Answer:
(2.2, 0.5, 1.1)
Step-by-step explanation:
The parametric equation of the line normal to the plane and through point (2, 0, 1) can be written ...
... L = (2, 0, 1) + t(2, 5, 1)
We want to find the value of t (and the corresponding point) that makes L satisfy the equation of the plane.
... 2(2+2t) +5(0 +5t) +1(1+t) = 8 . . . . . put values from L in for x, y, z in plane
... 5 + 30t = 8 . . . . . simplify
... t = (8 -5)/30 = 0.1 . . . . solve for t (subtract 5, divide by 30)
For this value of t, L is ...
... (2, 0, 1) + 0.1(2, 5, 1) = (2.2, 0.5, 1.1)
solve 3m+7/2=−2m+5/2 what is m
Answer:
-2/5
Step-by-step explanation:
3m + 7/2 = -2m + 5/2
3m + 7 = -2m + 5
5m = -2
m = -2/5
Alisa hopes to play beach volleyball in the olympics someday. She has convinced her parents to allow her to set up a beach volleyball court in their backyard. A standard volleyball court is 26 feet by 52 feet. She figures she will need the sand to be one foot deep.
Sand a is 60 lbs for $5
Sand b is 150 lbs for $12
A. What's is the rate brand a is selling for? Give rate and then specify the unit rate.
B.Which brand is offering the better value? Explain.
Brand A is selling the sand at a rate of $0.0833 per pound, which is a slightly better value compared to brand B's rate of $0.08 per pound.
Explanation:A. To find the rate at which brand A is selling the sand, we need to calculate the cost per pound. The rate for brand A is $5 for 60 lbs. To find the unit rate, we divide the cost by the amount, which gives us $5 / 60 lbs = $0.0833 per lb.
B. To determine which brand is offering the better value, we compare the unit rates. Brand A has a unit rate of $0.0833 per lb, while brand B has a unit rate of $12 / 150 lbs = $0.08 per lb.
Therefore, brand A is offering a slightly better value since it has a lower unit rate.
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56 books 75% decrease
What is the correct solution for the arithmetic expression 2+8/2*9/3 using the order of operations employed by oracle10g when solving equations?
Arithmetic expressions involve several arithmetic operations
The correct solution of [tex]\mathbf{2 + \frac 82 \times \frac 93}[/tex] is 14
The expression is given as:
[tex]\mathbf{2 + \frac 82 \times \frac 93}[/tex]
Divide 8 by 2
[tex]\mathbf{2 + \frac 82 \times \frac 93 = 2 + 4 \times \frac 93}[/tex]
Divide 9 by 3
[tex]\mathbf{2 + \frac 82 \times \frac 93 = 2 + 4 \times 3}[/tex]
Multiply 4 by 3
[tex]\mathbf{2 + \frac 82 \times \frac 93 = 2 + 12}[/tex]
Add 2 and 12
[tex]\mathbf{2 + \frac 82 \times \frac 93 = 14}[/tex]
Hence, the correct solution of [tex]\mathbf{2 + \frac 82 \times \frac 93}[/tex] is 14
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Let k(t) be a measure of the knowledge you gain by studying for a test for t hours. which do you think is larger, k(8) − k(7) or k(3) − k(2)
To determine which is larger between k(8) - k(7) and k(3) - k(2) , compare the specific values. If the graph of k(t) is concave upward, studying more hours yields a larger knowledge increase.
To determine which is larger between k(8) - k(7) and k(3) - k(2) , and to understand the concavity of the graph of k(t) , consider the following:
1. Larger Increase in Knowledge:
- Evaluate k(8) - k(7) and k(3) - k(2) .
- If k(8) - k(7) is greater, it implies that studying for an additional hour (from 7 to 8 hours) provides a larger increase in knowledge than studying for an hour from 2 to 3 hours.
2. Concavity of the Graph:
- If k''(t) > 0 (second derivative is positive), the graph is concave upward.
- If k''(t) < 0 (second derivative is negative), the graph is concave downward.
3. Reasoning for Concavity:
- If the graph is concave upward, it suggests that the rate of knowledge gain is increasing. Studying more hours leads to a larger increase in knowledge.
4. Final Answer:
- The comparison between k(8) - k(7) and k(3) - k(2) depends on the specific function k(t) . As for concavity, if the graph is concave upward, studying more hours yields a larger increase in knowledge.
In summary, compare the specific values k(8) - k(7) and k(3) - k(2) and analyze the concavity of the graph to determine the relationship between studying hours and knowledge gain.
Question. Let k(t) be a measure of the knowledge you gain by studying for a test for t hours, . Which do u think is larger, k(8)-k(7) or k(3) - k(2) ? is the graph of k concave upward or concave downward? why?
Billy Anderson is choosing between two fitness centers. Center A charges $395 per year for unlimited use of all facilities. Center B charges a $25 sign up fee, a $15 monthly fee, and $5 per aerobics class. If Billy goes to aerobics once a week, which club is least expensive for him to use for a year?
which facility is cheaper?
The Least expensive club for Billy to use for a year would be; Center B
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Let just compare the cost of both the centers.
Cost of Center A:
One time charge of $495 in one complete year.
Cost of Center B:
Flat $25 dollar sign up fee
$15 per month, thus 15 x 12 = 180 dollars a year
$5 per aerobic class, so 5 x 52 = 260. dollars a year (given that Billy goes to class once a week)
There are 52 weeks in a year.
260 + 180 + 25 = 465 dollars
Hence, Center B would cost 30 dollars cheaper.
The Least expensive club for Billy to use for a year would be; Center B
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An amount of $31,000 is deposited in a bank that pays interest at the rate of 4%/year, compounded annually. what is the total amount on deposit at the end of 6 years, assuming there are no deposits or withdrawals during those 6 years? (round your answer to the nearest cent.)
The total amount on deposit at the end of 6 years if an amount of $31,000 is deposited in a bank that pays interest at the rate of 4% per year, compounded annually is $38440.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The principal amount, P = $31000,
The time, t = 6 years,
The rate of interest, r = 4% per annum,
Calculate the simple interest by the formula given below,
[tex]SI = P\times r\times t / 100[/tex]
SI = 31000 × 4 × 6 / 100
SI = $7440,
Calculate the by the formula given below,
[tex]Total \ amount = P + SI[/tex]
Total amount = $31000 + $7440
Total amount = $38440
Therefore, the total amount on deposit at the end of 6 years if an amount of $31,000 is deposited in a bank that pays interest at the rate of 4% per year, compounded annually is $38440.
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What are the slope and the y-intercept of the linear function that is represented by the table?
Answer:
The answer is D.
Step-by-step explanation:
I got it correct on my test.
Correct me if I'm wrong.
You are sailing from your lakeshore cabin to a marina 60º north of east and 0.5 miles across the lake.
Which of the following expressions uses the complementary angle of 60° to determine how far you would travel on your trip west?
a.
0.5cos30°
b.
0.5cos60°
c.
0.5sin30°
d.
0.5sin60°
Answer:- c. 0.5sin30°
Explanation:-
Let AB= 0.5 miles be the distance across the lake to 60º north of east.
AC= distance travel to the east
Now, in right ΔABC
[tex]sin60^{\circ}=\frac{AC}{AB}\\\\\Rightarrow\ AB=ACsin60^{\circ}\\\Rightarrow\ AB=0.5\ sin60^{\circ}[/tex]
Now Distance towards west [tex]AD=|\ -0.5\ sin60^{\circ}|[/tex] [distance is a positive quantity]
[tex]AD=0.5\ sin60^{\circ}[/tex]
[tex]AD=0.5\ cos(90^{\circ}-60^{\circ})[/tex] [Taking complementary angle of 60° ]
[tex]AD=0.5\ cos(30^{\circ})[/tex]
Thus C. is the right option.
Answer:
the answer is C.
Step-by-step explanation:
stacy says the 4 in 643 has a value of 4 tens or 40 do you agree with stacy reasoning explain use picture,words or number in your answer.
Final answer:
Stacy is correct in saying that the 4 in 643 has a value of 4 tens or 40, as numbers can be broken down by place value, with each digit representing a different value depending on its position.
Explanation:
I do agree with Stacy's reasoning. The number 643 can be broken down into its place values: the 6 is in the hundreds place, representing 600; the 4 is in the tens place, representing 40; and the 3 is in the ones place, representing 3. Therefore, the value of the 4 in 643 is indeed 4 tens, or 40, as Stacy has indicated.
To visualize this, imagine the number 643 written on a place value chart:
Hundreds: 6
Tens: 4
Ones: 3
This confirms that the digit 4 in the tens place contributes 40 to the overall value of the number 643.
Heather, Chang, and Justin served a total of 93 orders Monday at the school cafeteria. Chang served 2 times as many orders as Justin. Heather served 5 more orders than Justin. How many orders did they each serve?
Use counters to find the quotient and remainder for 36 divide a by 8
A rectangular floor is 5 yards long and 4 yards wide. What is the area of the floor in square feet?
Final answer:
To calculate the area of the floor in square feet, the dimensions in yards are first converted to feet (1 yard = 3 feet), and then the length and width in feet are multiplied to get the area (15 feet x 12 feet = 180 square feet).
Explanation:
The student is asking about the area of a rectangular floor in square feet when the dimensions given are in yards. To find the area of the floor, we first convert the measures from yards to feet, knowing that 1 yard equals 3 feet. Therefore, the rectangular floor measures 5 yards long (which is 5 x 3 = 15 feet long) and 4 yards wide (which is 4 x 3 = 12 feet wide).
Now we can calculate the area by multiplying the length by the width. The area in square feet is thus 15 feet x 12 feet = 180 square feet.
What is the value of 4 in the number 358.547? please help!!!!!
A) 0.0004
B) 0.004
C) 0.04
D) 4
Which choice solves the problem?
1467÷7=
A) 27
B) 29 with a remainder of 4
C) 207 with a remainder of 4
D) 209 with a remainder of 4
Bailey’s horse is growing fast. She ate 2 scoops of feed in the morning, 4 scoops in the afternoon and 3 scoops at night. She did this all week long. How many scoops of feed did Bailey’s horse eat over the course of the week?
A) 2 x 3 x 4
B) 2 x (3 + 4)
C) 2 + 3 + 4 + 7
D) (2 + 3 + 4) x 7
In circle Y, what is m∠SZT? 86° 94° 108° 128°
Answer:
It's 94
Step-by-step explanation:
Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 + y2 = 4 and the plane x + y + z = 9.
The length of the curve of intersection of the cylinder 4x2 + y2 = 4 and the plane x + y + z = 9 is found by parameterizing the ellipse formed by the intersection, finding the derivatives with respect to the parameter, and integrating these derivatives over one period of the parameter.
Since the equation of the cylinder has x and y terms, we'll start by solving the plane's equation for z: z = 9 - x - y. Substituting this into the cylinder's equation gives 4x² + y² = 4, which is indeed the equation of an ellipse in terms of x and y. Next, we parameterize this ellipse using trigonometric functions: x = cos(t), y = 2sin(t), where 0 ≤ t < 2π.
Substituting these into the plane's equation gives z = 9 - cos(t) - 2sin(t). Now we'll use the formula for arc length, which is the integral of the square root of the sum of the derivatives squared:
L = ∫ √((dx/dt)² + (dy/dt)² + (dz/dt)²) dt. We evaluate this integral from t = 0 to t = 2π using the derivatives of x, y, and z with respect to t.
Finally, we can compute this integral and round the result to four decimal places. The analytical computation of the integral may be complex and require special functions such as elliptic integrals, depending on the resulting expression after derivatives are calculated.
Explain why the relationship between how much steven charges and time is a promotioninal relationship
Giuliana has 22 quarters and dollar coins worth a total of $10.75.
Which equation can be used to find d, the number of dollar coins Giuliana has?
d – 22 + 0.25d = 10.75
0.25d + 22 – d = 10.75
0.25(22 – d) + d = 10.75
d + 0.25(d – 22) = 10.75
Let
q------> the number of quarters coins
d------> the number of dollars coins
we know that
[tex]1\ quarter=\$0.25[/tex]
[tex]q+d=22[/tex]
[tex]q=22-d[/tex] ------> equation A
[tex]0.25q+d=10.75[/tex] -----> equation B
substitute equation A in equation B
[tex]0.25[22-d]+d=10.75[/tex]
therefore
the answer is the option
[tex]0.25[22-d]+d=10.75[/tex]
An equation is formed when two equal expressions are equated together with the help of an equal sign '='. The correct option is C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Giuliana has 22, quarters and dollar coins worth a total of $10.75.
Let the number of dollar coins be represented by d, while the number of quarter coins be represented by (22-d). Therefore, the sum of the total amount that is with Giuliana can be written as,
(1 x d) + (0.25 x (22-d)) = 10.75
d + 0.25(22-d) = 10.75
Hence, the equation can be used to find d, the number of dollar coins Giuliana has is 0.25d + 22 – d = 10.75.
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The cost of having a package delivered has a base fee of $9.70. Every pound over 5 lbs cost an additional $0.46 per pound. Write a linear model that represents the cost, C, for the total weight, w, in pounds of the package. Assume w > 5 lbs.
a. C = 9.7w + 0.46
b. C = 0.46w + 12
c. C = 0.46w + 9.7
d. C = 0.46(w - 5) + 9.7
Answer:
d. C=0.46(w-5)+9.7
Step-by-step explanation:
the cost of having a package delivered has a base fee of $9.70, that means that independently of the pounds of the package, the cost is always going to be $9.70
Then, there is an additional cost, that just count if the package have more than 5 lbs. Every pound over this 5 lbs, cost $0.46 per pound. So, the additional cost is:
0.46*(w-5)
Where (w-5) are the number of pound that over 5 lbs.
Finally the total cost is the sum of the base cost and the additional cost, that can be written as:
C=0.46*(w-5)+9.7
Answer:
It is D.
Step-by-step explanation:
took the assessment.
In the diagram, what is the value of x
The sum of angles on a straight line is 180degrees. The measure of the value of x from the figure is 98degrees
Sum of angle on a straight lineThe measure of angles 82 degrees and the unknown are on a straight line, Since the sum of angles on a straight line is 180degrees, hence;
x + 82 = 180
Subtract 82 from both sides
x + 82 - 82 = 180 - 82
x = 180 - 82
x = 98 degres
Hence the measure of the value of x from the figure is 98degrees
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Sean Michael has a jar of nickels and dimes he has 1530 coins that total 127.45 how many of each coin does he have
What is the slope, m, and the y-intercept of the line that is graphed below?
Answer: The correct option is
(A) m = 1; (0, 3).
Step-by-step explanation: We are given to find the slope, m, and the y-intercept of the graphed line.
We know that
the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
From the graph, we note that the line passes through the points (-3, 0) and (-1, 2).
Therefore, the slope of the graphed line will be
[tex]m=\dfrac{2-0}{-1-(3)}=\dfrac{2}{2}=1.[/tex]
Also, at x = 0, the value of the y-coordinate is 3. So, the y-intercept of the line is (0, 3).
Thus, the slope, m = 1 and the y-intercept is (0, 3).
Option (A) is CORRECT.
estimate the answer to: 3772 divided by 44
Find the quotient 5/18 divided by 2/6
To divide fractions, multiply the first fraction by the reciprocal of the second fraction and simplify if possible.
Explanation:To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is found by switching the numerator and denominator. So, to divide 5/18 by 2/6, we will multiply 5/18 by 6/2.
First, we cancel out any common factors between the numerators and denominators:
5/18 * 6/2 = (5 * 6)/(18 * 2) = 30/36.
Now, we can simplify 30/36 by finding the greatest common divisor (GCD) of 30 and 36, which is 6.
Dividing both the numerator and denominator of 30/36 by 6, we get the final quotient of 5/6.
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whats the cubed root 64/343
HELP NEEDED IN MATHS
mr. john doe was figuring out his federal income tax.his income tax is 26,800, but he was able to subtract 5,000 in deducations he paid 15% of the remaning income tax . how much did he pay
subtract 5ooo from 26800
26800 - 5000 = 21800
now multiply that by 15%
15% = 0.15
21800 * 0.15 = 3270
he paid $3,270 in taxes
Which of the following are valid names for the given triangle below? Check all that apply.
Answer:
Triangle LMZ
Triangle MLZ
Triangle ZML
Step-by-step explanation:
Option A,B and E are all the valid names.
The valid names of the triangle are those that has all the angles withing. The angles are Angle l, M and Z.
C and D are not angles, so any triangle cannot be formed using these.
Hence, the valid triangles here are:
Triangle LMZ
Triangle MLZ
Triangle ZML
Answer:
LMZ,ZML,MLZ
Step-by-step explanation:
What is the solution set of -9x ≥ 27?
Answer:
x<=-3
Step-by-step explanation:
@countrygurl4464
snap
Point A has a _____ abscissa and a _____ ordinate.
positive, negative
negative, positive
negative, negative
positive, positive
Answer:
Negative,Positive
Step-by-step explanation:
The coordinate geometry, plane is divided into four parts and each part is known as quadrant. The abscissa denotes the point lies on X- axis whereas ordinate denotes the point on Y-axis.
Since the point A lies in second quadrant. In second quadrant, abscissa is negative and ordinate is positive because here x lies to left of x axis and y lies to right of y axis.
Thus, the correct answer is option (2)