The answer to the operation is as follows:
5^(2) + 1^(2) = 5*5 + 1*1 = 25 + 1 = 26.
Here, we have to remember PEMDAS. First, we solve parentheses, then exponents (or exponentiation operations); then, multiplications, divisions, and, after all this, addition and subtractions.
In the above operation, we solve first the raising of 5 to 2, then 1 raised to 2. We sum the result of both operations. So the value of 36 is not correct. The correct value is 26.
Let U={1, 2, 3, 4, 5, 6, 7}, A={4, 5, 6, 7}, and B={3, 4, 7}. Find the set A' ∩ B'.
The intersection between the complements of A and B is:
A' ∩ B' = {1, 2}
How to find the intersection?
We have the sets:
A={4, 5, 6, 7}
B={3, 4, 7}
And we want to find the intersection between the complements, where the complements are all the elements that are in the universal set and not are in the given sets, so:
A' = {1, 2, 3}
B'= {1, 2, 5, 6}
The intersection between two sets is the set of the common elements, so we have:
A' ∩ B' = {1, 2}
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A population has parameters μ=164.8 and σ=72.8. You intend to draw a random sample of size n=160.
The value of mz is 164.8 and sigma z is 5.755 for the given sample.
What is the sample standard deviation?
The dispersion of data distribution is measured by standard deviation. The average distance between every data point is measured.Yet if the data is being treated as a population unto itself or as a sample of a broader population will affect the standard deviation calculation formula.We divide by the N number of data points if the data is being seen as a population on its own.If the data come from a sample of a larger population, then divide by n-1n1n, or n minus 1, which is one less than that of the number of points in the sample.Given that,
m=164.8
sigma=72.8
n=160
The mean of the sample means' distribution
mz=m
mz=164.8
The standard deviation of the sample mean's distribution
sigma z= sigma/√n
sigma z= 72.8/√160
=5.755
The value of mz is 164.8 and sigma z is 5.755 for the given sample.
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312p - 2) 16) -10n + 31 ap-2=40-8x6pto lapto 9p+uptop=-8+6+2 P20/19=0 17) 10(x + 3) - (-9x - 4) = x - 5+ 3 18) 12
Answer:
x = -2
Explanation:
The initial expression is:
10( x + 3) - ( -9x - 4) = x - 5 + 3
To solve for x, we first need to apply the distributive property as:
10x + 10(3) -(-9x) - (-4) = x - 5 + 3
10x + 30 + 9x + 4 = x - 5 + 3
Then, add the like terms to get:
(10x + 9x) + (30 + 4) = x + (-5 + 3)
19x + 34 = x - 2
Subtract x from both sides:
19x + 34 - x = x - 2 - x
18x + 34 = -2
Subtract 34 from both sides:
18x + 34 - 34 = -2 - 34
18x = -36
Finally, divide both sides by 18:
18x/18 = -36/18
x = -2
Therefore, the answer is x = -2
HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
here are is answer and the steps it's in the pic below go check it out sorry if it's wrong have a nice day:)
The equation to find the constant of proportionality or k is?
2K = Y + X
Y = 2K + X
None of the above
K = Y / X
The equation to find the constant of proportionality or k is K=Y/X.
The value of the ratio between two proportional quantities, known as the constant of proportionality, is constant. When the product or ratio of two changing amounts gives a constant, that relationship is said to be proportionate. Depending on the kind of proportion between the two specified quantities—direct variation or inverse variation—the proportionality constant's value will vary.
When two variables are proportional to one another either directly or indirectly, their relationship can be expressed as y = kx or y = k/x, where k specifies how the two variables are related to one another. This k is referred to as the proportionality constant.
Hence the equation to find the constant of proportionality or k is
K = Y/X
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4x^2-36 is divided by x+3
[tex] \frac{4 {x}^{2} - 36 }{x + 3} \\ = \frac{4( {x}^{2} - 9)}{x + 3} \\ = \frac{4(x + 3)(x - 3)}{x + 3} \\ = 4(x - 3) \\ = 4x - 12[/tex]
NOTE THE x+3 in the numerator cancels with the x+3 in the denominator.
Find m BDC. B C (-3x + 20° { (-2x + 55) ° D А a. 290 b. 61° c. 25° d. 759
Let's begin by listing out the information given to us:
We will observe that these two angles are complementary (they sum up to 90 degrees)
[tex]\begin{gathered} m\angle BDC=-3x+20 \\ m\angle CDA=-2x+55 \\ m\angle BDC+m\angle CDA=90^{\circ} \\ -3x+20+(-2x+55)=90 \\ \text{Put like term}s\text{ together, we have:} \\ -3x-2x+20+55=90 \\ -5x+75=90 \\ Subtract\text{ 75 from both sides, we have:} \\ -5x+75-75=90-75 \\ -5x=15 \\ \frac{-5x}{-5}=\frac{15}{-5} \\ x=-3 \\ \\ m\angle BDC=-3x+20=-3(-3)+20 \\ m\angle BDC=9+20=29 \\ \therefore m\angle BDC=29^{\circ} \end{gathered}[/tex]Hence, option A is the correct answer
The ages of people who attend a local church are normally distributed . The mean age is 39.5 , and the standard deviation is 18. First sketch a normal curve. Then find the probability that that a person chosen at random from this church is ages 21.5 or younger
Given:
The ages of people who attend a local church are normally distributed.
The mean age = μ = 39.5
And the standard deviation = σ = 18
The sketch of the normal curve will be as follows:
As shown the peak of the curve at the mean value = 39.5
and the distance between the consecutive numbers = 18
now, we will find the probability that a person chosen at random from this church is ages 21.5 or younger
So, we will find P( x < 21.5)
As shown, from the graph:
The answer will be = 0.1587
Graph the system of equations.{8x+8y=642x−2y=−4} Use the Line tool to graph the lines.
Given,
The equation of system is,
8x+8y=64
2x−2y=−4
The graph of the equation is,
Hence, the graph of the system is obtained.
The point A(7, -3) is reflected over the point (6, -5) and it's image is pointB. What are the coordinates of point B?
We have a point A=(7,-3) that is reflected over point C=(6,-5). This means that is refected in an axis that is perpendicular to the segment AC.
The image is point B, and we need to calculate its coordinates.
We can relocate the center of coordinates to point C, do the reflection and then relocate the original center of coordinates.
If now C became the center of coordinates A becomes:
[tex]A^{\prime}=A-C=(7-6,-3-(-5))=(1,2)[/tex]Now, we can reflect it as normal:
[tex]\begin{gathered} (x,y)\longrightarrow(-x,-y) \\ A^{\prime}=(1,2)\longrightarrow B^{\prime}=(-1,-2) \end{gathered}[/tex]Now, we convert this to the original coordinates as:
[tex]B^{\prime}=B-C\longrightarrow B=B^{\prime}+C=(-1+6,-2-5)=(5,-7)[/tex]The point B is (5,-7).
Find the area of this figure. [?] square meters 6 m 6 m 12 m 9 m
The area of this figure is 89 m².
What is the area of a rectangle?
The territory a rectangle occupies inside its four sides or limits is known as its area. A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.
Mathematically, Area of a rectangle = length*breadth = l*b -(i)
What is the area of a triangle?
The territory a triangle occupies inside its three sides or limits is known as its area. A triangle's sides determine its area. In essence, the length and base of the rectangle multiplied together with 0.5 gives the area of the triangle.
Mathematically, Area of a triangle = 0.5*height*base = 0.5*h*b -(ii)
r
Given, the length of the rectangle = l = 8 m
The breadth of the rectangle = b = 13 m
Area of the rectangle = 8*13 = 104 m² [Using (i)]
Also, the base of the triangle = b = 13 - 4 -4 = 5 m
The height of the rectangle = h = 6 m
Area of the triangle = 0.5*5*6 = 15 m²
Therefore, area of the shaded region = Area of the rectangle - Area of the triangle = (104 - 15) = 89 m²
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help meeee pleasee!!!
thank youu
Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
The students in Mr. Kim's class are discussing how to apply the properties of equality. Juan started with the equation 4 +5 = 9. He multiplied the left side by 3. He said that he could divide the right side by another
B. 3
1) Let's examine Juan's work
4+5 = 9 Multiplying the left side
(4+5)*3 =9
27 = 9 Divide only the right side by 3
9 = 3 False!
2) Then we can state that
B.
The only way Juan can maintain equality is by multiplying the right side by
3
27= 9
27 = 9 x 3
27 = 27 True!
3) The answer is B and 3.
Describe how to find the anti logarithm of ln x= 2 to the nearest ten-thousandths
The expression is given as
lnx=2.
ExplanationTo find the antilogarithm of the expression,
To compute the antilogarithm of a natural logarithm, take e to that power.
[tex]lnx=2[/tex][tex]x=e^2[/tex][tex]x=7.389[/tex]AnswerHence the antilogarithm of lnx =2 to the nearest ten-thousandths is 7.3891.
use the figure at right. if jk=6x+8 and NO=16, what is the value of x?
The short line on the sides of the triangle tells us that those sides are equal.
We can see that LN = NJ and
LO = KO
This means that triangle LNO is similar to triangle triangle LJK
LO/NO = (LO + OK)/JK
Given that NO = 16 and JK = 6x + 8, it means that
LO/16 = (LO + OK)/(6x + 8)
Since LO = OK, it means that
LO + OK = LO + LO = 2LO
Therefore
LO/16 = 2LO/(6x + 8)By cross multiplying, it becomes
LO(6x + 8) = 2LO * 16
LO(6x + 8) = 32LO
Dividing both sides of the equation by LO, it becomes
6x + 8 = 32
6x = 32 - 8
6x = 24
x = 24/6
x = 4
find the volume of the figure below (hint: you may need to find 2 separate volumes and combine them)
The shape consist of a cone and a cylinder
As such the volume of the shape is the sum of the volume of the two shapes.
The volume of a cone is given as
V = 1/3 Pi R^2H
and that of a cylinder is
V = Pi R^2H
where Pi is a constant 22/7, R is the radius and H is the height
Hence the volume of the figure
=1/3 * 22/7 * 6^2 * 10 + 22/7 * 6^2 * 12
= 22/7 (120 + 432)
= 22/7 * 552
= 1734.86 m^2
Mr. Clayton is contemplating which chauffeured car service to take to the airport. The first costs $5 up front and $4 per kilometer. The second costs $15 plus $3 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? Write a system of equations, graph them, and type the solution.______ kilometers
Given in the question:
a.) The first costs $5 upfront and $4 per kilometer.
b.) The second costs $15 plus $3 per kilometer.
Let's generate the equation of each of the car service charges,
Let,
y = total cost of service
x = distance traveled
a.) The first costs $5 upfront and $4 per kilometer.
[tex]\text{ y = 5 + 4x}[/tex]b.) The second costs $15 plus $3 per kilometer.
[tex]\text{ y = 15 + 3x}[/tex]Let's determine the driving distance when the two companies charge the same.
We get,
[tex]y_{1st\text{ Company}}=y_{2nd\text{ Company}}_{}[/tex][tex]\text{ 5 + 4x = 15 + 3x}[/tex][tex]\text{ 4x - 3x = 15 - 5}[/tex][tex]\text{ x = 10}[/tex]Therefore, the two companies charge the same at a driving distance of 10 kilometers.
Summary:
1. The system of equations.
y = 5 + 4x
y = 15 + 3x
2. The solution.
x = 10
3. Graphing the system of equations.
0.5 is the coefficient of ² in the expression v + 0.5v²
A True
B False
True, 0.5 is the coefficient of v² in the expression v + 0.5v².
What is a Coefficient?A coefficient is a number or quantity related to a variable. It is usually an integer multiplied by the variable and displayed next to it. Variables that do not have a numerical value are assumed to have a coefficient of one. A coefficient might be positive or negative, real or imaginary, and expressed in decimals or fractions.Given expression is v + 0.5v².
Follow the methods below to find the coefficient of a variable in a term:
Step 1: Encircle the variable and its power whose coefficient we're looking for.
So here we are looking for the coefficient of v²
Step 2: Forget about that variable and think about all the other numbers or variables that were written with it. That is the coefficient.
Hence, the required coefficient is 0.5.
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Petroleum pollution in oceans stimulates the growth of certain bacteria. An assessment of this growth has been made by counting the bacteria in each of 6randomly chosen specimens of ocean water (of a fixed size). The 6 counts obtained were as follows.48, 67, 64, 61, 63, 69Send data to calculatorFind the standard deviation of this sample of numbers. Round your answer to two decimal places.
σ =6.78
Count, N:6
Sum, Σx:372
Mean, μ:62
The standard deviation(σ) can be calculated using the formula below:
[tex]\sigma=\sqrt[]{\frac{1}{N}\sum ^n_{i=1}(x_i-\mu)^2}[/tex]To calculate Mean( μ);
[tex]\text{Mean}=\frac{48+67+64+61+63+69}{6}[/tex]Mean( μ) = 62
[tex]\sigma=\sqrt[]{\frac{(48-62)^2+(67-62)^2+(64-62)^2+(61-62)^2+(63-62)^2+(69-62)^2}{6}}[/tex][tex]=\sqrt[]{\frac{276}{6}}[/tex][tex]=\sqrt[]{46}[/tex][tex]=6.78[/tex]Therefore, the standard deviation(σ) = 6.78
Laura needs to buy chips and soda for the guests at her party. Each large bag of chips cost $2.40 and each large bottle of soda cost $2.00. She has $48.00 to spend. Part A Create an inequality using two variables to represent this situation. Be sure to explain the meaning of each variable.Part B Which of the following graphs represent the number of chips and soda bottles that Laura can buy? Part C Which combination of bottles of soda and bags of chips can Laura buy?
Part A.
To write the inequality we have to introduce variables that represent the things Laura needs to buy. For this reason let x be the number of sodas she buys and let y be the number of chips she buys.
Now, we know that each bag of chips cost $2.40 then tha ammount she spends in chips will be
[tex]2.4y[/tex]Following the same reasoning, the ammount she spends in sodas will be
[tex]2x[/tex]The total ammount she spends will be the sum of each ammount, that is:
[tex]2x+2.4y[/tex]Finally, we know that Laura has $48, so she can only spend less or equal this ammount.
Therefore the inequality representing this situation is
[tex]2x+2.4y\leq48[/tex]Part B.
To graph this inequality, first we have to graph the line given by
[tex]2x+2.4y=48[/tex]Doing this we obtained the following graph
Now we need to decide which semi plane represent the solution set of the inequality. Since we have a less or equal sign the right choice is the left one, then the graph of the inequality is
Therefore the graphs representing the number of chips and soda bottles Laura can buy is option B.
Part C.
To determine which combination of bottles of soda and chips Laura can buy we can graph the options we have. Remember that the x-axis represents the soda and the y-axis the chips. Hence the option we have will be equivalent to the points (4,24), (12,8), (16,8) and (28,4). Graphing this points we have
The only option allowed is the one that lies within the shaded region, therefore Laura can buy 12 bottles of soda and 8 bags of chips.
A car rental company charges $15 per day and $0.55 per kilometer to rent a car. What is the total bill if a car is rented for 4 days and is driven 146 kilometers? Andy how would I solve it
Answer:
$140.30
Step-by-step explanation:
The best way to solve this is to make an equation.
y = 15x + 0.55k
In simple terms this is:
Total = $15(number of days) + $0.55(Number of kilometers)
Plug in the values
15(4) + 0.55(146)
60 + 80.3
140.3
Since this is dollars it would $140.30!
Hope this explanation was good enough.
Answer: $140.30 is the total bill
Step-by-step explanation:
First, you would time 15 by 4 to get the price for the number of days you have rented the car. Which is $60
Now times $0.55 by 146 to get the price for the kilometers you have driven. Which is $80.30
Add both $60 and $80.30
The total bill is $140.30
[tex] \frac{3}{2} ln( {4x}^{6} ) - \frac{4}{5} ln( {2m}^{5} ) = [/tex]how do I do this
Original expression
[tex]\frac{3}{2}\ln 4x^6-\frac{4}{5}\ln 2m^5[/tex][tex]\begin{gathered} \frac{3}{2}\ln 4x^6-\frac{4}{5}\ln 2m^5 \\ \ln (4x^6)^{\frac{3}{2}}-\ln (2m^5)^{\frac{4}{5}}^{} \end{gathered}[/tex][tex]\begin{gathered} \ln (4^{3/2}x^{6\cdot3/2})-\ln (2^{4/5}m^{5\cdot4/5}) \\ \ln (2^{2\cdot3/2}x^9)-\ln (2^{4/5}m^4) \\ \ln (2^3x^9)-\ln (2^{4/5}m^4) \end{gathered}[/tex][tex]\begin{gathered} \ln (\frac{2^3x^9}{2^{4/5}m^4}) \\ \ln (\frac{2^{11/5}x^9}{m^4}) \end{gathered}[/tex]The answer would be
[tex]\ln (\frac{2^{\frac{11}{5}}x^9}{m^4})[/tex]A junk drawer at home contains eight pens for of which work what is the probability that you randomly grab three pens from the drawer and don’t end up with a Penn that works express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
Given:
Total no of pens is 8.
No of pens that works =4
No of pens that don't work = 4
[tex]\text{Probability }of\text{ selecting 3 pens }from\text{ the drawer=}\frac{3}{8}[/tex][tex]\text{Probability of selecting }a\text{ pen thta don't work=}\frac{4}{8}[/tex][tex]\begin{gathered} \text{Probability of getting 3 pens from a drawer }and\text{ don't} \\ \text{ end up with a pen }that\text{ work is } \end{gathered}[/tex][tex]=\frac{3}{8}\times\frac{4}{8}[/tex][tex]=\frac{3}{16}[/tex][tex]=0.1875[/tex]On a standardized test, the mean is 38 and the standard
deviation is 4.5. Approximately what percent of the scores
fall in the range 29-47?
The percentage of scores that fall in the range 29-47 is of 95%.
Empirical RuleThe Empirical Rule states that, for a normally distributed random variable:
The percentage of scores within one standard deviation of the mean is 68%.The percentage of scores within two standard deviations of the mean is 95%.The percentage of scores within three standard deviations of the mean is 99.7%.In the context of this problem, the mean and the standard deviation of scores are given as follows:
Mean = 38.Standard deviation = 4.5.Hence the range of 29 to 47 is within two standard deviations of the mean, as 38 - 2 x 4.5 = 29 and 38 + 2 x 4.5 = 47, meaning that the percentage of scores that fall in the range is of 95%.
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explain the structure and creation of regular and semi-regular tessellations
A regular polygon is repeated to create a tessellation known as a normal tessellation. Recognize that the angles and sides of an ordinary polygon are the same. An equilateral triangle, a rectangular shape, or a hexagon can all be used to create regular tessellations.
Tessellations made from or larger than common polygons are known as semi-regular tessellations. Hexagons and equilateral triangles make up the semi-typical tessellation shown in the image. If we concentrate on the hexagons, we can see that the triangles are rotated around the hexagonal components to generate the pattern. It is a three.3.6 tessellation, as determined by our system for naming tessellations. The hexagon is represented by the six and the trees are the two triangles.
Regular polygons of the same size and shape make up regular tessellations. Multiple regular polygons combine to form semi-regular tessellations. There are only eight ways to arrange regular polygons to produce semi-regular tessellations.
Hence we derived the necessary information.
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Find three rational numbers between (-6) and (-7)
Answer: Option (b) 21:18, option(c) 42:36, option(d) 63:54, option(e) 84:62 are equivalent ratios of 7:6
Step-by-step explanation: Hope this helped
Answer: -6 1/4, -6 9/10, -6 11/20
Step-by-step explanation: You find any number in decimals between them, then you covert into fractions if needed.
If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting two queens and two kings.
If you are dealt 4 cards from a shuffled deck of 52 cards, the probability of getting two queens and two kings is: 0.000133.
ProbabilityNumber of ways to get two of the four queens = 4C2 = 6 ways
Number of ways to get two of the four kings = 4C2 = 6 ways
Number of ways to get none of the deck = 48C0 = 1 way
Hence,
Number of ways to get four cards = 6 x 6 x 1
Number of ways to get four cards = 36 ways
Number of ways 4 cards can be chosen from 52 cards = 52C4 = 270725 ways
So,
Probability = 36 ways / 270725 ways
Probability = 0.0001329
Probability = 0.000133 (Approximately)
Therefore the probability is 0.000133.
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At take-off, an airplane weighs 220000 pounds. Convert the weight to tons.
220000 pounds.
[tex][/tex]The final answer
[tex]110[/tex]What is the initial value and what does it represent?The table shows the total cost of purchasing x same-priced items and a catalog.Total CostNumber of Items Total Cost(x)1$102$143$184$22O $4, the cost per itemO $4, the cost of the catalog$6, the cost per item$6, the cost of the catalogMy
Duck if the cost of 1 item and the catalog is $ 10 and onwards, the cost for every additional item is $ 4, then:
• The cost per item is $ 4
,• The cost of the catalog is $ 6
I know you are able to select the correct choices.
Thanks for coming, Duck!
Answer:
Step-by-step explanation:
6$ cost of the catalog
Find the simple interest.Principal: $6000 Rate: 4% Time in months: 3
Given:
Principal, P = 6000
Rate, r = 4%
Time, t = 3 months
To find:
The simple interest
Explanation:
Using the simple interest formula,
[tex]SI=P\times\frac{r}{100}\times\frac{t}{12}[/tex]Where t represents the number of months.
On substitution, we get
[tex]\begin{gathered} SI=6000\times\frac{4}{100}\times\frac{3}{12} \\ SI=\text{ \$}60 \end{gathered}[/tex]Final answer:
The simple interest is $60.
