 will be 2.35 and negative 0.85.
More about the roots of the equation link is given below.
https://brainly.com/question/12029673
#SPJ2
Andrew owns a food truck that sells tacos and burritos. He only has enough ingredients to make 113 tacos or burritos.Write an inequality that could represent the possible values for the number of tacos sold, tt, and the number of burritos sold, bb, that would satisfy the constraint.
Answer:
heres the actual answer.
Step-by-step explanation:
Someone bought a car for $5,000. During the first year, its value depreciated by 20%. What was the value of the car after one year?
Answer:
The value of the car after one year is $1000
Step-by-step explanation:
$5000 * 0.2 = 1000.
You can say the 20% = 0.2.
So it is depreciated by 0.2.
You multiply the number (5000) by 0.2
5000 * 0.2 = 1000.
Answer:
The answer is 1,000
Step-by-step explanation:
because 20% of 5000 is the answer which is 1,000
Please help!!
What is the range of y = sin 1x?
O f-1, 1]
[O, TI]
ol-
(_00,00)
Answer:
C
Step-by-step explanation:
C is what I get when I put it into desmos. someone else may be able to explain why
10. What is the greatest common factor of 500; 1,000 ;
and 12,500 ?
A. 5
B. 100
C.
125
D. 250
E. 500
Answer:
E. 500
Step-by-step explanation:
All 3 are divisible by 500
look at picture
look at picture
Answer:
point ??????? I think not sure
Solve −3−4x≤21.
A
x≤−6
B
x≥6
C
x≥−6
D
x≤4
Answer: A
Step-by-step explanation:subtract then multipy the see which one is least to greaest
Solve equation.
X^2-4x-12 = 0
Answer:
Step-by-step explanation:
x2 - 4x - 12 = 0
x2 - 6x + 2x - 12= 0
x(x - 6) + 2(x - 6) = 0
x + 2 = 0
x = - 2
x - 6 = 0
x = 6
Is this a function or not a function? (Picture)
Answer:
a function
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The function has more than one point on one line of Y.
3/4of 16/27/23/14+12/18 using bodmas rule
Use the graph of f(x) provided to answer the question. What is f(f(-4)?
Answer:
f(f(-4) = -2
Step-by-step explanation:
f(f(-4))
First find the value of f(-4)
f(-4) = 2
Now find f(2)
f(2) = -2
The formula I = PRT where I = Interest, P = Principal, R = rate, and T = Time is used to calculate the amount of simple interest earned, solve this formula for T
I = PRT
Divide both sides by PR
I/(PR) = T
x^2-10x+27 in the form (x-a)^2+B
Answer:
(x-5)^2+2
Step-by-step explanation:
To convert between standard and vertex form, you have to complete the square (which, as a reminder, (a+b)^2 = a^2+2ab+b^2).
Since a^2 is x^2, and 2ab is -10x, then b must be -5, so b^2 is 25. Therefore, we add and subtract 25 from the expression:
(x-10x+25)+27-25
Then, we can make (x-10x+25) to (x-5)^2:
(x-5)^2+2
Suppose you are working with a data set that is normally distributed, with a mean of 350 and a standard deviation of 48. Determine the value of x from the following information.
a. 70% of the values are greater than x.
b. x is less than 10% of the values.
c. 24% of the values are less than x.
d. x is greater than 60% of the values.
Answer:
324.848
288.464
316.112
337.856
Step-by-step explanation:
Given that :
Mean (m) = 350
Standard deviation (σ) = 48
Determine the value of x for the following :
Using the z probability calculator :
a.) 70% of the values are greater than x.
1 - 0.7 = 0.3
P(x < 30%) = P(x < 0.3) = - 0.524 = z
Z = (x - m) / σ
x = (z * σ) + m
X = (- 0.524 * 48) + 350 = 324.848
b.) x is less than 10% of the values.
P(x < 0.1) = - 1.282 = z
X = (- 1.282 * 48) + 350 = 288.464
C.) 24% of the values are less than x
P(x < 0.24) = - 0.706 = z
X = (- 0.706 * 48) + 350 = 316.112
D.) x is greater than 60% of the values
P(x > 0.6) = -0.253 = z
X = (- 0.253 * 48) + 350 = 337.856
Whats 28,456 +92 / 2 * 8 + 3?
Answer:
37485947
Step-by-step explanation:
Answer:
I think that the answer is 28827
.............................
4. What is 44% of 35?
Answer:
15.4
Step-by-step explanation:
35 x 0.44 = 15.4
1 point) The joint probability mass function of XX and YY is given by p(1,1)=0.1p(2,1)=0.1p(3,1)=0.05p(1,2)=0.05p(2,2)=0.3p(3,2)=0.1p(1,3)=0.1p(2,3)=0.05p(3,3)=0.15 p(1,1)=0.1p(1,2)=0.05p(1,3)=0.1p(2,1)=0.1p(2,2)=0.3p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.15 (a) Compute the conditional mass function of YY given X=3X=3: P(Y=1|X=3)=P(Y=1|X=3)= P(Y=2|X=3)=P(Y=2|X=3)= P(Y=3|X=3)=P(Y=3|X=3)= (b) Are XX and YY independent? (enter YES or NO) (c) Compute the following probabilities: P(X+Y>2)=P(X+Y>2)= P(XY=3)=P(XY=3)= P(XY>1)=P(XY>1)=
Answer:
Step-by-step explanation:
The given information shows that X and Y are two variables with joint probability distribution as follows:
X/Y 1 2 3 Total
1 0.1 0.05 0.1 0.25
2 0.1 0.3 0.05 0.45
3 0.05 0.1 0.15 0.3
Total 0.25 0.45 0.3 1.00
Thus, the required probability is:
[tex]P(Y = 1|X=3) = \dfrac{P(Y=1,X=3)}{P(X=3)}[/tex]
[tex]P(Y = 1|X=3) = \dfrac{0.05}{0.1}[/tex]
[tex]P(Y = 1|X=3) =0.5[/tex]
The calculated probability value of Y =1, given that X = 3 is 0.5
[tex]P(Y = 2|X=3) = \dfrac{P(Y=2,X=3)}{P(X=3)}[/tex]
[tex]P(Y = 2|X=3) = \dfrac{0.1}{0.1}[/tex]
[tex]P(Y = 2|X=3) = 1.00[/tex]
The calculated probability value of Y =2, given that X = 3 is 1.00
[tex]P(Y = 3|X=3) = \dfrac{P(Y=3,X=3)}{P(X=3)}[/tex]
[tex]P(Y = 3|X=3) = \dfrac{0.15}{0.1}[/tex]
[tex]P(Y = 3|X=3) =1.5[/tex]
The calculated probability value of Y =3, given that X = 3 is 1.50
B.
From the joint probability distribution table, we can see that the probability value of the intersection X = 3 and Y = 3 is 1.50
i.e
P(X =3, Y =3) = 1.5
However;
the marginal probability of X = 0.3
the marginal probability of Y = 0.3
P(X =3)(Y=3) = 0.3 × 0.3 = 0.09
∴
≠ P(X =3)(Y=3)
Thus;
NO, the random variables X and Y are not independent.
C.
P(X+Y > 2) = P(X =2, Y = 1) + P( Y =2, X=1) + P(Y = 3, X= 1) + P( Y =2, X=2) +
P(Y =3, X=2) + P(Y =1, X =3) + P( Y =2, X =2) +P(Y =3, X =3)
P(X+Y > 2) = 0.1 + 0.05 + 0.1 + 0.3 + 0.05 + 0.05 + 0.1 + 0.15
P(X+Y > 2) = 0.9
P(XY =3) = P(X =2, Y =1 ) + P( Y =1 , X = 2)
P(XY =3) = 0.10 + 0.05
P(XY =3) = 0.15
P(XY > 1) = 0.1 + 0.05 + 0.1 + 0.1 + 0.3 + 0.05 + 0.05 + 0.1 + 0.15
P(XY > 1) = 1.00
