Answer:
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{11}{2}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x - 6 ← is in slope- intercept form
with slope m = 2
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , thus
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (1, 5) into the partial equation
5 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = 5 + [tex]\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{11}{2}[/tex] ← equation of perpendicular line
1. Calculate your total revenue for the summer at each price. w a. $25.00 per lawn x 35 lawns per weekx 12 weeks = b. $30.00 per lawn x 20 lawns per weekx 12 weeks = c. $35.00 per lawn x 5 lawns per weekx 12 weeks =
Step-by-step explanation:
Average Cost to Mow a Lawn Per Square Foot
Most mowing pros do not charge by the square foot. For smaller properties, expect to pay between $0.01 and $0.04 per square foot.
National Average: $132
Typical Range: $49 - $219
Low End - High End: $30 - $520
Suppose your car averages 38 miles per gallon on the high-
way if your average speed is 55 miles per hour, and it aver-
ages 32 miles per gallon on the highway if your average speed
is 70 miles per hour.
a. What is the driving time for a 2000-mile trip if you drive
at an average speed of 55 miles per hour? What is the driving
time at 70 miles per hour?
b. Assume a gasoline price of $2.55 per gallon. What is the
gasoline cost for a 2000-mile trip if you drive at an average
speed of 55 miles per hour? What is the gasoline cost at
70 miles per hour?
Some one please help me on these questions! They’re getting a little harder now!!
Answer:
a. around 36.36 hours; around 28.57 hours
b. $134.21; $159.38
Step-by-step explanation:
a. The driving time at 70 miles per hour is 28.57 hours
b The gasoline cost for this trip would be $159.38.
How to calculate the costa. At an average speed of 55 miles per hour:
Time = 2000 miles / 55 miles per hour = 36.36 hours
At an average speed of 70 miles per hour:
Time = 2000 miles / 70 miles per hour = 28.57 hours
b. At an average speed of 55 miles per hour:
The car averages 38 miles per gallon on the highway.
Therefore, the gasoline required for a 2000-mile trip would be: 2000 miles / 38 miles per gallon = 52.63 gallons
The gasoline cost for this trip would be: 52.63 gallons * $2.55 per gallon = $134.13.
At an average speed of 70 miles per hour:
The car averages 32 miles per gallon on the highway.
Therefore, the gasoline required for a 2000-mile trip would be: 2000 miles / 32 miles per gallon = 62.50 gallons.
The gasoline cost for this trip would be: 62.50 gallons * $2.55 per gallon
= $159.38.
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write a real world problem for the following experssions. m+9
Answer:
A number increased by 9.
Step-by-step explanation:
A number= can be denoted by any letter.
increased= +
by 9= 9
Hope this helps ;) ❤❤❤
royal paid 48 dollars for 12 cartons of orange juice. wha is the unit rate per carton of orange juice that royal paid
Answer:
$4
Step-by-step explanation:
If 1 carton is $4 than 12 cartons would be 48 dollars because 12*4 is 48. So each carton is $4. Please give brainliest Thanks
Why does 9,324 have a different value than 9,234?
One way to determine this is to take the difference of numbers.
If the difference results in 0 then we can assume numbers that we subtracted are the same, mathematically:
[tex]a-a=0\implies a = a[/tex]
So,
[tex]9324-9234=90\implies 9324\neq9234[/tex].
Hope this helps.
Step-by-step explanation:
9,324 have a different value than 9,234 because 9,324 is greater than 9,234.
9,324-9,234=90
9,324 is 90 more than 9,234.
A maritime flag is shown. What is the area of the shaded part of the flag? Explain
or show your reasoning.
8 in
6 in
6 in
4 in
Answer:
[tex]Area = 72in^2[/tex]
Step-by-step explanation:
Your question is incomplete without an attachment (See attachment)
Required
Determine the area of the shaded part
From the attachment;
Assume that the shaded portion is closed to the right;
Calculate the Area:
[tex]Area_1 = Length * Width[/tex]
[tex]Area_2 = 8in * (6in + 6in)[/tex]
[tex]Area_2 = 8in * 12in[/tex]
[tex]Area_1 = 96in^2[/tex]
Next;
Calculate the Area of the imaginary triangle (on the right)
[tex]Area_2 = \frac{1}{2} * base * height[/tex]
[tex]Area_2 = \frac{1}{2} * (6in + 6in) * 4in[/tex]
[tex]Area_2 = \frac{1}{2} * 12in * 4in[/tex]
[tex]Area_2 = \frac{1}{2} * 48in^2[/tex]
[tex]Area_2 = 24in^2[/tex]
Lastly, calculate the Area of the Shaded Part
[tex]Area = Area_1 - Area_2[/tex]
[tex]Area = 96in^2 - 24in^2[/tex]
[tex]Area = 72in^2[/tex]
Hence,
The area of the shaded part is 72in²
In a report prepared by the Economic Research Department of a major bank the Department manager maintains that the average annual family income on Metropolis is $48,432. What do you conclude about the validity of the report if a random sample of 400 families shows and average income of $48,574 with a standard deviation of 2000?
Answer:
This report is valid
Step-by-step explanation:
We use this z score formula to solve for a question where a random number of samples is given:
z-score is z = (x-μ)/σ/√n
where x is the raw score
μ is the population mean
σ is the population standard deviation
n = number of samples
When σ/√n = Standard error
From the above question,
x = $48,574
μ = $48,432
σ = 2000
n = 400 families
z = $48, 574 -$48,432/(2000/√400)
= $48, 574 -$48,432/(2000/20)
= $48, 574 -$48,432/100
= 1.42
The z score is 1.42
H0 = μ = $48,432
At 0.05, we reject H0 if z < - 1.96 or > 1.96
z = 1.42
Therefore, H0 cannot be rejected.
The central limit theorem also holds because a sufficiently large amount of random samples (400) where taken from the population and replaced and this causes the mean to be randomly distributed.
Therefore, from the above z score, what we can conclude about the validity of the report is that the REPORT IS VALID because H0 cannot be rejected and the central limit theorem holds.
What number makes the equation true 9= 18 ÷?
Answer:
2
Step-by-step explanation:
9= 18 ÷x
Multiply each side by x
9x = 18
Divide each side by 9
9x/9 = 18/9
x = 2
Answer:
[tex]2[/tex]
Step-by-step explanation:
[tex]9=18[/tex] ÷ [tex]?[/tex]
Let's solve your equation and make it true.
[tex]9+9=18[/tex]
Since we added 9 twice, it would be *2. So now it would be 9*2 = 18. So 18 divided by 9 would be 2.
So, [tex]9=18[/tex] ÷ [tex]2[/tex]
So now you got your answer!
Hope this helps!
Prove that \P(A) \cup \P(B) \subseteq \P(A \cup B) and find a counter-example to show that we don't always have equality
Answer:
P(A) ∪ P(B) ⊆ P(A ∪ B) can be proved when [tex]X[/tex] ∈ P ( A U B )
Step-by-step explanation:
To Prove that P(A) ∪ P(B) ⊆ P(A ∪ B) is attached below and also a counter example to prove that we do not always get an equality is attached below as well
Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = (x2 − 1)3, [−1, 2]
Given :
[tex]F(x)=3(x^2-1)[/tex]
To Find :
the absolute minimum and absolute maximum values of f on the given interval
[-1,2] .
Solution :
Now , getting first order differential equation and equating its equal to zero.
[tex]\dfrac{d(3x^2-3)}{dx}=0\\\\6x=0\\x=0[/tex]
So , x=0 is critical point .
Now , coefficient of [tex]x^2[/tex] is positive .
Therefore , it is increasing function after x=0 .
So , min value will be at , x=0.
[tex]Min = (0^2-1)\times 3=-3[/tex]
And maximum value will be the maximum at the x=2 because it is increasing function .
[tex]Max=(2^2-1)\times 3=9[/tex]
Therefore , max and min value is 9 and -3 respectively .
Hence , this is the required solution .
slope m=-1/2 passing through (2,-8)
I hope this helps you
the theoretical probability choosing a purple marble out of a 2/3 bag is. The bag has 16 purple marbles. How many marbles are in the bag?
Answer:
24 marbles
Step-by-step explanation:
P( purple) = 2/3 = purple/total
2/3 = 16/total
Using cross products
2 * total = 3 *16
2 * total = 48
total = 24
There are 24 marbles
21. Name 8 different rays.
22. Name 2 pairs of opposite rays.
23. Name 2 lines that intersect at point Z.
W
24. Draw three noncollinear points A, B, and C. Sketch. AB Then add a point D and
sketch CD so that CD intersects AB at point B.
Focus
00
8
Answer:
See below
Step-by-step explanation:
21. Name 8 different rays.
ZX, ZY, ZV, ZW, XY, YX, VW, WV22. Name 2 pairs of opposite rays.
ZX and ZY, ZV and ZW23. Name 2 lines that intersect at point Z.
XY and VW24. Draw three noncollinear points A, B, and C. Sketch. AB Then add a point D and sketch CD so that CD intersects AB at point B.
See attachedThe ratio of yes votes to no votes was 4 to 7. If there were 4746 no votes, what was the total number of votes?
Answer:
7458
Step-by-step explanation:
I hope this helps you
A certain element has a half life of 2.5 billion years. a. You find a rock containing a mixture of the element and lead. You determine that 45% of the original element remains; the other 55% decayed into lead. How old is the rock? b. Analysis of another rock shows that it contains 65% of its original element; the other 35% decayed into lead. How old is the rock?
Answer:
Step-by-step explanation:
For a first order decay, fraction remaining = 0.5n where n = number of half lives elapsed.
fraction remaining = 55% = 0.55
0.55 = 0.5n
log 0.55 = n log 0.5
-0.2596 = -0.301 n
n = 0.8625 = # of half lives elapsed
0.8625 half lives x 2.5 billion years/half live = 2.16 billion years have elapsed = age of the rock
b) 0.15 = 0.5n
log 0.15 = n log 0.5
-0.824 = -0.301 n
n = 2.74 half lives
2.5 billion years/half life x 2.74 half lives = 6.85 billion years = age of rock
Find the value of x. Round you answer to the nearest tenth.
20
18
X
Answer:
21.9
Step-by-step explanation:
The altitude of an isosceles triangle bisects the base. So, x represents the hypotenuse of a right triangle with legs of 9 and 20. It can be found using the Pythagorean theorem:
x^2 = 9^2 +20^2 = 81 +400
x = √481 ≈ 21.932
The length x is about 21.9 units.
—7times(—8) help plz
Answer:
[tex]56[/tex]
Step-by-step explanation:
[tex]-7*(-8)[/tex]
The only one thing we have to do on this question is simplify.
[tex](-7)(-8)[/tex]
And this equals
[tex]56[/tex]
Now you got your answer!
Hope this helps!
The solution to the expression -7 times (-8) is 56
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
-7 times (-8)
Express using product expression
So, we have
-7 times (-8) = -7 * -8
Evaluate all the products in the expression
so, we have the following representation
-7 times (-8) = 56/1
Evaluate all the quotients in the expression
so, we have the following representation
-7 times (-8) = 56
Lastly, we have
-7 times (-8) = 56
Hence, the solution is 56
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Solve 2x + 2 > 10
A. x < 6
B. x > 4
C. x > 6
D. x < 4
Answer:
2x + 2 > 10
2x > 10 - 2
2x > 8
x > 8
B. x > 4.
Answer:
B. x>4
Step-by-step explanation:
2x + 2 > 10
In order to solve this inequality, we must isolate the variable, x , on one side of the inequality.
2 is being added to 2x. The inverse of addition is subtraction. Subtract 2 from both sides of the inequality.
2x+ (2-2) > 10-2
2x > 10-2
2x > 8
x is being multiplied by 2. The invers of multiplication is division. Divide both sides of the inequality by 2.
2x/2 > 8/2
x > 8/2
x > 4
The solution to the inequality 2x+2 > 10 is x > 4 and the correct answer is B.
m+q+ p; use m = 2, p = 1, and q = 3
You are at a family reunion and the cooler contains ten bottles of soda; four Sprite, three Dr. Pepper, and three Cherry Coke. Three times, you randomly pick up a drink for your grandmother. The first time, you get a Dr. Pepper. The second and third times, you get Cherry Coke. What is the probability of getting Dr. Pepper the fourth time and then an Dr. Pepper the fifth time without replacement?
Answer:
[tex]Probability = \frac{18}{1860480}[/tex]
Step-by-step explanation:
Given
Soda = 10
Sprite = 4
Dr. Pepper = 3
Cherry Coke = 3
Required
Determine the probability of picking Dr. pepper the fourth and fifth
First, we need to sum up the number of drinks
[tex]Total = 10 + 4 + 3 + 3[/tex]
[tex]Total = 20[/tex]
First Selection: Dr. Pepper
[tex]P_1= \frac{3}{20}[/tex]
Since its probability without replacement;
At this stage: Dr. Pepper = 2 and Total = 19
Second Selection: Cherry Coke
[tex]P_2= \frac{3}{19}[/tex]
At this stage: Dr. Pepper = 2; Cherry Coke = 2 and Total = 18
Third Selection: Cherry Coke
[tex]P_3= \frac{2}{18}[/tex]
[tex]P_3= \frac{1}{9}[/tex]
At this stage: Dr. Pepper = 2; Cherry Coke = 1 and Total = 17
Fourth Selection: Dr. Pepper
[tex]P_4= \frac{2}{17}[/tex]
At this stage: Dr. Pepper = 1; Cherry Coke = 1 and Total = 16
Fifth Selection: Dr. Pepper
[tex]P_5= \frac{1}{16}[/tex]
Multiply the calculated probabilities, to give the required probability
[tex]Probability = P_1 * P_2 * P_3 * P_4 * P_5[/tex]
[tex]Probability = \frac{3}{20} * \frac{3}{19} * \frac{1}{9} * \frac{2}{17} * \frac{1}{16}[/tex]
[tex]Probability = \frac{3 * 3 * 1 * 2 * 1}{20 * 19 * 18 * 17 * 16}[/tex]
[tex]Probability = \frac{18}{1860480}[/tex]
Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used. He has another gift card for $145 that loses $3.50 for each 30-day period it is not used. Write an equation for the number of 30-day periods until the value of the gift cards will be equal. Let x represent the number of 30-day periods.
Answer:
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
Step-by-step explanation:
Let x represent the number of 30-day periods.
Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used.
Therefore the equation =
$165 -$4 × x
= 165 - 4x.......... Equation 1
He has another gift card for $145 that loses $3.50 for each 30-day period it is not used.
$145 -$3.50 × x
= 145 - 3.50x........... Equation 2
Hence, an equation for the number of 30-day periods until the value of the gift cards will be equal is obtained by equating Equation 1 and Equation 2 together
So, we have
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
We simplify further:
165 - 145 = -3.50 + 4.0x
20 = 0.5x
x = 20/0.5
x = 40
Therefore, number of each 30-day periods until the value of the gift cards will be equal is 40
Ms. Sanders invested in a stock. During the first year, the value of the stock tripled. The next year, the value of the stock decreased by $600. Write an expression that can be used to represent the value of her stock at the end of the second year. Be sure to indicate what the variable in your expression represents. (please help I am lost)
Answer:
Value in $= 3x -600
Step-by-step explanation:
Let the value of the stock before investment= x
At the first year , the value tripled
Value after first year=3x
The second year , the stock reduces by $600.
So
The value of the stock after the second year
Value in $= 3x -600
A bicycle wheel with diameter 16 inches rides over a screw in the street. The screw is on level ground before it
punctures the bike's tire. After the bike has moved forward another 56 inches, how high above the ground is the
screw? Round to the nearest tenth of an inch.
O 4 inches
O 8 inches
O 12 inches
O 16 inches
Answer:
16 inches
Step-by-step explanation:
Note: it should say 56π inches instead of 56 inches otherwise no option is correct
Given
Diameter of the wheel = 16 inFull circumference of the wheel
C =πd = 16πBike moves
56πThe wheel turns:
56π /16π = 3.5 timesWe only consider her 0.5 of full turn of the wheel to identify the screw position
Since we consider the turns from the ground level as the initial position of the screw, the screw position in the end will be half turn opposite to ground level.
This is the full diameter length, which is 16 inches
So correct answer option is 16 inches
Find the volume of a sphere with a diameter of 3 cm.
Answer:
9/2π
=14.13716694
Step-by-step explanation:
The equation of the volume of the sphere:
V=4/3πr^3
If the diameter is 3cm, the radius is divided by 2, so 1.5cm.
Plug that in, 4/3π1.5^3
Use a calculator:
9/2π
=14.13716694
[tex]14,14~cm^{3}[/tex]
Step-by-step explanation:d = 3cm = 2r => r = d/2 = 3cm/2 = 1,5 cm
[tex]V=\frac{4}{3}\pi*r^{3}\\\\=\frac{4}{3}*\frac{22}{7}*3.375cm^{3}\\ \\=\frac{4*22*3.375}{21}cm^{3}\\ \\=\frac{297}{21}cm^{3}\\ \\[/tex]
≈ [tex]14,14~cm^{3}[/tex]
Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 3.9288. 6.2597 is the standard deviation of the second sample.
Answer:
F test = 2.54
Step-by-step explanation:
We are given two samples
Standard deviation of the first sample = 3.9288
Standard deviation of the second sample = 6.2597
F test statistic = Variance of the Larger sample/ Variance of the smaller sample
Variance = (Standard deviation)²
Variance for the first sample = 3.9288²
= 15.43546944
Variance for the second sample = 6.2597² = 39.18384409
F test = 39.18384409/15.43546944
= 2.5385586258
Therefore, the F test approximately = 2.54
Answer:
2.539
Step-by-step explanation:
Standard deviation of sample 1 = 3.9288
Standard deviation of sample 1 = 6.2597(
Standard deviation = √variance
Variance = (standard deviation)^2
Variance of sample 1 = (3.9288)^2 = 15.43546944
Variance of sample 2 = (6.2597)^2 = 39.18384409
For two samples:
F stat = (variance 1) / (variance 2)
Since the variance of sample is large, we place it in th e numerator
F stat = (39.18384409) / (15.43546944)
F stat = 2.5385586
F stat = 2.539
Factor 9x2 - 4y2 Group of answer choices
(3x - 2y) (3x + 2y )
(3x - 2y) (3x - 2y )
(x - 2y) (x + 2y )
(3x - y) (3x + y )
Answer:
(3x-2y)(3x+2y)
Step-by-step explanation:
Proof:
(3x-2y)(3x+2y)-use FOIL method (First, Outer, Inner, Last)
3x*3x+2y3x-2y3x-2y*2y
9x^2+0-4y^2
9x^2-4y^2
The answer is (3x-2y)(3x+2y).
7m+11=-4(2m+3) answer
Answer:
See below.
Step-by-step explanation:
So we have the equation:
[tex]7m+11=-4(2m+3)[/tex]
Distribute the right:
[tex]7m+11=-8m-12[/tex]
Add 12 to both sides:
[tex]7m+23=-8m[/tex]
Subtract 7m from both sides:
[tex]23=-15m[/tex]
Divide by -15:
[tex]m=-23/15\approx-1.5333[/tex]
Please Help! I'm stuck!
Answer:
C. [tex]5 (\frac{x}{z}) ^1^0[/tex]
Step-by-step explanation:
Hey there!
Given
[tex]\frac{15 x^-^3 z^5}{3 x^7 z ^-^5}[/tex]
Well to solve this we first need to do 15 ÷ 3
= 5
When dividing exponents we actually subtract.
-3 - 7 = -10
5 - -5 = 10
[tex]5 x^-^1^0 z^1^0[/tex]
Hope this helps :)
Answer:
D. 5 (z/x)^10.
Step-by-step explanation:
15/3 = 5
x^-3 / x^7 = x^-10 = 1/x^10
z^5 / z^-5 = z ^10
So the answer is 5 * z^10 * 1/x^10
= 5 z^10 / x^10
= 5 (z/x)^10.
Pablo drew a square that had a side of length of 6 inches. What is the perimeter of pablos square
Answer:
24 inches
Step-by-step explanation:
Because we know that Pablo drew a square, we can correctly assume that all sides have equal lengths. There are four sides to a square, so taking the number 6, 4 times (6*4) gives us 24!
a pack of cinnamon-scented pencils sells for 5.00 dollars what is the sales tax rate if the total cost of the pencils is 5.15
calculate the percentage increase,work out the difference (increase) between the two numbers you are comparing. Then divide the increase by the original number and multiply the answer by 100.
520-500 = 20
20÷500 =.04
.04 ×100= 4%