Answer:
[tex]a_{n}[/tex] = n - 5
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
- 3 - (- 4) = - 2 - (- 3) = - 1 - (- 2) = 1
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 4 and d = 1 , then
[tex]a_{n}[/tex] = - 4 + 1 (n - 1) = - 4 + n - 1 = n - 5
Expand and simplify:
3(2p - 5) + 2(p + 3)
Answer:
8p - 9
Step-by-step explanation:
→ Expand brackets
6p - 15 + 2p + 6
→ Collect like terms
8p - 9
a researcher measures the amount of sugar in several cans of the same soda. the mean is 39.01 with a standard deviation of 0.5. the researcher randomly selects a sample of 100. find the probability that the sum of the 100 values is greater than 3,908. (round your answer to four decimal places.)
Using the concepts of probability, we got that 0.0764 is the probability that the sum of the 100 values is greater than 3,908 when a researcher measure the amount of sugar in several cans of the same soda.
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
Z=(X-μ)/σ
The z-score measures how many standard deviations the measure is above or below the mean.Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation .For this problem, these parameters are given as follows:
μ=39.01,σ=0.5,n=100,s=0.5/√100=0.05
A sum of 3908 is equivalent to a sample mean of 3908/100 = 39.08, which means that the probability is the p-value of Z when X = 39.08, hence:
Z=(X-μ)/σ
By the Central Limit Theorem:
Z=(X-μ)/s
=>Z=(39.08-39.01)/0.05
=>Z=(0.07)/0.05
=>Z=7/5
=>Z=1.4
Z = 1.4 has a p-value of 0.0764.
Hence, the probability that the sum of the 100 values is greater than 3,908 is 0.0764.
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answer the question please i would appreciate it man
The scientific notation representation is 2.6 x [tex]10^{-2}[/tex].
What is scientific Notation?Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
Given:
(0. 00032) (5.2 x [tex]10^6[/tex])/ 6.4 x [tex]10^5[/tex]
Now, solving the above expression
= 0.001664 x 10² / 6.4
= 0.00026 x 10²
= 2.6 x [tex]10^{-2}[/tex]
Hence, the scientific notation representation is 2.6 x [tex]10^{-2}[/tex].
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There is a line that includes the point (-1, 1) and has a slope of 9. What is its equation in slope-intercept form?
Answer: would be y=9x+10
Step-by-step explanation: Use the point slope form
Jason is training to run in a marathon. His goal for this week is to run a minimum of 45 miles. So far this week, he has already run 10 miles. Which inequality could be used to determine the mean number of miles, m, he would need to run each day for 5 more days to achieve his goal?
The inequality that could be used to determine the mean number of miles Jason would need to run each day for 5 more days to achieve his goal is 10 + 5m ≥ 45
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let the number of miles be given as m.
Since his goal for this week is to run a minimum of 45 miles. So far this week, he has already run 10 miles. This will be:
10 + 5m ≥ 45
This expresses the inequality.
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the graph of y=f(x) is shown below. find the value of f(5)
Answer:
f(5) = -5
Step-by-step explanation:
To find the value of f(5), find the value of y when x = 5.
To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line.
Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.
Therefore, the value of f(5) is -5.
See attachment.
Answer:
f(5) = - 5
Step-by-step explanation:
Given the graph of the function f(x).
In order to find the value of f for any value of x on the graph, find the point x on the x-axis, then add a vertical line from this point to the graph. The y-coordinate of the intersection is the value of the function at given x-coordinate.
We are asked to find the value of f(5).
This is f(5) = - 5 as per above explanation.
See the attached for better understanding.
For a given function f (x), the domain is -4 < x <7, the range is 2 < y < 9, and has the point (4,8) on the graph. If h (z) = f(x+4), then
the domain of h (z) would be
type your answer....
the range would be type your answer.....
and the corresponding point would be moved to (type your answer.....
type your answer.....
y< type your answer.....
Submit
The domain of h(z) would be (-8,3).
The range of h(z) would be (2,9).
Point (4,8) would be moved to (0,8)
What are the domain and range of a function?
The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.
A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)
For the function f(x):
Domain: (-4,7)
Range: (2,9)
The function f(x+4) is equal to 1 (f(x+4)).
This shows, inputs: -4, outputs: 1
Domain of f(x+4):
add -4 to the Domain values of f(x)
Domain:(-4-4,7-4)=(-8,3)
Range of f(x+4):
Multiply the range values of f(x) by 1
Range: (1*2,1*9)= (2,9)
Find, where the point (4,8) would be moved:
add -4 to 4, and multiply 8 by 1
(4-4,8*1)
=(0,8)
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Need help quick look at photo
Answer: the slope is unidentified
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
71°
(2x+5)
62⁰
Answer:
x=21
Step-by-step explanation:
The angles of a triangle always add up to 180°
71+62+(2x+5)=180
First add 71 and 62
133+(2x+5)=180
Then you subtract 133
2x+5=47
Subtract 5 too
2x=42
Then divide by 2
x=21
We can check our answer by adding all the angles
71+62+(2*21+5)
71+62+(42+5)
71+62+47=180
The cost
C
, in £, of a monthly phone contract is made up of the fixed line rental
L
, in £, and the price
P
, in £, of the calls made. Enter a formula for the cost and, enter the cost if the line rental is £20 and the price of calls made is £15.
The formula for the cost if the line rental is £20 and the price of calls made is £15 will be 20 + 15p.
How to calculate the cost?It should be noted that an expression is used to illustrate the relationship given between the variables.
In this case, the monthly phone contract is made up of the fixed line rental and the price represented by p.
The appropriate expression to illustrate this information will be:
= Fixed cost + Calls made
= 20 + 15(p)
= 20 + 15p
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Find the two solutions to the equation
(x − 10) (x + 7) = 0
Answer:
x = - 7 , x = 10
Step-by-step explanation:
(x - 10)(x + 7) = 0
equate each factor to zero and solve for x
x - 10 = 0 ⇒ x = 10
x + 7 = 0 ⇒ x = - 7
rearrange the formula below to make 'a' the new subject:
[tex]c + \frac{1}{2} a^{2}b = d[/tex]
Answer:
a = ± [tex]\sqrt{\frac{2d-2c}{b} }[/tex]
Step-by-step explanation:
c + [tex]\frac{1}{2}[/tex] a²b = d ( multiply through by 2 to clear the fraction )
2c + a²b = 2d ( subtract 2c from both sides )
a²b = 2d - 2c ( divide both sides by b )
a² = [tex]\frac{2d-2c}{b}[/tex] ( take square root of both sides )
a = ± [tex]\sqrt{\frac{2d-2c}{b} }[/tex]
14. the mean price of a pound of ground beef in 75 cities in the midwest is $2.11 and the standard deviation is $0.56. suppose the histogram of the data shows that the distribution is unimodal and symmetrical. a local grocer is selling a pound of ground beef for $3.50. what is this price in standard units? assuming the empirical rule applies, would this price be unusual or not? round to the nearest hundredth.
For a unimodal distribution which is symmetrical with a mean price of $2.11 and standard deviation of $0.56, a local grocer’s price of $3.50 in standard units would be 2.282 and it is unusually expensive.
A unimodal distribution refers to a distribution with one clear peak as the values increase to a single highest point after which they. It can be symmetrical or non-symmetrical. A symmetrical distribution refers to a distribution whose mean, mode, and median are all equal.
The standard score (z) is given by:
z = (x - µ)/σ where µ is the mean and σ is the standard deviation.
To determine the value of z for $3.50 price:
z = (3.5 – 2.11)/0.56 = 2.482
From the z-table, the probability of z ≥ 2.282
P (z ≥ 2.282) = 1 – P (z < 2.282) = 1 – 0.98876 = 0.0112 or 1.12%
Hence, the price of $ 3.50 is unusually high.
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Solve this system of linear equations without graphing: {5x+4y=810x−4y=46[tex]Solve this system of linear equations without graphing: {5x+4y=810x−4y=46[/tex]
The solution of given system of linear equations is x = 3.6 and y = 2.5.
A "system" of equations is a collection of equations that you answer all at once. Ax + By + C = 0, where A and B are the coefficients and C is the constant, can be used to describe a linear equation. Non-linear equations are more difficult to comprehend than linear equations.
Solving the equations,
5x +4y = 8
10x − 4y = 46
Adding the above equations, we get
5x + 10x + 4y - 4y = 8 + 46
15x=54
Dividing by 15,
x = 3.6
Now, putting the value of x in second equation,
10(3.6) - 4y = 46
36 - 4y = 46
4y = -10
Dividing by 4, we get
y = -2.5
Therefore, the solution of given system of linear equations is x = 3.6 and y = 2.5.
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Fig. 3.3 shows an equilateral triangle with the lengths of its sides given in terms of x and y. Find the values of x and y. A 4x cm B 3y cm C (x + y + 5) cm
The values of x and y are 3 and 4.
Given:
shows an equilateral triangle with the lengths of its sides given in terms of x and y.
A 4x cm B 3y cm C (x + y + 5) cm
In equilateral triangle all sides are equal:
4x = 3y = x+y+5
4x = 3y
4x - 3y = 0. ---------eq(1)
4x = x + y + 5
3x - y = 5. ----------eq(2)
solving eq 1 - eq 2*3 we get,
4x - 3y - 9x + 3y = 0 - 15
-5x = -15
x = 3
4x - 3y = 0
4*3 - 3y = 0
12 = 3y
y = 12/3
y = 4
Therefore The values of x and y are 3 and 4.
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Select all the equations that are equivalent to this equation. 14 (8x + 56) = 20 56 + 8x = 80 14 = 20 – 8x 2x + 14 = 5 2x = 6 x = 3
The equation that are equivalent to the equation 1/4 (8x + 56) = 20 are 56 + 8x = 80 and 2x = 6
The equation is
1/4 (8x + 56) = 20
Solve the equation
8x + 56 = 80
8x = 80 - 56
8x = 24
x = 24/8
x = 3
The first equation is
56 + 8x = 80
8x = 80 - 56
8x = 24
x = 24/8
x = 3
The second equation is
14 = 20 - 8x
8x = 20 - 14
8x = 6
x = 6/8
x = 3/4
The third equation is
2x + 14 = 5
2x = 5 - 14
2x = -9
x = -9/2
The fourth equation is
2x = 6
x = 6/2
x = 3
Hence, the equation that are equivalent to the equation 1/4 (8x + 56) = 20 are 56 + 8x = 80 and 2x = 6
The complete question is:
Which equations are equal to this equation? Select all that apply.
1/4 (8x + 56) = 20
a. 56 + 8x = 80
b. 14 = 20 - 8x
c. 2x + 14 = 5
d. 2x = 6
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The volume of a cylinder does not change
if you slant the (fill in the blank)
the cylinder but keep the
of(fill in the blank)
the same. The
volume of an oblique cylinder is the same
as the volume of an upright cylinder with
the same base and height.
If you slant the height of the cylinder but keep the radius the same then the volume of an oblique cylinder is the same.
What is an oblique cylinder?
When a cylinder "leans over," that is when its sides are not parallel to its bases, then the cylinder is said to be an oblique cylinder. The bases (ends) of an oblique cylinder stay parallel to one another, while the sides tilt outward at an angle that isn't quite 90°.
An oblique cylinder will have the same volume as a right cylinder with the same radius and height. As long as the radius and height are the same, the volume does not vary, but the height must equal the perpendicular height.
From the above observations, we can say that If you slant the height of the cylinder but keep the radius the same then the volume of an oblique cylinder is the same.
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A sample of a radioactive isotope had an initial mass of 110 mg in the year 1990 and decays exponentially over time. A measurement in the year 1993 found that the sample's mass had decayed to 90 mg. What would be the expected mass of the sample in the year 2002, to the nearest whole number?
50 mg be the expected mass of the sample in the year 2002, to the nearest whole number
In 1990, a sample of a radioactive isotope had an initial mass of 110 mg and decayed exponentially over time.
A measurement in 1993 revealed that the sample's mass had decayed to 90
110 mg - 90 mg = 20 mg (amount decayed in the 3 total years)
20 mg ÷ 3 years = 6.6 mg decayed per year
6.6 × 9 years (years between 1993 and 2002) = 60 mg
110 mg - 60 mg = 50 mg, rounded to 50 mg
50 mg be the expected mass of the sample in the year 2002, to the nearest whole number
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solve for x and find each angle measure
(7x-32)
(5x-27)
(9x-8)
equation
x:
please help me !!
it’s for a quiz
Answer:
Step-by-step explanation:
187
Will give u brainliest! on thses 2 questions
Answer:
1: [tex]2\sqrt{2}[/tex]
2: [tex]10\sqrt{55}[/tex]
Step-by-step explanation:
[tex]\sqrt{16-8}[/tex]
[tex]\sqrt{8}[/tex]
[tex]\sqrt{8}=2\sqrt{2}[/tex]
2:
[tex]\sqrt{\frac{11}{16+4}[/tex]
[tex]\sqrt{\frac{11}{20}[/tex]
[tex]\sqrt{.55}[/tex]
[tex]10\sqrt{55}[/tex]
Hopes this helps
PLEASE HELP QUICK (no links pls)
The total length of the sari Divya make is 6 yards, so option A is correct.
What is rectangle?Four sides, four corners, and four right angles (90°) make up the enclosed 2-D shape known as a rectangle. A rectangle has opposite sides that are parallel and equal. A rectangle has length and width because it is a two-dimensional form. The length of a rectangle is its longer side; its breadth is its shorter side.
Given:
The length of saris Divya can make = 6 yards,
As the graph is showing, to make a sari Divya required 6 yards of fabric,
Therefore, the total length of the sari Divya make is 6 yards.
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Simplify negative 1 and 2 over 3 minus 9 and 2 over 5.
11 and 1 over 15
negative 10 and 4 over 8
negative 16 over 15
negative 166 over 15
The simplified form of the given expression; negative 1 and 2 over 3 minus 9 and 2 over 5 as required is; -166/15 (negative 166 over 15).
What is the simplified form of the expression?It follows from the task content that the simplified form of the given expression is to be determined.
Since the given expression is; -1 ⅔ - 9 ⅖.
First, the mixed numbers as in the task content must be converted to fractions so that we have;
- 1 ⅔ = -5/3 and
9 ⅖ = 47/5
Therefore, the required evaluation is; -5/3 - 47/5
= -25/15 - 141/15
= (-25 - 141) / 15
= -166/15
Therefore, the required simplified form of the expression is; negative 166 over 15.
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.
In the given question we have to find the maximum area of the rectangular area.
Liana has 3200 yards of fencing to enclose a rectangle.
So we know that the perimeter of rectangle is
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 3200
Divide by 2 on both side we get
x+y = 1600................(1)
As we know the area of rectangle is
A = xy
From the equation the value of y is 1600-x.
Now putting the value of y
A = x(1600-x)
A = 1600x-x^2
On differentiating
dA/dx = 1600-2x
Putting dA/dx=0
1600-2x=0
Subtract 1600 on both side we get
-2x= -1600
Divide by -2 on both side we get
x = 800 yards
Now putting the value of x in the y=1600-x
y=1600-800
y=800 yards
So the maximum area is
A= 800*800
A= 640,000 square yards
Hence, a rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.
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Graph the linear function.
f(x) = 3x + 4
The graph of the linear function f(x) = 3x + 4 is plotted.
Define the term linear function?To find a linear function, we utilise the slope-intercept form or even the point-slope form.If the function's details are presented in its algebraic form, then f(x) = mx + b designates a linear function. Instead, to check if the data presented in table style reflects a linear function:Get the x-value variations.Get the y-value differences.Determine that there is a steady correspondence between the difference in y values and the difference in x values.For the given question, the function is given as;
f(x) = 3x + 4
Put x = 0, f(x ) = 4 ;(0, 4)
Put f(x) = 0, x = -1.33 ;(-1.33, 0)
Plot the points of the coordinate axis as shown in the graph.
Thus, the graph of the linear function f(x) = 3x + 4 is plotted.
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PLEASE HELP ASAP
What are the steps to writing the equation of a line, parallel
given line through a given point? Parallel lines have the _____ slope. Perpendicular lines have ____.
Answer:
parallel- same slope so the slope is 5, the slope will also be 5
perpendicular- reciprocal slope (if a whole # like 5, it goes to -1/5)
Step-by-step explanation:
The quotient of x and 2 is less than or equal to 5.
\Step-by-step explanation:
convert to math form:
[tex]\frac{x}{2} \le5[/tex]
simplify:
[tex]x \le 10[/tex]
convert to word form(optional):
x is less than or equal to 5.
For every 1/3 cups of flour, there are
7/8 cups of pumkin. How much flour (in
cups) should I use for 1 cup of
pumpkin?
Answer: 0.4176 cups of flour
Step-by-step explanation: First you'll need to convert both amounts to the same denominator, using their LCM, which is 24. 1/3 x 8 = 8/24, 7/8 x 3 = 21/24. Then calculate what you need to multiply 21/24 with to get 24/24, 21/24 = 0.875 1.000- 0.875 = 0.125. Finally, multiply 1/3 by 0.125 which is 0.416... / 0.4167, so you'll need 0.4167 cups of flour, or 4,167/10,000 of a cup os flour.
For which equation will f(-2) = -6?
f(x) = x³ + x
f(x)=x² - 5x
f(x) = 4x³ + 6x² − x
f(x) = -3x³-4x² + 4x
The correct equation is f(x) = 4x³ + 6x² − x . A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
What is Function ?A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. This form is called the slope-intercept form.
The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope.
in question f(-2) = - 6
so x= -2
In function f(x) = 4x³ + 6x² - x
F(-2) = 4(-2)³ + 6 (-2)² - (-2) = - 6
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Here is an equation: 5x - 5 = 5x + ___. What could you write in the blank so the equation would be true for:
1. No values of x.
2. All values of x.
3. One value of x.
Answer:
1 ; -5 ; 2x
Step-by-step explanation:
1. We must have 0x equal to a number that is not 0
example = 1
5x - 5x = 5 + 1
0 = 6 (false)
2 we must have 0 = 0
-5
5x - 5x = 5 - 5
0 = 0
3 the x must stay
example = 2x
5x - 5 = 5x + 2x
2x = -5
2/2 x = -5/2
x = -5/2
equation of the line that passes through the points (1,-4)(1,−4) and (5,-1)(5,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The points are given below.
(1, −4) and (5, −1)
The equation of the line that passes through (1, −4) and (5, −1) will be given as,
(y + 4) = [(−1 + 4) / (5 − 1)](x − 1)
y + 4 = (3/4)x − 3/4
y = (3/4)x + 13/4
The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.
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