Step-by-step explanation:
The solution is one-solution
.3(12x-16)=.4(12-3x) (you do the distributive property)
3.6x-4.8=4.8-.12x (you add 1.2 to both sides)
3.6x-3.6=4.8 (You add 3.6 to both sides)
3.6x=8.4 ( You divide 3.6 both numbers)
x=0.4285...
Its a one-solution
A water tank holds 693 gallons but is leaking at a rate of 4 gallons per week. A second water tank holds 924 gallons but is leaking at a rate of 7 gallons per week. After how many weeks will the amount of water in the two tanks be the same?
Answer:
Simple....
you have: one is leaking 3 gallons per week and holds 256 gallons; whereas, the other one is leaking 5 gallons per week and holds 384 gallons.
Set up both the equations....
In y=mx+b form--->>>
y=-3x+256
y=-5x+384
To figure out when they will be equal..set the equations equal to each other....(remember to isolate the variable)
-3x+256=-5x+384
-3x+256=-5x+384
-256 -256
-3x=-5x+128
-3x=-5x+128
+5x+5x
2x=128
x=64
After 64 weeks the amount of water in both tanks will be the same.
Thus, your answer.
1. (5pt) In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also,
12,883 women finished and 163 dropped out. We want to use a 0.01 significance level to test
the claim that the rate of those who finish is the same for men and women.
a) Test the claim using a hypothesis test (identify the null hypothesis, alternative hypothesis,
test statistic, critical value (or P-value) and conclusion)
b) Test the claim by constructing an appropriate confidence interval.
Answer:
(a) Explained below.
(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).
Step-by-step explanation:
The information provided is:
n (Men who finished the marathon) = 25,221
n (Women who finished the marathon) = 12,883
Compute the proportion of men and women who finished the marathon as follows:
[tex]\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988[/tex]
The combined proportion is:
[tex]\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989[/tex]
(a)
The hypothesis is:
H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.
Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.
Compute the test statistic as follows:
[tex]Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78[/tex]
Compute the p-value as follows:
[tex]p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075[/tex]
The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.
Thus, concluding that the rate of those who finish is the same for men and women.
(b)
Compute the 99% confidence interval for the difference between proportions as follows:
The critical value of z for 99% confidence level is 2.58.
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]
[tex]=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\[/tex]
Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).
Write two hundred thousand and fifty seven in figures
The Historic Triangle in Virginia connects Jamestown, Williamsburg, and Yorktown. The interior angle at Williamsburg is 120°. The interior angle at Jamestown is twice the measure of the interior angle at Yorktown. Find the measures of the interior angles at Jamestown and Yorktown.
Answer: Interior angles at Jamestown and Yorktown are 40° and 20°, respectively
Step-by-step explanation: Jamestown, Williamsburg and Yorktown form a triangle. The sum of the interior angles of a triangle is 180°.
Suppose interior angle at Yorktown is x. As Jamestown is twice the measure at Yorktown, it means this interior angle is 2x.
Then, the measures will be:
2x + x + 120 = 180
3x = 60
x = 20
Angle at Yorktown is 20°.
So, angle at Jamestown is
2x = 2.20 = 40°
The measures of the interior angles at Jamestown and Yorktown are 40° and 20°, respectively.
A cyclist estimates that he will bike 80 miles this week. He actually bikes 75.5 miles. What is the percent error of the cyclist's estimate? Round the percent to the nearest hundredth if necessary.
Answer:
6%
Step-by-step explanation:
Estimated distance = 80 miles
Actual distance covered = 75.5 miles
We need to find the percent error of the cyclist's estimate. Its formula is given by :
[tex]\%=\dfrac{|\text{actual value-estimated value}|}{\text{actual value}}\times 100[/tex]
Put all the values,
[tex]\%=\dfrac{80-75.5}{75.5}\times 100\\\\=5.96\%[/tex]
or
= 6%
So, the percentage error is 6%.
Answer:
5.96
Step-by-step explanation:
y/2 = 9 What is the value of y that satisfies the equation
Answer:
y=18
Step-by-step explanation:
pls give brainliest
Identify the equation in slope-intercept form for the line containing the point (2,4) and perpendicular to y=1/2x+1/2.
Answer:
y = − 2 x
Step-by-step Explanation:
Y + 2 = − 2 ⋅ ( − 1 ) Write in y = m x + b form.
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
m in perpendicular = − 1 2
(1,-2),y=(1)/(2)x+4
I hope I helped!
Answer:
y = -2x + 8
Step-by-step explanation:
For this problem we need to consider that the equation of a line perpendicular to another line will have a "negative reciprocal" slope so that when they cross, it forms a 90-degree angle, hence perpendicular. Additionally, we will need to use the point-slope form and re-write it into the slope-intercept form to incorporate (2,4) into our equation. With these things in mind, let's do that.
y = (1/2)x + (1/2)
We want a "negative reciprocal" so:
y = -2x + (1/2)
Since -2 is the "negative reciprocal" of 1/2.
And now we want to use the point-slope form to incorporate (2,4)
y - y0 = -2 ( x - x0 )
Where, y0 = 4 and x0 = 2.
y - y0 = -2 ( x - x0 )
y - 4 = -2 ( x - 2 )
y - 4 = -2x + 4
y = -2x + 8
So, the equation that is perpendicular to y = (1/2)x + (1/2) and includes the point (2,4) is y = -2x + 8.
Cheers.
Which values for x make this inequality true?
−15x+4≤39
Answer:
x ≥ -7/3
Step-by-step explanation:
General Formulas and Concepts:Pre-Algebra
Order of Operations: BPEMDASBrackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Left to Right
Equality Properties
Step-by-step explanation:
Step 1: Define Inequality
-15x + 4 ≤ 39
Step 2: Solve for x
Subtract 4 on both sides: -15x ≤ 35
Divide -15 on both sides: x ≥ -7/3
Here we see that any value x greater than or equal to -7/3 would work as a solution to the inequality.
help plzz Charli pays $18.00 for 5 t-shirts he needs your help to answer the following questions.
Answer:
What do you but in the chart? Also, part 2 is 72
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
If each t-shirt costs 3.6 dollars then you would have to multiply 3.6 by 20 shirts which will equal to 72. So Charlie has to pay 72 dollars for 20 shirts.
What is a good estimate for 1,710 2,740 4.322 5,700 7,810 6,395
Answer: If you want to round is so you have a small amount of decimals, you could round to the nearest tenths which would give you 17,102,740 4.3
Step-by-step explanation:
The greater of two integers is 10 more than twice the smaller integer. The sum of the two integers is -8. Find the integers.
Answer:
-6, -2
Step-by-step explanation:
At the bookstore, Tim bought a magazine for $4, and five books that all cost the same amount. He spent a total of $129. Which equation expresses how much each book cost?
Answer:
25(b) + 4 = 129
Step-by-step explanation:
b=5
25(5) + 4=129
These fraction are part of a list of students quiz scores. Choose ALL scores that are equal to 80%
A.) 8/20
B.) 8/10
C.) 24/30
D.) 16/20
E.) 16/30
Answer:
B and D
Step-by-step explanation:
I'm pretty sure but definitely B
Find the slope of the line passing through the points (-7, -4) and (8,8).
Answer:
Hope its work for you
Step-by-step explanation:
As we know that,
slope=m=(Y2-Y1)/(X2-X1)As given values
take, (X1,Y1)=(-7,-4)
(X2-Y2)=(8,8)
hence X1=-7 , Y1= -4 , X2=8 , Y2= 8
putt the values in the above equation of slope we get ,
m=(8-(-4))/(8-(-7)
m=12/15 AnsAnswer:
0.8
Step-by-step explanation:
Slope=(y2-y1) (8--4) (12)
(x2-x1)= (8--7)= (15)= 0.8
What is the third term of the expression
4x+8y+12xy
Answer:
12xy
Step-by-step explanation:
Each term is separated by a function sign. In this case, an addition symbol.
Antwaun waters his lawn 3 times a week. If he watered his lawn 24 times in all, which equation could be used to find how many weeks he has been watering his lawn?
(It's not 8, I know that) PLEASE HURRY
Answer:
Antwanun waters his lawn 3 times a week, he watered his lawn 24 . So what you will need to do is divide 3 in 24 to find how many weeks he has been watering his lawn, You get 8. Mr. Antwanun has been watering for 8 weeks. Equation- Antuwantun waters his lawn 3 times a week so if he watered his lawn 24 times, 3 times a week he would have been watering his lawn for 8 weeks.
Answer:
3x=24
Step-by-step explanation:
3 times a certain amount equals 24 times in total
given f (x) = 5x + 1, find f (-3)
Answer:
f(- 3) = - 14
Step-by-step explanation:
To evaluate f(- 3), substitute x = - 3 into f(x), that is
f(- 3) = 5(- 3) + 1 = - 15 + 1 = - 14
Select all the true statements.
- 1.9 is to the left of -1.48.
-1.9 is to the right of -1.48.
1.9 is closer to 0.
-1.48 is closer to 0.
-1.48 is less than – 1.9.
-1.48 is greater than -1.9.
Answer:
-1.9 is to the left of -1.48.
-1.48 is closer to 0.
-1.48 is greater than -1.9.
Answer:
statements 1,4,5
Step-by-step explanation:
If f(x) = 4-x* and g(x) = 6x, which expression is equivalent to (g -)(3)?
O 6-3- (4 + 3)²
O6-3- (4- 3)
O 6(3) -4 +32
O 6(3) –4 -32
Answer:
The expression that equivalent to (g - f)(3) is 6(3) - 4 + 3² ⇒ C
Step-by-step explanation:
Let us solve the question
∵ f(x) = 4 - x²
∵ g(x) = 6x
→ Find at first (g - f)(x) by subtracting f(x) from g(x)
∵ (g - f)(x) = 6x - (4 - x²)
→ Remember (-)(+) = (-) and (-)(-) = (+)
∴ (g - f)(x) = 6x - 4 + x²
→ Substitute x by 3 to find (g - f)(3)
∵ (g - f)(3) = 6(3) - 4 + (3)²
∴ (g - f)(3) = 6(3) - 4 + 3²
The expression that equivalent to (g - f)(3) is 6(3) - 4 + 3²
please help me i’ve tried so many of these and i can’t figure out how to do it
Answer:
15.4%
Step-by-step explanation:
Calculate the volume of both containers.
The volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
[tex]V_{A}[/tex] = π × 10² × 11 = 1100π ft³
[tex]V_{B}[/tex] = π × 7² × 19 = 931π ft³
Subtract volume of B from volume of A to find quantity left in A
quantity left in A = 1100π - 931π = 169π ft³
To calculate the percentage left in A after B has been filled
[tex]\frac{left}{full}[/tex] × 100%
= [tex]\frac{169\pi }{1100\pi }[/tex] × 100%
= [tex]\frac{169}{1100}[/tex] × 100%
= 15.4% ( to the nearest tenth )
Solve by using substitution. Express your answer as an ordered pair.
ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!
In how many years will $12,000 yield an interest of $4,800 at 10% simple interest? *
A. 25 years
B. 0.04 year
C. 4 years
D. 0.25 years or 3 months
Answer:
Time= 4 years
Step-by-step explanation:
Giving the following information:
Principal (P)= $12,000
Interest rate (r)= 10% = 0.10
Interest earned (I)= $4,800
To calculate the time required to gain $4,800 interest, we need to use the following formula:
T= I / (P*r)
T= 4,800/(12,000*0.1)
T= 4 years
What is the general form of the equation of the line shown?
Answer:
the general form of the equation of the line will be:
[tex]y-x=2[/tex]
Step-by-step explanation:
Finding the slope:
Taking two points from the line as shown in figure
(-2, 0)(0, 2)Finding the slope between (-2, 0) and (0, 2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:2\right)[/tex]
[tex]m=\frac{2-0}{0-\left(-2\right)}[/tex]
[tex]m=1[/tex]
Finding the y-intercept
We know that the y-intercept can be calculated by setting x=0
From the figure, it is clear that at x=0, y=2
Thus, the y-intercept is (0, 2)
We know that the slope-intercept form of the equation line is:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
As we have already determined the slope = m = 1 and the y-intercept b=2.
Substituting the values in the slope-intercept form of the equation line
[tex]y=mx+b[/tex]
[tex]y=(1)x+2[/tex]
[tex]y=x+2[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
As we already know the equation in slope-intercept form
[tex]y=x+2[/tex]
so just simplify the equation to write in standard form
[tex]y-x=2[/tex]
Thus, the general form of the equation of the line will be:
[tex]y-x=2[/tex]
I beg you to help me .
Answer:
16+3=y
y=19
Step-by-step explanation:
What is the value for 3-2m<7
Answer:
m>−2
Step-by-step explanation:
3-2m<7
subtract 3 from both sides
-2m<4
divide by 2
m>−2
Penelope earned $50 in May. She earned $60 in June.
What is the percent increase or decrease in Penelope's monthly earnings?
A. 30% decrease
B. 25% increase
C. 20% decrease
D. 20% increase
b)25%
espero ter ajudado
Someone please help I absolutely suck at these
Answer:
I believe it is C
Step-by-step explanation:
is this proportional relationship? please help!!
Answer:
yes, the slope is the same throughout the table
Step-by-step explanation:
Answer:
Yes, the graph shown is a proportional relationship.
Step-by-step explanation:
If you divide the distance (6) by the time (1) you get the same thing (6). Repeat for all the terms in the graphs. Since 6/1 is 6, 12/2 is 6, 18/3 is 6 and 24/4 is 6, The relationship is proportional.
DO IT ASAP ONLY 3 PROBLEMS Please find x thanks!!! (There’s a link)
1.) x = 3.5
2.) x = -40
3.) x = -10
. Austin wants to buy some pens and pencils. He has $30 in his bag. Each pen costs $5 and each pencil costs $1.50. He needs 5 more pencils than pens.Part A how many pencils can $ustin buy at most" Write your answer and your work or explanation in the space below. Part If Austin had $40 in his bag, how many pens could Austin buy at most" Explain how you found the answer in the space below.
Answer:
3 pens
Step-by-step explanation:
Total expenditure (Price x Quantity) on pens & pencils = $30
Let pen quantity be = x , Let pencil quantity be = y
Given : Pen (x) price = 5 , Pencil (y) price = 1.5 , Pencils (y) = Pen (x) + 5
So, 5x + 1.5y = 30
5x + 1.5 (x + 5) = 30 → 5x + 1.5x + 7.5 = 30 → 6.5x + 7.5 = 30
6.5x = 30 - 7.5 → 6.5x = 22.5
x = 22.5 / 6.5 → x = 3.46 ≈ 3 pens