Before starting his job, Clayton had been on an airplane 3 times. Since then, he has flown 6 times each year.
Let y represent the number of years since Clayton started his job and f represent the total number of times he has flown.
Complete the equation that represents the relationship between y and f.
y f
1 9
2 15
3 21
4 27
f=
y+
Answer:
f = 6y + 3
Step-by-step explanation:
The equation to reflect this condition is:
f = 6y + 3Where
3 - is constant, the initial number of flights6 - coefficient, number of flights per yeary- number of yearsf- total number of flightsLet y = [5 5] and u = [6 8] . Compute the distance from y to the line through u and the origin.
Answer:
The distance d = 1
Step-by-step explanation:
The objective is to compute the distance from y to the line through u and the origin.
Given that :
[tex]y = \left[\begin{array}{cc}5\\5\end{array}\right][/tex] and [tex]u = \left[\begin{array}{cc}6\\8\end{array}\right][/tex]
Recall that:
from the slope - intercept on the graph, the equation of line can be expressed as :
y = mx + b
where;
m = slope = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
b = y - intercept
Similarly, we are being informed that the line passed through [tex]u = \left[\begin{array}{cc}6\\8\end{array}\right][/tex] and origin, so ;
[tex]x_1 = 0 , y_1 = 0 \\ \\ x_2 =6 , y_2 = 8[/tex]
the slope m = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]=\dfrac{8 - 0}{6-0}[/tex]
[tex]= \dfrac{4}{3}[/tex]
Also, since the line pass through the origin:
Then
y = mx + b
0 = m(0) + b
b = 0
From y = mx + b
y = mx + (0)
y = mx
[tex]y = \dfrac{4}{3}x[/tex]
3y = 4x
3y - 4x = 0
4x - 3y =0
The distance of a point (x,y) from a line ax +by + c = 0 can be represented with the equation:
[tex]d = \dfrac{|ax+by +c|}{\sqrt{a^2 +b^2}}[/tex]
∴ the distance from [tex]y = \left[\begin{array}{cc}5\\5\end{array}\right][/tex] to the line 4x - 3y = 0 is
[tex]d = \dfrac{|4x-3y +0|}{\sqrt{4^2 +3^2}}[/tex]
[tex]d = \dfrac{|4(5)-3(5) +0|}{\sqrt{16+9}}[/tex]
[tex]d = \dfrac{20-15 }{\sqrt{25}}[/tex]
[tex]d = \dfrac{5}{5}[/tex]
The distance d = 1
The distance from y(5,5) to the line through u(6,8) and the origin(0,0) is √2 units.
What is the distance between the two points on a graph?The distance or length of any line on the graph is given by the formula,
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where,
d = distance/length of the line between points 1 and 2,
(x₁, y₁) = coordinate of point 1,
(x₂, y₂) = coordinate of point 2,
In the given equation, we need to find the distance between the line and the point u (6,8). Now, we try to find the equation of the line, with points y=(5,5) and origin (0,0). Therefore, the slope of the equation can be written as,
[tex]m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{5-0}{5-0} = 1[/tex]
Now, if we substitute the value of the slope and a point in the general equation of the line, we will get,
[tex]y = mx+c\\\\0 = 1(0)+c\\\\c = 0[/tex]
Further, if we draw the line on the graph, the nearest point to point u(6,8) is a(7,7). Therefore, the distance between the two points can be written as,
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\D = \sqrt{(7-6)^2+(7-8)^2}\\\\D = \sqrt2[/tex]
Hence, the distance from y(5,5) to the line through u(6,8) and the origin(0,0) is √2 units.
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Answer two questions about Equations A and B:
A. 5x=20
B. X=4
1) How can we get Equation B from Equation A?
Choose 1 answer:
Multiply/divide both sides by the same non-zero constant
Multiply/divide both sides by the same variable expression
Add/subtract the same quantity to/from both sides
Add/subtract a quantity to/from only one side
Answer:
Multiply/divide both sides by the same non-zero constant
Step-by-step explanation:
5x = 20
Divide each side by 5
5x/5 = 20/5
x = 4
Brianna started a business making customized dog beds. She can make one bed every two hours. Wesley had a similar business, but used a different method. He can make two beds every threehours. They decided to combine their business ventures and received their first order for 49 beds from a local shop. How many hours will be required to fill the order?
Answer:
It will take them 42 hours
Step-by-step explanation:
Brianna rate = one bed for 2 hours
But for one hour = 0.5 bed per hour
Wesley rate = two bed for 3 hours
For one hour= 2/3 bed per hour
So their total rate for one hour
= 1/2 +2/3
= 7/6 bed per hour
If they received an order of 49 beds
It will take them x hours
Rate= bed/hour
7/6= 49/x
X= 49/(7/6)
X= 49 * 6/7
X= 7*6
X= 42 hours
The theatre has 4 chairs in a row. there are 5 rows. Using rows as your unit of measurement,what is the perimeter.
Answer: 18 rows.
Step-by-step explanation:
The theatre has 4 chairs in a row.
There are 5 rows.
If we consider rows as unit, then we observed that
Length = 4 rows
Width = 5 rows
Perimeter of Rectangle = 2(length +breadth)
= 2(5+4)
= 2(9)
=18 rows
Hence, the perimeter is 18 rows.
Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the level of significance with degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the level of significance based on a sample size of n. (c) Determine the critical value(s) for a two-tailed test of a population mean at the level of significance based on a sample size of n.
Answer:
(a) The critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.
(b) The critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.
(c) The critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.
Step-by-step explanation:
We have to find the critical t values for each of the following levels of significance and sample sizes given below.
As we know that in the t table there are two columns. The horizontal column is represented by the symbol P which represents the level of significance and the vertical column is represented by the symbol '[tex]\nu[/tex]' which represents the degrees of freedom.
(a) A right-tailed test of a population mean at the α=0.01 level of significance with 15 degrees of freedom.
So, here the level of significance = 0.01
And the degrees of freedom = n - 1 = 15
Now, in the t table, the critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.
(b) A left-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 20.
So, here the level of significance = 0.05
And the degrees of freedom = n - 1
= 20 - 1 = 19
Now, in the t table, the critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.
(c) A two-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 13.
So, here the level of significance = [tex]\frac{0.05}{2}[/tex] = 0.025 {for the two-tailed test}
And the degrees of freedom = n - 1
= 13 - 1 = 12
Now, in the t table, the critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.
To make lemonade you can mix 4 teaspoons of lemonade powder with 16 ounces of water. What is the ratio of powder to
water?
4:32
32:8
24:64
32:128
Answer:
32:128
Step-by-step explanation:
divide all of it by 2, you get 16:64. Again, 8:32. Again, 4:16
5x+2y=12
Solve for y
Answer:
y = 1
Step-by-step explanation:
5·x
x=2
5·2=10
10+2y
y=1
2·1=2
10+2=12
Answer:1
Step-by-step explanation:5(x)+2(y)=12
5 x 2 =10
2 x 1=2
10 + 2=12
HELPPPP
A penny has a mass of 2.5 grams, I just cashed in 75$ in pennies at the coin star.
How many Kg is that? *
Answer:
18.750kgStep-by-step explanation:
If a mass of 2.5 grams costs a penny, we want to know the amount of mass that will cost $75. Before we get the mass, we need to convert 75 dollars to penny. Using the conversion:
$1 = 100pennies
$75 = (75*100)pennies
$75 = 7,500 pennies
Using the law of equivalence
1 penny = 2.5 grams
7,500pennies = x grams
Cross multiply
1 * x = 2.5 * 7500
x = 18,750 grams
Hence 18,759 grams will cost $75
Converting grams to kilograms
If 1000 grams = 1kg
18,750grams -= y
cross multiply
1000*y = 18750
Divide both sides by 1000
1000y = 18750/1000
y = 18.750kg
Hence the amount in kilogram of $75 coin in pennies is 18.750kg
Simplify the expression below:
3(2x - 5) - (4x + 1) +2(6 – 5x + 2x)
into the form AX + B
1. What is the value of A?
Do not include spaces, units, or commas in your response.
2. What is the value of B
Do not include spaces units, or commas in your response.
Answer:
The value of A is -4, and that of B is -10
Step-by-step explanation:
We must carry out the indicated multiplication (and removal of parentheses) according to Order of Operations rules:
6x - 15 - 4x - 1 + 6 - 10x + 4x
Grouping like terms together, we get:
6x - 4x - 10 x + 4x - 15 -1 + 6
this, in turn, simplifies to:
-4x-10
The value of A is -4, and that of B is -10
what's the answer for (2+i)(i+2i)?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{3 {i}^{2} + 6i}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{(2 + i)(i + 2i)}[/tex]
Use the distribute property to multiply each term of the first binomial by each term of the second binomial.
⇒[tex] \sf{2(i + 2i) + i(i + 2i)}[/tex]
⇒[tex] \sf{2i + 4i + {i}^{2} + 2 {i}^{2} }[/tex]
Collect like terms
⇒[tex] \sf{3 {i}^{2} + 6i}[/tex]
Hope I helped!
Best regards!
An advertiser goes to a printer and is charged $37 for 80 copies of one flyer and $54 for 209 copies of another flyer. The printer
charges a foced setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost of a printing job, if 2 is the
number of copies made. C(x)
Answer: c(x) = y = $0.132*x + $27.16
Step-by-step explanation:
The chargers are a fixed price plus a charge for every copy, then we have a linear relationship.
A linear relationship can be written as:
c(x) = y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, c(x) = y represents the cost in dollars, x is the number of copies bought, and b is the fixed cost.
We know two points in this line:
(80, $37) and (209, $54)
Whit those two points we can find the slope:
a = ($54 - $37)/(209 - 80) = $17/129 = $0.132 per copy.
Then our equation is:
c(x) = y = $0.132*x + b
To find the value of b, we know that 80 copies cost $37, we can replace those values in the equation:
$37 = $0.132*80 + b
$37 = $9.84 + b
($37 - $9.84) = $27.16 = b.
Then the equation is:
c(x) = y = $0.132*x + $27.16
The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 118 . Use a significance level of 0.05.
Full Question:
The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 113. use a significance level of 0.05.
Systolic| 150 129 142 112 134 122 126 120
Diastolic| 88 96 106 80 98 63 95 64
a. What is the regression equation?
^y = __ + __x (Round to two decimal places as needed.)
b. What is the best predicted value?
^y is about __ (Round to one decimal place as needed.)
Answer:
A. yhat = a + bx = -10.64 + 0.75x
B. 74.0
Step-by-step explanation:
A. To find the regression equation here, we apply the formulas and then apply it to find the value of y given value of x:
calculate xbar and ybar which is the average of the variables:
Where n(number of values in x or y)=8
xbar = sum of x/n = 129.375
ybar = sum of y/n = 86.25
to calculate b
b= [Sum x^2 * Sum y - Sum x * Sum x*y] / [N*Sum x^2 - (Sum x)^2]
b = 0.74891
To calculate a
a = ybar - b * xbar = -10.64023
Regression equation:
y=mx+b= -10.64 + 0.75x
B. given x = 113,
y = -10.64023 + 0.74891 * 113
y= 74.0
Create formulas for the following in an Excel worksheet: Add the values of 3 and 5 to one another. Subtract the value of 5 from 10 and multiply the outcome by 7. Average the values 5, 6, 7, and 8. Find the sum of the squared values of 3, 4, and 5.
Answer:
Please see the Excel formulas used in the attached image
Step-by-step explanation:
Use the simple addition, simple subtraction, average value built-in function, and addition of squares as indicated in the attached image
A question includes logarithm and trigonometry. Could anybody help me to solve this,please?
[tex]\log_2(2\sin x)+\log_2(\cos x)=-1[/tex]
Condense the logarithms on the left side:
[tex]\log_2(2\sin x\cos x)=-1[/tex]
Recall the double angle identity for sine, [tex]\sin(2x)=2\sin x\cos x[/tex]:
[tex]\log_2(\sin(2x))=-1[/tex]
Write both sides as powers of 2:
[tex]2^{\log_2(\sin(2x))}=2^{-1}[/tex]
Simplify this:
[tex]\sin(2x)=\dfrac12[/tex]
Solve for [tex]2x[/tex]:
[tex]2x=\sin^{-1}\left(\dfrac12\right)+2n\pi\text{ OR }2x=\pi-\sin^{-1}\left(\dfrac12\right)+2n\pi[/tex]
(where [tex]n[/tex] is any integer)
Recall that [tex]\sin^{-1}\left(\frac12\right)=\frac\pi6[/tex]:
[tex]2x=\dfrac\pi6+2n\pi\text{ OR }2x=\dfrac{5\pi}6+2n\pi[/tex]
Solve for [tex]x[/tex]:
[tex]x=\dfrac\pi{12}+n\pi\text{ OR }x=\dfrac{5\pi}{12}+n\pi[/tex]
We get solutions in the interval [tex]2\pi <x<\frac{5\pi}2[/tex] when [tex]n=2[/tex], giving
[tex]\boxed{x=\dfrac{25\pi}{12}}\text{ OR }\boxed{x=\dfrac{29\pi}{12}}[/tex]
Jasmine used the number line to find the distance between 0 and 5. What was Jasmine's error?
1 2 3 4 5
The distance is -5.
-2 -1
0 1 2 3
4
+
8
5
6
7
Jasmine should have counted from 5 to 0.
Jasmine started with the wrong integer.
Jasmine gave a negative answer for distance.
Jasmine ended with the wrong integer.
Done
Intro
Answer:
c
Step-by-step explanation:
thats the answerrrrrrrr
Answer:
c
Step-by-step explanation:
edg 2021
The prime factorization of 25 is
Given that P(A|B) =......... rest of question is on the diagram.
Answer:
C. 2/25
Step-by-step explanation:
The probability that Events A and B both occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B). It is calculated by Rule of Multiplication.P(A ∩ B) = P(A) P(A|B)
P(A ∩ B) = 2/5 * 1/5 = 2/25
Answer option is:
C. 2/25
15 POINTS if you get iy=t right
Answer:
C.
Step-by-step explanation:
Step 1: Isolate [tex]V_{0}[/tex]
Multiple t on both sides
at = [tex]V_{1} -V_{0}[/tex]
Subtract [tex]V_{1}[/tex] on both sides
[tex]at - V_{1} = V_{0}[/tex]
Therefore the answer is C
what is the product of -12 and -4
Answer:
The answer is 48.
-12 × -4=48.
Solve 5h+2(11−h)=−5
.
Answer:
h =-9Step-by-step explanation:
[tex]5h+2\left(11-h\right)=-5\\\mathrm{Expand\:}5h+2\left(11-h\right):\quad 3h+22\\\\3h+22=-5\\\\\mathrm{Subtract\:}22\mathrm{\:from\:both\:sides}\\\\3h+22-22=-5-22\\\\Simplify\\\\3h=-27\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3h}{3}=\frac{-27}{3}\\\\h=-9[/tex]
The value of h is -9.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
5h + 2 (11 - h) = - 5
Remove the parenthesis.
5h + 2 x 11 - 2h = -5
5h + 22 - 2h = -5
Subtract the like terms.
3h + 22 = -5
Subtract 22 on both sides.
3h = - 5 - 22
3h = -27
Divide both sides with 3.
h = -9
Thus,
The value of h is -9.
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A square has the following vertices. Find the area of the square.
(−7, −5), (−4, −2), (−4, −8), (−1, −5)
6√ square units
18√ square units
6 square units
18 square units
Answer:
18 square units
Step-by-step explanation:
A square has the following vertices
(−7, −5), (−4, −2), (−4, −8), (−1, −5)
To determine if the are we look for the length of just one of it's sides, because it's a square,all of it's side are equal.
And the are is determined by squaring one of it's sides.
An attachment of the figure is given below to help us know the vertices to use to determine the length.
Length= √ ((-4-(-7))²+(-2-(-5))²)
Length= √((3)²+(3)²)
Length= √(9+9)
Length= √18
So area is the square of the length
Area= (√18)²
Area= 18 square unit
Answer:
D
Step-by-step explanation:
In the exercise, X is a binomial variable with n = 5 and p = 0.2. Compute the given probability. Check your answer using technology. HINT [See Example 2.] (Round your answer to five decimal places.) P(X = 3)
Answer:
0.0512
Step-by-step explanation:
We are told in the question that X isa Binomial variable. Hence we solve this question, using the formula for Binomial probability.
The formula for Binomial Probability = P(x) = (n!/(n - x) x!) × p^x × q ^n - x
In the above question,
x = 3
n = 5
p = probability for success = 0.2
q = probability for failures = 1 - 0.2 = 0.8
P(x) = (n!/(n - x) x!) × p^x × q ^n - x
P(3) = (5!/(5 - 3) 3!) × 0.2^3 × 0.8^5-3
P(3) =( 5!/2! × 3!) × 0.2³ × 0.8²
P(3) = 10 × 0.008 × 0.64
P(3) = 0.0512
how many ways can you arrange 10 people in a circle if two arrangements are considerded the same if each persons left and right neighbors are the same
Answer:
1814400 ways
Step-by-step explanation:
From the question, since it doesn't matter which seat you sit in as long as the neighbors either side of you still remain in the same order, thus;
Number of possible seat arrangements = 10! = 3628800
Now, we know that two seatings are the same when each person has the same two neighbors to the right or left. This simply means that it will be considered the same if the seats are placed around the circular table either clockwise or counter clockwise. With respect to this condition, we have to divide the number of possible seat arrangements by 2.
Thus;
Number of possible ways with the condition in the question = 3628800/2 = 1814400 ways
A piece of wire 23 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.
Required:
a. How much wire must be used for the square in order to maximize the total area?
b. How much wire must be used for the square in order to minimize the total area?
Answer:
wire for square to maximize total area = 23 m
Wire to minimize total area = 2.019 m
Step-by-step explanation:
For the square, let's say the total length of the square is "y" m.
Thus, length of one side is = y/4
And area of the square = (y/4) = y²/16
Since the wire is 23 m, then total length of equilateral triangle is; 23 - y.
Thus, length of one side of equilateral triangle = (23 - y)/3
Using trigonometric ratio, we can find the height of the triangle and thus area.
Area of triangle = (√3)/4) × ((23 - y)/3)²
Area of triangle = (√3)/36)(23 - y)²
So, total area of square and triangle is;
A_total = (y²/16) + (√3)/36)(23 - y)²
Now, extremizing this function by derivatives, we have;
dA/dy = (y/8) - (√3)/18)(23 - y)
d²A/dy² = ⅛ + (√3)/18)
So, d²A/dy² > 0
Now,let's find the maximum or minimum of the function.
So, we equate dA/dy to zero.
Thus;
(y/8) - (√3)/18)(23 - y) = 0
y/8 = (√3)/18)(23 - y)
(y/8) + (√3)/18)y = 23((√3)/18)
Multiply through by 8 to give;
y + 0.0962y = 2.2132
1.0962y = 2.2132
y = 2.2132/1.0962
y = 2.019 m
2.019 will be a minimum because d²A/dy² > 0
The maximum will occur at a boundary of the allowed values. Thus, the absolute maximum is for y = 23.
Note that a square has more area than a triangle and as such it is normal for the square to get the largest area over the triangle and therefore we will have to use all of the wire to construct the square.
Please answer this thanks!
Answer:
F. 5
Step-by-step explanation:
For 9 to be a common factor, x must be a multiple of 9. For the greatest common factor to be 9, not 18 or 36, x must be an odd multiple of 9.
There are 5 2-digit odd multiples of 9:
27, 35, 63, 81, 99
There are 5 possible 2-digit values for x.
A plant is already 57cm talk and it will grow one centimeter every month the plant height h in centimeters after m months is given by the following function what is the plants height after 22 months
Answer:
the plant is 79 cm
Step-by-step explanation:
every month = 1 cm
months = 22 months
57 cm + 22 cm
= 79cm
Simplify. Square root of 144 a^2 b^4 c^6
12abc
12ab2c2
12ab2c3
Answer:
12 ab²c³
Step-by-step explanation:
√144 a² b⁴ c6
144 would be 12
a² would be a
b⁴ would be b²
c6 would be c³
What is the equation for each reflected graph of f(x)=x^2-4? Reflect across the x-axis, reflect across the y-axis.
A function assigns the values. The equation for each reflected graph of f(x)=x²-4 can be written as shown below.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) Reflect across the y-axis, to find the equation replace x with -x,
f(-x) = (-x)² - 4
= x² - 4
No, Change because the function is symmetrical about the y-axis
B.) Reflect across the x-axis, to find the equation replace y with -y,
y = f(x) = y
-y = -f(x)
= -(x² - 4)
= -x² + 4
Hence, The equation for the reflection of the function can be done as shown below.
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Find the domain of y = 4 square root 4x + 2
Answer:
[tex]\Large \boxed{x\geq -\frac{1}{2}}[/tex]
Step-by-step explanation:
The domain is all possible values for x.
[tex]y=4\sqrt{4x+2}[/tex]
There are restrictions on the value of x.
A square root of a negative number is undefined.
The number in the square root has to be equal to 0 or be greater than 0.
[tex]4x+2\geq 0[/tex]
Subtract 2 from both sides.
[tex]4x\geq -2[/tex]
Divide both sides by 4.
[tex]\displaystyle x\geq -\frac{2}{4}[/tex]
[tex]\displaystyle x\geq -\frac{1}{2}[/tex]