Answer:
10) 10n
12) 19-n
14) 7(x+2)
15) x/3 -11
11) n+5
13) n^2
Step-by-step explanation:
product = multiply
difference= subtract
sum = add
quotient = divide
Answer:
lo siento soy nuevo en este aplicación ay mis sierras disculpas
If y = cos x, how many periods will there be between -5pi and 9pi ?
Answer:
7 periods.
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
[tex]f(x) = A \cos(B(x + C)) + D[/tex]
where:
A = amplitude (height from the mid-line to the peak).2π/B = period (horizontal distance between consecutive peaks).C = phase shift (horizontal shift - positive is to the left).D = vertical shift.Therefore, for y = cos x:
Amplitude = 1Period = 2πPhase shift = 0Vertical shift = 0The maximum of the function is when x = 0 + 2πn.
The minimum of the function is when x = π + 2πn.
To find the number of periods, first find the difference between the two given values:
⇒ 9π - (-5π) = 9π + 5π = 14π
As the period of the function is 2π, then the number of periods is:
⇒ 14π ÷ 2π = 7 periods.
suppose that the ages of medical residents are normally distributed with a mean of 27 years and standard deviation 2 years. what percent of medical residents are less than 28 years old?
The percent of medical residents less than 28 years old is 69.15%.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 28
μ = mean = 27
σ = standard deviation = 2
z-score = (28 - 27) / 2
z-score = (1) / 2
z-score = 0.5
Find the probability that corresponds to the z-score in the z-table. (see attached images)
at z = 0.5, p = 0.6915
Multiply the probability by 100 to get the percentage.
% = p x 100
% = 0.6915 x 100
% = 69.15
Hence, the percent of medical residents that are less than 28 years old is 69.15%.
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A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 1200 feet of fencing is used. Find the dimensions of the playground that will enclose the greatest total area.
The greatest total area, length will be 300 ft. and width will be 200 ft.
Given,
In the question:
A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 1200 feet of fencing is used.
Now, According to the question:
Lets assume, the length of the playground is l ft. and width is w ft.
Suppose, the playground is divided into two parts by a fence parallel to width. That means the length of the divider fence will be w ft.
So, the total length of the fence needed = (2l+ 3w)ft.
It is given in the question that 1200 feet of fencing is used.
2l + 3w = 1200
2l = 1200 - 3w
l = 600 - [tex]\frac{3}{2}w[/tex] ......(1)
Now, the area of the playground....
A = l × w
A = ( 600 - [tex]\frac{3}{2}w[/tex] ) × w
A = 600w - [tex]\frac{3}{2}w^2[/tex]
Taking derivative on both side in respect of "w" ,
we will get:
dA/dw = 600 - [tex]\frac{3}{2} (2w)[/tex]
dA/dw = 600 - 3w
A will be maximum when dA/dw = 0
600 - 3w = 0
600 = 3w
w = 600/3
w = 200
Now plugging this w = 200 into equation (1)...
l = 600 - [tex]\frac{3}{2}[/tex] × 200
l = 600 - 300
l = 300
Hence, for the greatest total area, length will be 300 ft. and width will be 200 ft.
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A server at a restaurant is hoping for a 15% tip from a large party. The
party's bill at the end of the night was $312.00. Write a proportion and
describe how you would solve it to calculate the amount of the tip the
server hopes to receive. Be sure to state your final answer as an amount of
money, rounded to the nearest cent.
*Use the "/" on your keyboard as a fraction bar for ratios when writing the
proportion. For example: I can show that one-half and two-fourths are
proportional by typing "1/2 = 2/4" for the proportion.
$57 is the amount of the tip the server hopes to receive.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
A server at a restaurant is hoping for a 15% tip from a large party.
The party's bill at the end of the night was $312.00.
Now we need to find 15% of $312
15% is converted to decimal by dividing with 100
15/100=0.15
Now multiply 0.15 with 380
0.15×380
57
Hence $57 is the amount of the tip the server hopes to receive.
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The dictionary wa about 1 kg and a paperclip weigh about 1 g how many paper clip would equal the weight of a dictionary
1000 paperclips would weigh equal to the dictionary.
Weight of the dictionary = 1 kg
weight of one paper clip = 1 gm
according to the mathematical conversion system of weights
1 kilogram = 1000 grams
on the basis of the statement
1 gram is the weight of = 1 clip
so , 1000gm would be the weight of = 1 x 1000
1000 gm would be the weight of = 1000 clips
to weigh equal to the dictionary , we would require 1000 clips .
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D. Are the points on the line included in the solution set to the inequality 2y-x>1? Why or why not?
[No/Yes]. The point (-7,-3), which is on the lone,[is/is not] a solution to the inequality
For given inequality 2y-x>1 point (-7,-3) is not the solution set of given inequality.
Inequality:
Inequalities are mathematical sentences formed by relating two expressions to each other.
Different inequality sign are:
x>y ,
x is greater than y
x≥y
x is greater than or equal to y
x<y
x is less than y
x≤y
x is less than or equal to y
Given inequality is,
2y - x > 1
In the given inequality
L.H.S (Left hand Side) = 2y - x
R.H.S (Right Hand Side) = 1
and the given point is (-7,-3)
Left hand Side at point (-7,-3)
L.H.S = 2y - x
= 2 (-3) - (-7)
= -6 + 7
= 1
and
Right Hand Side = 1
Here we can see both L.H.S and R.H.S are equal,but in the given inequality there is no equality,so the point (-7,-3) is not the solution set.
Thus we conclude,
(-7,-3) is not the solution set of given inequality.
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a rectangular container with a square base and open top must have volume of 16 \text{} cubic meters. if material for the base costs $8 per square meter, and material for the sides costs $2 \text{} per square meter, find the dimensions of the container so that the cost of material to make it will be a minimum. as your answer, please input the value of the minimal cost.
The minimal cost of the box is $96.
Given data;
The volume of the box (v) = x²y
Given that, volume = 16 m³
So, 16 = x²y
y = 16/x² → (I)
Material for the base costs $8 per square meter, and material for the sides costs $2 per square meter.
Total cost (C) = 8 (x²) + 2*(xy)(4)
= 8x² + 8xy
Using (I),
C(x) = 8x² + 8x(16/x²)
C (^) = 8x² + 128/x
Now find critical points from
∴ [tex]\frac{d}{dx} = [8x^2+\frac{128}{x} ]=0[/tex]
x³ = 8
x = 2
So, the minimal cost will be given by x= 2,
Now, y = 16/x²
= 16/4
= 4
Dimension of the box that minimizes the cost is;
height = 4m, width=2m and breadth = 12m
Now,
Minimum cost = 8 (2)² + 128/2 = 32 + 64
= 96
Hence, The minimal cost of the box is $96.
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write a system of linear equations containing 2x+y=0 and that has the solution (2,-4)
The linear equation y = 5 · x - 14 is a possible equation that intercepts the line 2 · x + y = 0 at point (x, y) = (2, - 4),
What is the remaining equation of a system of linear equations?
To generate a system of linear equations, we need to derive an additional that intercepts the line 2 · x + y = 0 at point (x, y) = (2, - 4). We need to find an equation of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.Please notice that there are more than a single choice. First, choose the slope of the line:
m = 5
Second, substitute the slope and the independent and dependent variables:
b = y - m · x
b = - 4 - 5 · 2
b = - 14
Third, write the resulting linear equation:
y = 5 · x - 14
The linear equation y = 5 · x - 14 is a possible equation of the system of equations.
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In a study of cell phone usage and brain hemispheric dominance, an internet survey was e-mailed to subjects randomly selected from an online group involved with ears. There were surveys returned. Use a 0. 01 significance level to test the claim that the return rate is less than 20%. Use the p-value method and use the normal distribution as an approximation to the binomial distribution.
The value of z statistics is -1.878,
Given,
In the question:
Number of random sample selected, n = 6967
Number of surveys returned, x = 1331
Now, According to the question:
Estimated proportion of return rate;
To find the value of p = 1331/6967 = 0.192
Significance level, ∝ = 0.01
z would represent the statistic
We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:
Null hypothesis, p₀ ≥ 0.2
Alternative hypothesis, p₀ < 0.2
The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)
z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878
Using the alternative hypothesis and the following probability, we can now get the p value:
p value = p(z < - 1.878) = 0.0302
We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.
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a c-chart is used for multiple choice means. ranges. percent defective. fraction defective per unit. number of defects per unit.
A C - chart is used for Number of defects per unit.
What is C - chart?
In statistical quality control, the c-chart is a sort of control chart used to track "count"-type data, often the total number of nonconformities per unit. On rare occasions, it is also used to keep track of all the events that take place in a given period of time.
C-charts are used to assess if a process is predictable and stable as well as to track the results of process improvements before and after they have been made. The C - chart is particularly useful when there are few actual flaws in the subgroup but many potential for defects exist.
Count type data, such as the number of non-conformities per unit, are monitored using a statistical quality control chart known as a C-Chart.
Hence, a C - chart is used for Number of defects per unit.
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the united nations stores data about energy production from animal waste and the use around the world. the following data set gives information for converting animal waste into electricity. country or area commodity - transaction year quantity unit united states animal waste - transformation in electricity 2014 171907 terajoules united states animal waste - transformation in electricity 2013 149233 terajoules united states animal waste - transformation in electricity 2012 104847 terajoules united states animal waste - transformation in electricity 2011 141347 terajoules united states animal waste - transformation in electricity 2003 185912 terajoules united states animal waste - transformation in electricity 2002 197120 terajoules united states animal waste - transformation in electricity 2001 104725 terajoules united states animal waste - transformation in electricity 2000 126745 terajoules united states animal waste - transformation in electricity 1999 133206 terajoules united states animal waste - transformation in electricity 1998 224425 terajoules united states animal waste - transformation in electricity 1997 129113 terajoules united states animal waste - transformation in electricity 1996 5274 terajoules united states animal waste - transformation in electricity 1993 21748 terajoules united states animal waste - transformation in electricity 1992 242924 terajoules united states animal waste - transformation in electricity 1991 210448 terajoules united states animal waste - transformation in electricity 1990 215437 terajoules what is the slope of the linear equation of the entire data set? round to nearest hundredth. provide your answer below:
The slope of the linear equation of the entire data set is -720.98
1. Bring data in to excel sheet
2.Select both x and y variable and insert scatter plot chart. Select any data point in the chart and add trend line. In the format trend line option choose "Linear" and also select "Display an equation on chart" & "Display R-squared value on chart"
To find: What is the slope of the linear equation of the entire data set? Round to nearest hundredth.
Regression equation : y = -720.98x + 15,90,277.32
Slope = -720.98 (Round to nearest hundredth.)
Intercept = 15,90,277.32
So, the slope of the linear equation of the entire data set is -720.98
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state police set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers. it would be too inconvenient and costly to check every vehicle that passes through a checkpoint, so they decide to stop about 1/20 of the vehicles. why would a simple random sample be unreasonable for this situation? responses if the police used a list of registered automobiles, they would have to track down each of those owners and the unregistered owners would not be on the list. if the police used a list of registered automobiles, they would have to track down each of those owners and the unregistered owners would not be on the list. randomly picking cars wouldn't be fair to the people who ride the bus. randomly picking cars wouldn't be fair to the people who ride the bus. police might choose cars based on how they look. police might choose cars based on how they look. if they randomly picked cars at a grocery store it wouldn't be a good sample size. if they randomly picked cars at a grocery store it wouldn't be a good sample size.
The set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers is given as below as
Cars, Are cars up to date, Select the car to check, Stopped cars, Convenience sampling ,The cars that are not stopped might be having more problems
Given that,
The Population
The Population parameter of interest
The Sampling frame
The Sample
The Sampling Method, Including whether or not randomization was employed.
Any potential source of bias you can detect any problems you see in generalizing to the population of interest.
To find : The set up a roadblock
A. Cars
B. Are cars up to date
C. Select the car to check
D. Stopped cars
E. Convenience sampling
F. The cars that are not stopped might be having more problems
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or
The radius of a semicircle is 2 millimeters. What is the semicircle's area?
The area of the semi circle with radius 2mm is 2[tex]\pi[/tex][tex]mm^{2}[/tex]
What is a semi-circle?A semicircle is formed when a lining passing through the centre touches the two ends on the circle. Thus, by joining two semicircles we get a circular shape.
When a circle is cut into two halves or when the circumference of a circle is divided by 2, we get a semicircular shape.
Area of a semi-circle = [tex]\frac{\pi r^{2} }{2}[/tex]
but radius r = 2mm
substitute r into the area equation, we have
Area of semicircle = [tex]\frac{\pi 2^{2} }{2}[/tex]
Area of semicircle is = 2[tex]\pi[/tex][tex]mm^{2}[/tex]
In conclusion the area of the semicircle is 2[tex]\pi[/tex][tex]mm^{2}[/tex]
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Which inequality represents all possible values for x in -2x>-48?
A X <-24
BX<24
CX-24
DX> 24
Answer:
Step-by-step explanation:
An inequality which represents all possible values for x in -2x>-48 is: B. x < 24.
What is an inequality?In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data such as integers, and variables in an equation based on any of the following inequality symbols:
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Next, we would find the solution and possible values to this given inequality as follows:
-2x > -48
Dividing both sides of the inequality by -2, we have:
-2x/-2 > -48/-2
x < 48/2
x < 24.
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Find the image of 4(3, 7) under a translation along the vector (-4, 2).
A'(7,5)
A'(1,-9)
A'(-1,9)
4'(-7,-5)
The image of A(3, 7) under a translation along the vector (-4, 2) is A'(-1,9).
Given:
A(3,7) under a translation along the vector (-4, 2).
A' = A + (-4,2)
= (3,7) + (-4,2)
= (3+(-4), 7+2)
= (3-4, 9)
= (-1, 9)
Therefore the image of A(3, 7) under a translation along the vector (-4, 2) is A'(-1,9).
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Which equation can be solved by using this system of equations?
[y-3x³-7x² +5
[y=7x²+2x
3x³-7x²+5=0
3x³-7x² +5-7x4 + 2x
7x²+2x=0
7x4+3x3-7x²+2x+5=0
The equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.
We are given;
y = 3x³ - 7x² + 5
y = 7x^4 + 2x
We will solve the given equation by substitution method:
Using the substitution method, let us substitute y = 7x^4 + 2x in the equation y = 3x³ - 7x² + 5, we get,
3x³ - 7x² + 5 = 7x^4 + 2x
So, 3x³ - 7x² + 5 = 7x^4 + 2x will be solved by using the given system of equations.
Thus, the equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.
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Instructions solve n given the equation -3(2n-3)=25 -8n
Answer:
n=7
Step-by-step explanation:
-6n-9=25-8n
2n=34
n=17
The difference between the digits of a two digit
number is 1. The number itself is 1 more than 5 times
the Sum of Its digit. If the units digit is greater than
the tens digit, find the number.
Answer:
56
Step-by-step explanation:
Number with two digits = 10y + x
x > y
x-y = 1
10y + x = 5(x+y) + 1
x = y + 1
10y + y + 1 = 5(y+1 +y) + 1
11y + 1 = 5(2y+1) + 1
11y + 1 = 10y + 5 + 1
11y - 10y = 5
y = 5
x = 5 + 1 = 6
Applying the translation (x, y) → (x – 3, y + 7) maps the point (–4, 7) onto the point ________.
A)
(14, –7)
B)
(–7, 14)
C)
(7, –14)
D)
(14, 7)
Answer:
B
Step-by-step explanation:
The rule means to subtract 3 from the x-coordinate and add 7 to the y-coordinate.
HELP ME PLEASE, NEEDED ASAP
Answer:
a x=10
b x=7
Step-by-step explanation:
(a) 2(x+3) = x - 4
2x+6 = x - 4
2x+6-6= x-4-6
2x=x-10
2x-x=x-10-x
x=10
(b) 4(5x-2) = 2(9x+3)
20x-8 =18x+6
20x-8+8=18x+6+8
20x=18x+14
20x-18x =18x+14-18x
2x=14
/2 /2
x = 7.
this was due last week pls help me
Answer:
X=-2
Step-by-step explanation:
5+0.1x=3(1-0.3x)
5+0.1x=3-0.9x
+0.9x +0.9x
5+x=3
-5. -5
x=-2
Hopes this helps
Answer:
the answer is B
Step-by-step explanation:
5+0.1x=3(1-0.3x)=}
5+0.1x=3-0.9x=}
0.1x+0.9x=3-5=}
x= - 2
A hardware store was charging $4.51 for a screwdriver but raised the price 17%. The new price after the increase is $5.28. Enter an expression to show how the new price was calculated.
please help asap! This is for a test and I need it to raise my grade.
When written in scientific notation, the number 1,240,000 will have a
Choose... as the exponent on the power of 10.
Using scientific notation, the number 1240000 can be expressed as 1.24×10⁶
Scientific NotationScientific notation is a form of presenting very large numbers or very small numbers in a simpler form. As we know, the whole numbers can be extended till infinity, but we cannot write such huge numbers on a piece of paper. Also, the numbers which are present at the millions place after the decimal needed to be represented in a simpler form. Thus, it is difficult to represent a few numbers in their expanded form. Hence, we use scientific notations.
Converting the number 1,240,000 to scientific notation, we will get
1,240,000 = 1.24×10⁶
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i really need help with this pls
Answer:
B. x=3/k
Step-by-step explanation:
5kx+6=7kx
first you can simplify the kx terms
6=7kx-5kx
6=2kx
now get x by itself
6/2k=x
3/k=x
9t(t-2) + 10(t-2) factor
Answer: (9t + 10)(t - 2)
Step-by-step explanation:
9t (t − 2) + 10(t − 2)
9t^2 − 8t − 20
= (9t + 10)(t − 2)
What is the solution to |x-9| -3 < 1
Answer:
[tex]x < 13[/tex] and [tex]x > 5[/tex]
Step-by-step explanation:
Take a look at the attachments...
Hope this helps! :)
10 Dakarai thought of a number. He subtracted 11 from the number then divided the result by 4.
a Use a mapping to write this as a function.
Dakarai's answer was -1.2.
b Use inverse functions to work out the number Dakarai thought of. Show all your working.
a) The function that represents the given situation is (x - 11) ÷ 4 = -1.2 and the number thought by Dakari is 6.2
b) The inverse function (y - 11) ÷ 4 = -1.2
Function:
The function that is from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Given,
Dakarai thought of a number. He subtracted 11 from the number then divided the result by 4.
Here we need to find the following
a) function that map the function and the number though by Dakarai
b) inverse of the function
Let us consider the number thought by Dakarai as "x"
First, he subtracted 11 from the number,
So it can be written as,
=> x - 11
After that, he divided it by 4
So, the it can be written as,
=> (x - 11) ÷ 4
Now, the result was -1.2
So the function is
=> (x - 11) ÷ 4 = -1.2
Now we have to solve this equation, in order to find the value of x,
=> (x - 11) ÷ 4 = -1.2
=> x - 11 = -1.2 × 4
=> x - 11 = -4.8
=> x = -4.8 + 11
Therefore, the value of x is 6.2
And the inverse of the function can be written as by change the x as y,
Then we get,
=> (y - 11) ÷ 4 = -1.2
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In a study of cell phone usage and brain hemispheric dominance, an internet survey was e-mailed to subjects randomly selected from an online group involved with ears. There were surveys returned. Use a 0. 01 significance level to test the claim that the return rate is less than 20%. Use the p-value method and use the normal distribution as an approximation to the binomial distribution.
The statistics z is -1.878 and the p value is 0.0302
Given,
Number of random sample selected, n = 6967
Number of surveys returned, x = 1331
Estimated proportion of return rate;
p = 1331/6967 = 0.192
Significance level, ∝ = 0.01
z would represent the statistic
We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:
Null hypothesis, p₀ ≥ 0.2
Alternative hypothesis, p₀ < 0.2
The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)
That is,
z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878
Using the alternative hypothesis and the following probability, we can now get the p value:
p value = p(z < - 1.878) = 0.0302
We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.
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which ratios are proportional ? (A. 2/3 = 3/4) (B. 5/6 = 11/12) (C. 6/9 = 9/12) (D. 3/5 = 9/15).
Answer:
D
Step-by-step explanation:
[tex]\frac{3}{5}[/tex] = [tex]\frac{9}{15}[/tex] It is the only one that you can multiply the top and the bottom of the fraction with the same number to get an equivalent fractions. Multiply the top and the bottom of the first fraction by 3 to get the top and the bottom of the second fraction.
c + 9 = -15. No se cual es la respuesta.