Answer:
6 < n < 56
Step-by-step explanation:
Let's translate that into a symbolic relationship:
1 < (56/n) < 7
This produces two inequalities to be solved: 1 < (56/n) and (56/n) < 7.
Dividing both sides of (56/n) < 7 by 7 results in (6/n) < 1
which can be rewritten as 6 < n or n > 6.
Multiplying both sides of 1 < (56/n) by n results in n < 56.
There's no one solution. Rather, the solution set is 6 < n < 56.
The solution set is 8 < n < 56 for number so 56 divide n is greater than 1 but less than 7
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given,
a number so 56 divide n is greater than 1. But less than 7
56/n>1
56/n < 7
This sentence can be written as
1 < (56/n) < 7
Two inequalities to be solved:
1 < (56/n) and (56/n) < 7.
n<56 and 56/7<n
n<56 and 8<n
Dividing both sides of (56/n) < 7 by 7 results in (8/n) < 1
which can be rewritten as 8 < n or n > 8.
Multiplying both sides of 1 < (56/n) by n results in n < 56.
There's no one solution.
Hence, the solution set is 8 < n < 56.
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help me answer the quesyion for 13 points
Answer: it is (-2,2)
Step-by-step explanation:
You go on the -2 point on the x axis and 2 block up from that point to get (-2,2).
Line k passes through the point (1, 5) and is perpendicular to the line y = 3x + 1. Which of the following points does line k also pass through?
Select one:
A. (4, 4)
B. (-2, -5)
C. (3, 6)
D. (9, -1)
Answer:
Option A. (4,4)
Step-by-step explanation:
step 1
Find the slope of the line k
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
[tex]m1*m2=-1[/tex]
The slope of the given line is [tex]m1=3[/tex]
so
The slope of the line k is
[tex]m2*(3)=-1[/tex]
[tex]m2=-\frac{1}{3}[/tex]
step 2
Find the equation of the line k
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{3}[/tex]
[tex]point(1,5)[/tex]
substitute the values
[tex]y-5=-\frac{1}{3}(x-1)[/tex]
step 3
Verify if the line k pass through the given points
Remember that
If the line passes through a point, then the value of x and the value of y of the point must satisfy the equation of the line
Verify each case
case A) (4,4)
[tex]4-5=-\frac{1}{3}(4-1)[/tex]
[tex]-1=-\frac{1}{3}(3)[/tex]
[tex]-1=-1[/tex] ----> is true
therefore
The line k pass through the point (4,4)
case B) (-2,-5)
[tex]-5-5=-\frac{1}{3}(-2-1)[/tex]
[tex]-10=-1[/tex] -----> is not true
therefore
The line k not pass through the point (-2,-5)
case C) (3,6)
[tex]6-5=-\frac{1}{3}(3-1)[/tex]
[tex]1=-\frac{2}{3}[/tex] -----> is not true
therefore
The line k not pass through the point (3,6)
case D) (9,-1)
[tex]-1-5=-\frac{1}{3}(9-1)[/tex]
[tex]-6=-\frac{8}{3}[/tex] -----> is not true
therefore
The line k not pass through the point (9,-1)
identify the conjugate: 7-18i
[tex]\overline{7-18i} = 7+18i[/tex]
Pls answer this pls
Answer:
nearsighted: A, C, Efarsighted: B, Dmost nearsighted: Emost farsighted: DStep-by-step explanation:
Since the questions are about which numbers are positive or negative and which have the largest magnitude, it is convenient to arrange them in order from least to greatest:
-3.00 (E), -2.25 (A), -1.50 (C), 1.00 (B), 3.25 (D)
Nearsighted patients are those with negative prescriptions: E, A, C.
Farsighted patients are those with positive prescriptions: B, D.
The most nearsighted patient has the most negative prescription: E
The most farsighted patient has the most positive prescription: D
at a bookstore, 8 similar books cost y dollars. what is the price of 3 such books?
[tex]\bf \begin{array}{ccll} books&price\\ \cline{1-2} 8&y\\ 3&x \end{array}\implies \cfrac{8}{3}=\cfrac{y}{x}\implies 8x=3y\implies x=\cfrac{3}{8}y[/tex]
Final answer:
To determine the price of 3 books when given the cost of 8 similar books, you divide the total cost by 8 to find the price per book, then multiply this price by 3.
Explanation:
The student asked: At a bookstore, 8 similar books cost y dollars. What is the price of 3 such books? To find the price of one book, we divide the total cost y by the number of books, which is 8. Let's call the price of one book x. So, x = y/8.
To find the price of 3 books, we multiply the price of one book by 3. Hence, the price of 3 books would be x times 3 or (y/8) times 3, which can be simplified to 3y/8.
Thus, the price of 3 such books is 3y/8 dollars.
Kari plans to sample 20 people of a population that contains 100 students. She wants to determine how many people wake up before 6 a.m. Which sample is the most random?
Answer:
5 students out of each of the 4 homeroom classes (C)
Step-by-step explanation:
Answer:
c 5 students out of each of the 4 homeroom classes
i got it right on edge
Point B is the midpoint of AC
Which statements about the figure must be true? Check all
that apply
a)
b)
c) <ВС = 1/2 AC
d)
e) DB congruent BC
f) 2m
BC=1/2 AC must be true because B is a mid point so BC=AB=1/2AC
Given that B is the midpoint of AC
AC= AB + BC
Since AB = BC
AC = 2 [tex]\times[/tex] BC
so BC = [tex]\frac{1}{2} \times[/tex]AC
If the Length of BC = Length of BD then they are said to be congruent.
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HELP NOW PLEASE. The yearly attendance at a ballpark is shown in the table. Which answer describes the average rate of change from Year 2 to Year 5?
I think the last one. Sorry if I’m wrong. Minus year 2 and 5
Answer:
Option. A is the correct option.
Step-by-step explanation:
The yearly attendance at a ballpark is shown in the table attached.
We have to describe the average rate of change in attendance from year 2 to year 5.
Since rate of change in the attendance will be described by [tex]\frac{\text{Difference in attendance}}{\text{Difference in years}}[/tex]
Therefore, average change in attendance = [tex]\frac{\text{Attendance in year 5 - attendance in year 2}}{\text{5-2}}[/tex]
= [tex]\frac{333.7-298.3}{5-2}=\frac{35.40}{3}[/tex]
= 11.80 thousands per year
≈ 11800 people per year
Therefore, there is an average rate of change of 11800 people per year from year 2 to year 5.
Option A. is the answer.
Priyanka and Ethan were asked to find an explicit formula for the sequence -3,-14,-25,-36,...
Answer:
[tex]a_{n}[/tex] = 8 - 11n
Step-by-step explanation:
These are the terms of an arithmetic sequence with n th term
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
here a = - 3 and
d = - 14 - (- 3) = - 14 + 3 = -11, thus
[tex]a_{n}[/tex] = - 3 - 11(n - 1)
= - 3 - 11n + 11
= 8 - 11n
The explicit formula for the sequence -3, -14, -25, -36, ... is An = -11n + 8.
The student asked for an explicit formula for the sequence -3, -14, -25, -36, and so forth. We notice that each term decreases by 11 from the previous term. To find an explicit formula, we can use the arithmetic sequence formula which is given by An = A1 + (n - 1)d, where An is the n-th term, A1 is the first term, n is the term number, and d is the common difference between the terms.
For the given sequence, the first term A1 is -3 and the common difference d is -11. Substituting these values into the formula, we get An = -3 + (n - 1)(-11). We can simplify this to An = -3 - 11n + 11, which simplifies further to An = -11n + 8. Hence, the explicit formula for the given sequence is An = -11n + 8.
The width of a rectangle is 5 cm less than the length. The perimeter is 38 cm. Find the dimensions of the rectangle
Answer:
Step-by-step explanation:
38=2(5)+2(x ) find X
2x5-10
38-10=28
28/2=14
14/2=7
x =7
so you length is 7
The dimensions of the rectangle are length = 12 cm and width = 7 cm by solving equations of given the width of a rectangle is 5 cm less than the length and the perimeter is 38 cm.
Let's represent the length of the rectangle as "L" and the width as "W".
According to the given information:
The width is 5 cm less than the length, so we can write W = L - 5.
The perimeter of a rectangle is given by the formula P = 2(L + W),
where P is the perimeter, L is the length, and W is the width.
In this case, the perimeter is 38 cm, so we have
38 = 2(L + W).
Now we can use these equations to find the dimensions of the rectangle.
Substitute the value of W from the first equation into the second equation:
38 = 2(L + (L - 5))
Simplify the equation:
38 = 2(2L - 5)
38 = 4L - 10
Add 10 to both sides:
48 = 4L
Divide both sides by 4:
L = 12
Now we can substitute the value of L into the first equation to find the width:
W = L - 5
W = 12 - 5
W = 7
Therefore, the dimensions of the rectangle are length = 12 cm and width = 7 cm by solving equations of given the width of a rectangle is 5 cm less than the length and the perimeter is 38 cm.
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Use the Distributive Property to write each expression in expanded form.
a. 3(x + 7) b. 5(5 - x) c. 2(4x - 8) d. (x + 4)(x + 2)
A. 3x+21
B. 25-5x
C.8x-16
D.x^2+6x+24
a. 3x + 21
b. 25 - 5x
c. 8x - 16
d. x^2 +6x + 8
The graph of f(x)=x^2 is shown. Use the parabola tool to graph g(x). g(x)=(x-1)^2+2 ..Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Please someone help me.
Answer:
See below.
Step-by-step explanation:
The graph of ƒ(x) = x² is the red parabola in Figure 1.
Step 1. Vertex of g(x)
g(x) = (x – 1)² + 2
The graph of g(x) will be a parabola like that of ƒ(x) translated one unit to the right and two units up.
The vertex of ƒ(x) is at (0, 0), so the vertex of g(x) is at (1, 2). See Figure 1.
Step 2. Calculate two more points
(a) Try x = 0
g(0) = (0 – 1)² + 2 = 1² + 2 = 1 + 2 = 3
So, there is a point at (0, 3).
(b) Try x = 2
The axis of symmetry is a vertical line passing through the vertex at x = 1. We have calculated a point one unit left of the axis (at x = 0), so let's calculate a point one unit to the right, at x = 2.
g(2) = (2 – 1)² + 2 = 1² + 2 = 1 + 2 = 3
So, there are points at (2, 3) and (1,3). See Figure 2.
Step 3. Sketch the graph of g(x)
Draw a smooth curve through the three points. Extend the arms of the parabola vertically so the graph has the same shape as that of ƒ(x).
Your graph should look like the blue parabola in Figure 3.
Answer:
they are correct, here's proof
What is the value of the expression when X=-1 and y=2
4x^3y^2
Answer: the answer is negative 52 (-52 goes in the box)
Answer is -16
Step-by-step explanation:
Which equation has an a-value of 1, a b-value of -3, and a c-value of -5 ?
Answer:
the equation is 0 = -3x - 5 + x^2
Answer: The correct option is
(A) [tex]0=-3x-5+x^2.[/tex]
Step-by-step explanation: We are given to select the correct quadratic equation that has an a-value of 1, b-value of -3 and c-value of -5.
We know that
a general quadratic equation is of the following form :
[tex]ax^2+bx+c=0,~~a\neq0,[/tex]
where a is the coefficient of x²,
b is the coefficient of x
and
c is the constant term.
For the given equation, we get
the coefficient of x², a = 1,
the coefficient of x, b = -3
and
the constant term, c = -5.
Therefore, the required equation is
[tex]1\times x^2+(-3)\times x+(-5)=0\\\\\Rightarrow 0=-3x-5+x^2.[/tex]
Thus, (A) is the correct option.
plz help me brainliest to whoever answers first.
Answer:B) (8x5)xb
Step-by-step explanation:
Answer: b
Step-by-step explanation:
what is x in equation 1-2x=21
See attached pic
x = -10 is your answer
factor completely, 128x 2 +96xy + 18y 2
Answer:
[tex]2(8x+3y)^2)[/tex]
Step-by-step explanation:
The given expression is [tex]128x^2+96xy+18y^2[/tex].
We factor the GCF to get:
[tex]2(64x^2+48xy+9y^2)[/tex]
This can be rewritten as:
[tex]2[(8x)^2+2(3\times8)xy+(3y)^2][/tex]
We can observe that the quadratic trinomial is a perfect square)
[tex]2(8x+3y)^2)[/tex]
Therefore the completely factored form of the given trinomial is [tex]2(8x+3y)^2)[/tex]
$14 is what percent of $70
$14 is about 10% of $70
14 percent of 70 is about 10%
Is the triangle below best described as right, acute, or obtuse? Explain your reasoning
Answer:
Right.
Step-by-step explanation:
It is not smaller or larger than a 90% angle, it is exactly at a 90% angle. Therefore, it is a right triangle.
The triangle above is known as a Right Triangle or as the question says it is a Right.
REASON: It is a Right Triangle because it has a Right angle & Right angles always are 90 degrees.
I HOPE U GOT THE ANSWER!....
Shelf A had 40 books and Shelf B had 16 books. After Katrina borrowed an equal number of books from Shelf A and Shelf B, there were 3 times as many books on Shelf A than Shelf B. How many books did Katrina borrow altogether?
Answer:
8 books; 4 from each shelf
Step-by-step explanation:
let x represent equal number of books from each shelf
from shelf A = 40 -x
from shelf B = 16 -x
shelf A has 3 times as many books than shelf B
3(16- x) = 40 -x
48 -3x = 40 -x
48 - 40 = -x + 3x
8 = 2x
x = 4
altogether she borrowed 4 + 4 = 8 books
Can someone please help me out
Answer:
C.-19
Step-by-step explanation:
add -2 to each interval
6 to 7 =-11-2=-13
7 to 8 =-13-2=-15
8 to 9=-15-2=-17
9 to 10=-17-2=-19
A line segment has endpoints at (-4,13) and (18,-3.5).
What is the y-coordinate of the midpoint of the line segment?
Answer:
4.75
Explanation:
Make a right triangle
It goes right 22 and down 16.5
Those are the two sides
22^2+16.5^2=h^2
484+272.25=h^2
h=27.5
If it were half, it would go right 11, down 8.25
With hypotenuse being=13.75
Being at (7,4.75)
Hope you get it!
The number of hours in a day is measured in the tens
A. True
B. False
Answer:
true
Step-by-step explanation:
took the test
The number of hours in a day is correctly measured in the tens, as a day comprises of 24 hours. This measurement is a human invention rather than a natural observation. Hence true.
The question you've asked is whether the number of hours in a day is measured in the tens. The answer is True. There are 24 hours in a complete day. This measure is not something that naturally exists but rather is a human invention for the purpose of timekeeping. The Babylonians are credited with dividing a circle into 360 degrees, and they chose 24 as it divides neatly into 360, which allows for hours of a reasonable length that can be measured throughout the day. Notably, all days do not have exactly 12 hours of day and 12 hours of night except at the equator, and this occurs every day of the year. Other locations may experience nearly equal amounts of day and night during the equinoxes.
When we say that the number of hours in a day is more than seven hours, we are observing a fact about the number of hours in a day, which is significantly more than seven hours since a full day consists of 24 hours.
What is the solution to the equation log2 (5x - 2) = 3?
From log BNE to BEN
X=2
if you want explaination then ask me
if y=2×-3 determine the value of y when x=-15
Answer:
-33Step-by-step explanation:
Put x = -15 to the equation y = 2x - 3:
y = 2(-15) - 3 = -30 - 3 = -33
Answer:
y = 27
Step-by-step explanation:
[tex]y=2x-3[/tex]
[tex]y=2(15)-3[/tex]
[tex]y=30-3[/tex]
[tex]y=27[/tex]
in 5 rounds of a game, jill scored -3, 8, 9, -7, and 13. what integer represents her average score for 5 rounds?
-3+8+9+-7+13 divided by 5 which is 4
The integer represents her average score for 5 rounds will be 4.
What is the interpretation of average?Arithmetic mean is the best central measure available for representing the values of a data set. It is also called average of the values of the considered data set. It serves as one representation of the values of the data set. If for a data set, only its average is given, then we can't say much about the values of the data set. Average provides ill information in case of skewed data.
WE have given that 5 rounds of a game, jill scored -3, 8, 9, -7, and 13.
Then total number of score = - 3+8+9+-7+13
= 20
The total number of round in game = 5
Therefore,
Average = the total number of score/ number of rounds
Average = - 3+8+9+-7+13 / 5
Average = 20/5
Average = 4
Hence, the integer represents her average score for 5 rounds will be 4.
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pls help. as soon as possible
Answer:
[tex]new\ lenght=24cm\\new\ width=16cm[/tex]
This will scale the drawing up to larger dimensions.
Step-by-step explanation:
You can observe in the figure that the rectangular drawing has these dimensions:
[tex]length=6cm\\width=4cm[/tex]
The new drawing will be obtained by multplying the dimensions of the original drawing by the scale factor 4.
Therefore, the new dimensions will be:
[tex]new\ lenght=(6cm)(4)=24cm\\new\ width=(4cm)(4)=16cm[/tex]
You can observe that this will scale the drawing up to larger dimensions.
given that f'(x) = 6lnx and f(2) = -3.682, find f(3).
Answer:
If you mean: y =(lnx)
3
then:
dy
/dx = [3(lnx)
Step-by-step explanation:
The value of the function f(3) when, given that differencial function f'(x) = 6lnx and f(2) = -3.682, is 1.7748.
What is integration of a function?Integration is the operation which is used to find the original function from its darivative form.
The differencial function is given that
[tex]f'(x) = 6\ln x[/tex]
Integrate this function, with respect to the x,
[tex]f(x) =\int { 6\ln x} \, dx\\f(x) =6(\int { \ln x} )\, dx\\f(x) =6(x\ln x-\int { 1} \, dx)+C\\f(x) =6(x\ln x-x)+C\\f(x)=6x(\ln x-1)+C[/tex]
The value of function at 2 is,
[tex]f(2) = -3.682[/tex]
Put this value in the above equation as,
[tex]f(2)=6(2)(\ln (2)-1)+C\\-3.682=12(0.6931-1)+C\\-3.682=-3.682+C\\0=C[/tex]
Hence the value of constat is 0. Thus, the value of function at 3 is,
[tex]f(3)=6(3)(\ln (3)-1)+0\\f(3)=18(1.0986-1)\\f(3)=1.7748[/tex]
Hence, the value of the function f(3) when, given that differencial function f'(x) = 6lnx and f(2) = -3.682, is 1.7748.
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Find the circumference and area of a circle with a diameter of 10 in. Leave your answers in terms of pi.
Answer:
Circumference of given circle = 10π in
Step-by-step explanation:
Points to remember
Circumference of a circle = 2πr
Where r is the radius of circle
To find the circumference of circle
It is given that diameter of circle d = 10 in
Radius r = d/2 = 10/2 = 5 in
Circumference = 2πr = 2 * π * 5 = 10π in
Therefore the correct answer is circumference = 10π in
Events A and B are independent. Find the missing probability.
P(b)=9/20,p(a|b)=1/5,p(a)=?
Answer:
4/9
Step-by-step explanation:
since they are independent
p(ab)=p(a/b)=p(a)*p(b)
1/5=p(a)*9/20
p(a)=[tex]\frac{\frac{1}{5} }{\frac{9}{20} } = 4/9[/tex]
Given that two events are independent, the probability of one event given the other is the same as the probability of the event itself. Therefore, the probability of event A is 1/5.
Explanation:In probability, the concept of independence plays a crucial role. If two events, A and B, are independent, then the probability of event A occurring, given that event B has already occurred, is the same as the probability of event A.
In your case, P(A|B) = P(A). So, P(A) = P(A|B) = 1/5.
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