Answer:
Dimensions of rectangular garden:
x = 25 feet ( sides along the driveway)
y = 50 feet
Step-by-step explanation:
Rectangular area is:
A(r) = x*y (1)
if we call x one the driveway side the cost of that side will be
6*x
The cost of the other side parallel to driveway side is 2*x and cost of the others two sides are 4*y
Total costs: C = 6*x + 2*x * 4*y (2)
From equation (1)
A(r) = 1250 = x*y ⇒⇒ y = 1250/ x
Plugging that value in equation (2) we get costs as a function of x
that is:
C(x) = 6*x + 2*x + 4* 1250/x
Taking derivatives on both sides of the equation
C´(x) = 6 + 2 - 5000/x²
C´(x) = 8 - 5000 /x²
C´(x) = 0 ⇒ 8 - 5000 /x² = 0
8*x² -5000 = 0
x² = 5000/8
x² = 625
x = 25 feet
and y = 1250/ 25
y = 50 ft
C(min) = 50*2*2 + 6*25 + 2*25
C(min) = 200 + 200
C(min) = 400 $
So, the minimum cost is $400.
Area of the rectangle:The area of a rectangle is the region occupied by a rectangle within its four sides or boundaries.
And the formula is,
[tex]A=l\times b[/tex]
Given that,
Area of the garden=1250 square feet.
Let, the length be [tex]x[/tex] and the breadth be [tex]y[/tex] then,
[tex]xy=1250...(1)[/tex]
The total cost of the fence is,
[tex]C(x,y)=6x+2x+4y\\C(x,y)=8x+4y\\C(x)=8x+4(\frac{1250}{x} )\\[/tex]
Now, differentiating the obtained equation we get,
[tex]C'(x)=8-\frac{4\times 1250}{x^2} =0\\x^2=625\\x=25\\y=50[/tex]
Therefore the length is 25 ft
And breadth is 50ft
Now, calculating the minimum cost,
[tex]8(25)+4(50)=50\\=400[/tex]
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Find the distance from the point (1, 4) to the line y = 1/3x – 3. A) 2(square root) 10 units B) 4 units C) 4(square root) 2 units D) 20 units
Answer:
Distance between line and point =
4√5 -3/2√10
Step-by-step explanation:
Distance between the line is
= √ ((9-0)²+(0+1)²)
= √ (89+1)
= √90
= 3√10
Half of the line = 3/2√10
Distance of one side of the line and the point.
= √((9-1)²+(0-4)²)
= √((8)²+(-4)²)
=√64+16
= √80
= 4√5
Distance between line and point =
4√5 -3/2√10
Answer: 2 square root 10 units
Step-by-step explanation: A
the equation of straight line passing through the point (2,3)&perpendicular to the line 4x-3y=10 is
Answer:
4y = -3x +18
Step-by-step explanation:
Let's get the gradient from this line equation first.
4x-3y=10
4x-10=3y
Y= 4/3x -10/3
The gradient is 4/3.
For a line perpendicular to another line.
M*M'= -1
M= -/(4/3)
M = -3/4
So the gradient to be used is -3/4
Formula for solving is
(Y-y1)/(x-x1)= M
X1= 2
Y1= 3
M = -3/4
(Y-y1)/(x-x1)= M
(Y-3)/(x-2)= -3/4
4(y-3)= -3(x-2)
4y -12 = -3x +6
4y = -3x +18
Evaluate f(x) = x2 + 1 for f(-1)
Answer: -1
Step-by-step explanation:
to calculate f(-1), you know that x = -1. so all you have to do is substitute:
f(-1) = (-1)2 + 1
f(-1) = -2 + 1
f(-1) = -1
Answer:
0
Step-by-step explanation:
This is algebra solving linear equations
P+7/20=19/20
Answer:
P = [tex]\frac{19}{7}[/tex] or the decimal answer is 2.71
Step-by-step explanation:
In rhombus MNOP, mMNO = 24. What is the measure of PMO
Given: AD≅ BC and AD ║ BC Prove: ABCD is a parallelogram. Assemble the proof by bragging tiles to the statements and reasons column.
Answer:
Step-by-step explanation:
A parallelogram is a quadrilateral with congruent opposite sides and pair of opposite angles.
Given: parallelogram ABCD
AD≅ BC
AD ║ BC
Thus;
<ABC + DAB = [tex]180^{o}[/tex] (supplementary angle property)
ΔABD = ΔCBD (each diagonal divides a parallelogram into two congruent triangles)
<ABC = <ADC (both pairs of opposite angles are congruent)
<DAB = <BCD (both pairs of opposite angles are congruent)
AB ≅ CD (opposite sides are congruent)
AB ║ DC (pair of opposite sides are parallel)
Therefore, the quadrilateral ABCD is a parallelogram.
Which will provide the largest yield on an annuity after 30 years with 6% annual interest, compounded monthly? Annuity A: Deposit $2400 per year. Annuity B: Deposit $600 per quarter. Annuity C: Deposit $72,000 one lump sum.
Answer:
Annuity C: Deposit $72,000 one lump sum
Step-by-step explanation:
The yield is improved when the money is on deposit for a longer period.
If the $2400 annual deposit is made at the first of the year, then it will yield more than $600 deposits made at the first of each quarter.
If the $72,000 deposit is made at the beginning of the period, the entire amount is earning interest for the entire period.
Annuity C will provide the largest yield.
A stock lost 7 1/8 points on Monday and then another 1 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the net gain or loss of the stock for these three days?
Answer:
It was gained 4 1/4 points.
Step-by-step explanation:
- 7 1/8 - 1 5/8 + 13 = - 8 6/8 + 13 = - 8 3/4 + 13 = - 8 - 3/4 + 12 + 4/4 = 4 1/4
Find the value of x for which line a is parallel to line b. 34 32 68 56
Answer
value of x is 34 degrees
Step-by-step explanation:
7th grade math I need help with this
Answer:
each bag of candy is $6.00
Step-by-step explanation:
1 bag would cost $6.00
1×$6.00=$6.00
6 bags × $6.00 = $36.00
Answer:
the constant of proportionally is 6
the prices of 6 bags of candy is 36
Step-by-step explanation:
to find the constant u divide 6 by 1 to find how they multiplying it by
the prices for six bags is 36 bc u can do 6 times 6 or look at the graph and see that it lands on 36
hope this helps
Please answer this correctly
Answer:
no
Step-by-step explanation:
No, it is not a random sample of the students in school.
Answer:
No
Step-by-step explanation:
A random sample is a sample that is taken from a larger set. Molly specifically chose to interview the youngest students, so the sample is not random.
A nighttime cold medicine’s label indicates the presence of 600 mg of acetaminophen in each fluid ounce of the drug. The FDA randomly selects 65 1-ounce samples and finds the mean content is 595 mg with a standard deviation of 20 mg. Is there evidence that the label is incorrect? Use a= .05.
Answer:
[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]
The degrees of freedom are given by:
[tex]df=n-1=65-1=64[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]
And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg
Step-by-step explanation:
Information given
[tex]\bar X=595[/tex] represent the sample mean
[tex]s=20[/tex] represent the sample standard deviation
[tex]n=65[/tex] sample size
[tex]\mu_o =600[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true mean is different from 600 mg, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 600[/tex]
Alternative hypothesis:[tex]\mu \neq 600[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]
The degrees of freedom are given by:
[tex]df=n-1=65-1=64[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]
And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg
Given a = 4 and b= -2, evaluate -Ib-al.
-2
-6
6
Jose can assemble 12 car parts in 40 minutes. How many minutes
would be needed to assemble 9 parts7
Answer:
12/40=0.3
0.3 car parts per minute
9 / 0.3 = 30 minutes
30 minutes for 9 parts
Hope this helps
Step-by-step explanation:
Jose required 30 minutes to assemble 9 parts.
Jose assemble 12 car parts in 40 minutes. Time consumed by jose to assemble 9 parts to be calculated.
In mathematics it deals with numbers of operations according to the statements.
Here,
40 minute = 12 parts
40/12 = 1 part
Time to assemble 9 parts: = 40/12 x 9
= 10/3 x 9
= 30
Thus, Jose required 30 minutes to assemble 9 parts.
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Three kinds of tickets were sold for a concert. Child tickets are $6, adult tickets are $12, and student tickets are $8. A total of 204 tickets were sold, bringing in a total of $2,008. If 4 more adult tickets were sold than the total number of student and child tickets combined, how many student tickets were sold? Type in your numerical answer only; do not type any words or letters with your answer.
Answer:
The number of children's tickets sold =12The number of adult's tickets sold =100The number of student's tickets sold =92Step-by-step explanation:
Let the number of children's tickets sold =c
Let the number of adult's tickets sold =a
Let the number of student's tickets sold =s
A total of 204 tickets were sold, therefore: c+a+s=204
Child tickets are $6, adult tickets are $12, and student tickets are $8.
Total revenue =$2,008
Therefore:
6c+12a+8s-2008
We are also told that 4 more adult tickets were sold than the total number of student and child tickets combined.
c+s=a+4
We then solve the resulting system of equation.
c+a+s=2046c+12a+8s=2008c+s=a+4Substituting c+s=a+4 into the first equation
c+a+s=204
a+4+a=204
2a=204-4
2a=200
a=100
Substitute a=100 into the second and third equation
6c+12(100)+8s=2008
6c+8s=2008-1200
6c+8s=808
From the third equation
c+s=100+4
c=104-s
Substitute c=104-s into 6c+8s=808
6(104-s)+8s=808
624-6s+8s=808
2s=808-624
2s=184
s=92
Since c=104-s
c=104-92
c=12
Therefore:
The number of children's tickets sold =12The number of adult's tickets sold =100The number of student's tickets sold =92There are 4 answers for a single question on the exam and only one answer is correct. If a student guesses the answer for this question, what is the probability that the student selects the correct answer? (round to 2 decimal places) Answer:
Answer:
Step-by-step explanation:
Each question has 4 options with only one correct answer and all other incorrect answers. Student is equally likely to pick any outcome in any given question. Hence, probability of choosing correct answer is 1/4 = 0.25
mark this as brainly pls.....
Answer:
0.25
Step-by-step explanation:
There are 4 answer choices given and only 1 is correct. The other 3 will be incorrect.
To find the probability of getting the right answer, divide the number of correct answers by the total number of answer.
P(correct answer)=correct/total
There is 1 correct answer out of a total of 4 answer.
P(correct answer)=1/4
The question asks us to round to 2 decimal places.
P(correct answer)=0.25
The probability that the student selects the correct answer is 0.25.
What are the four major categories of securities? How are they evaluated?
Answer:
Cash, Bonds, Stocks and Mutual funds
Step-by-step explanation:
The four major categories of securities are:
Cash Bonds Stocks Mutual fundsThese 4 major categories are evaluated as given below:
Cash: Cash is your normal money. You can use it to buy your everyday goods and services or invest in cash in various asset classes.Bonds: Bond is debt instrument and bonds are the agreement of debt. and bonds carry coupon rate that is (interest equivalent), tenure and final capital repayment Stocks: Ownership of stock in a company. A group (or a single) share of any company is called stock. Stock means you have some stake in the company. Mutual Funds: A mutual fund is an asset basket that can hold cash, bonds, stocks, real estate, and so on. The type and structure of mutual funds will vary depending on the client's choice of the fund manager and the category of the categoryAs part of a physics experiment, Ming drops a baseball from the top of a 315-foot building. To the nearest tenth of a second, for how many seconds will the baseball fall? (Hint: Use the formula h = 16t^2, which gives the distance h, in feet, that a free-falling object travels in t seconds.)
Answer: 4.4 seconds
Step-by-step explanation:
h(t) = -16t² + 315
Since we want to find the total time the baseball is in the air, we need to find the time (t) when the ball lands on the ground --> h(t) = 0
0 = -16t² + 315
-315 = -16t²
[tex]\dfrac{315}{16}=t^2\\\\\\\sqrt{\dfrac{315}{16}}=t\\\\\\\dfrac{\sqrt{315}}{4}=t\\\\\\\large\boxed{4.4=t}[/tex]
Answer:
≈ 4.44 sec
Step-by-step explanation:
h= 315 ft
h= 16t²
315 = 16t²
t²=315/16
t=√315/16 ≈ 4.44 sec
represent 5 20 30 25 10 on a pie chart
Answer :
I have solved for the points.
Explanation :
Just get a protractor and plot out the angles into a circle. Starting with the largest angle.
Jessica is walking home from a friend's house. After two minutes she is 0.8 miles from home. Twelve minutes after leaving, she is 0.3 miles from home. What is her rate in miles per hour
Answer:
3 miles per hour
Step-by-step explanation:
Jessica is walking home from a friend's house.
After 2 minutes she is 0.8 miles from the home and after 12 minutes she is 0.3 miles away fro her house.
Her rate will be = (change in distance)/change in time
= (0.8-0.3)/(12-2)
= 0.5/10
= 0.05 miles per minute
Now we will convert timings from minutes to hour.
Or = 0.05×60
= 3 miles per hour
If f(x) = 3x - 2, find f-1(x).
Answer:
f-1(x)=x/3+2/3
Step-by-step explanation:
Replace f(x) with Y
y=3x-2
interchange variables
x=3y-2
solve for y
rewrite equation
3y-2=x
add 2 to both sides
3y=x+2
divide both side by 3
3y/3=x/3+2/3
Y=x/3+2/3
Answer:
x/3 +2/3
Step-by-step explanation:
Pls and thank u i need help
Answer: see table below
Step-by-step explanation:
Simply add the digit on the left to the digit on the top
1, 2 --> 1 + 2 = 3
3, 4 --> 3 + 4 = 7
4, 2 --> 4 + 2 = 6
6, 6 --> 6 + 6 = 12
[tex]\begin{array}{c|c|c|c}&\underline{\quad 2\quad }&\underline{\quad 4\quad }&\underline{\quad 6\quad }\\\underline{\quad 1 \quad}&\bold{\underline{\quad 3\quad}}&\underline{\quad 5\quad}&\underline{\quad 7\quad}\\\underline{\quad 2 \quad}&\underline{\quad 4\quad }&\underline{\quad 6\quad }&\underline{\quad 8\quad}\\\underline{\quad 3 \quad}&\underline{\quad 5\quad }&\bold{\underline{\quad 7\quad}}&\underline{\quad 9\quad}\\\end{array}[/tex]
[tex]\begin{array}{c|c|c|c}{\underline{\quad 4 \quad}&\bold{\underline{\quad 6\quad }}&\underline{\quad 8\quad }&\underline{\quad 10\quad }\\\underline{\quad 5 \quad}&\underline{\quad 7\quad}&\underline{\quad 9\quad}&\underline{\quad 11\quad}\\\underline{\quad 6 \quad}&\underline{\quad 8\quad }&\underline{\quad 10\quad }&\bold{\underline{\quad 12\quad}}\\\end{array}[/tex]
Someone please help ASAP
Answer:
[tex]\boxed{\sf \ \ \ k = 1 \ \ \ }[/tex]
Step-by-step explanation:
hello,
saying that p-1 is a factor of [tex]p^4+p^2-p-k[/tex]
means that 1 is a root of this expression, so it comes
1+1-1-k=0
<=> 1-k=0
<=> k = 1
I need help pleaseeee!
Answer:
[tex]m({\angle CHF})[/tex] = 115°
Step-by-step explanation:
Intersecting chord theorem,
"When two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle."
By this theorem.
[tex]m({\angle CHF})[/tex] = [tex]\frac{1}{2}[m(\widehat{AB}+m(\widehat{FC})][/tex] ---------(1)
[tex]m(\widehat{AB})[/tex] = 40°
[tex]m(\widehat{FC})=m(\widehat{CD})+m(\widehat{DE})+m(\widehat{EF})[/tex]
[tex]m(\widehat{FC})[/tex] = 100° + 60° + 30°
= 190°
By substituting these values in the expression (1)
[tex]m({\angle CHF})[/tex] = [tex]\frac{1}{2}[40+190][/tex]
= 115°
Therefore, [tex]m({\angle CHF})[/tex] = 115°
Answer:
115°Step-by-step explanation:
If two chords intersect inside a circle, the measure of one of the angles formed equals half the sum of its intercepted arc and that angle's vertical angle's intercepted arc.
For angle CHF, the two arcs are arc CDF and arc AB
so (100 + 60 + 30) + 40 = 230, times 1/2 = 115º
What is the conjugate?
2x2 + √3
Answer: 2x²-√3
Step-by-step explanation:
Another way to say the conjugate is the opposite. All you have to do is to change the sign in the binomial, which is 2x²+√3. When you change the sign, it becomes 2x²-√3.
Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm.Use function notation to complete the following tasks
a. Represent the area (in square cm) of a circle whose radius is 4 cm.
b. Represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm.
Answer:
(a)f(4) square cm.
(b)f(10.91)-f(10.9) Square centimeter.
Step-by-step explanation:
f(r)=the area of a circle (in square cm) that has a radius of r cm.
(a)Area (in square cm) of a circle whose radius is 4 cm.
Since r=4cm
Area of the circle = f(4) square cm.
(b) When the radius of the increases from 10.9 to 10.91 cm.
Area of the circle with a radius of 10.91 = f(10.91) square cm.Area of the circle with a radius of 10.9 = f(10.9) square cm.Change in the Area = f(10.91)-f(10.9) Square centimeter.
Which expression are equivalent to 4m-2+(-8m)
Answer:
combine 4m -8m to get -4m
[tex] - 4m - 2[/tex]
Answer:
− 4m-2
Step-by-step explanation:
A lumber company is making boards that are 2564.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 21 is made, and it is found that they have a mean of 2567.0 millimeters with a variance of 121.00. A level of significance of 0.1 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=21-1=20[/tex]
the p value for this case would be given by:
[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]
For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm
Step-by-step explanation:
Information given
[tex]\bar X=2567[/tex] represent the mean height for the sample
[tex]s=\sqrt{121}= 11[/tex] represent the sample standard deviation
[tex]n=21[/tex] sample size
[tex]\mu_o =2564[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true mean is equal to 2564 mm, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2564[/tex]
Alternative hypothesis:[tex]\mu \neq 2564[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=21-1=20[/tex]
the p value for this case would be given by:
[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]
For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm
Can someone help me please
Answer:
Option (2)
Step-by-step explanation:
The given table represents the relation between the velocity and the time for an object is falling under the gravity.
Change in velocity with respect to time is directly proportional so the change is linear.
Acceleration due to gravity of this object is defined by the slope of the line joining the ordered pairs given in the table.
Let the two points lying on the line are (0, 0) and (1, 9.8)
Slope of the line passing through two points = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
= [tex]\frac{9.8-0}{1-0}[/tex]
= 9.8 [tex]\frac{m}{s^{2} }[/tex]
Option (2) will be the answer.
Which table shows the correct methods used to justify the solution steps?
3 (x minus 5) + 7 x = 65
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, distributive property, addition property of equality.
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, combine like terms, addition property of equality, division property of equality.
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, addition property of equality, combine like terms division property of equality.
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, addition property of equality, distributive property.
Answer:
B.
Step-by-step explanation:
The correct table that shows the justified solution steps is the second table.
The correct option is B.
The correct table that shows the justified solution steps is:
A 2-column table with 4 rows.
Column 1: Solution step
3x - 15 + 7x = 65
10x - 15 = 65
10x = 80
x = 8
Column 2: Method to Justify
Distributive property
Combine like terms
Addition property of equality
Division property of equality
In this table, the solution steps are correctly listed in the first column, showing the step-by-step process of solving the equation. The methods to justify each step are accurately provided in the second column, demonstrating the mathematical properties used at each stage.
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