The answer to the equation X + 5 3 2 a + 20 3 a + 2 3 3x + 2 12 2 3 4x-1 1/4-x is [tex]33 x-\frac{1}{4}$$[/tex] .
What is the basic rule for solving any equation?Simplify [tex]$34 x-1 \cdot \frac{1}{4}-x: \quad 33 x-\frac{1}{4}$[/tex]
[tex]$$34 x-1 \cdot \frac{1}{4}-x$$[/tex]
like phrases together
[tex]$$=34 x-x-1 \cdot \frac{1}{4}$$[/tex]
Add comparable elements: [tex]34 x-x=33 x$[/tex]
[tex]$$=33 x-1 \cdot \frac{1}{4}$$[/tex]
Multiply: [tex]$1 \cdot \frac{1}{4}=\frac{1}{4}$[/tex]
[tex]=33 x-\frac{1}{4}$$[/tex]
Both the addition rule and the multiplication/division rule are introduced to us in algebra 1 as the two rules for solving equations. According to the equation addition rule, an equation's solution set can be changed by adding the same amount to either side of an equation without doing so.
Identification, prioritisation, and selection of potential solutions are all steps in the process of problem solving, which also involves characterising the issue at hand, figuring out its root cause, and putting a plan of action into action. Algebraic Golden Rule: "Do unto one side of the equal sign as you will unto the other."
To learn more about equation refer to :
https://brainly.com/question/2972832
#SPJ1
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match each verbal description to its equivalent function rule as applied to the given function below.
The function f stretched vertically by a
factor of 4 and translated up by 9 units
arrowBoth
The function f stretched vertically
by a factor of 2 and translated up by 5 units
arrowBoth
The function f translated
6 units up and 2 units right
arrowBoth
The function f reflected about the y-axis
and translated 7 units left
arrowBoth
the final equations are.:
g(x) = 3x - 7g(x) = -3x - 28g(x) = 6x - 9g(x) = 12x - 19What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
We have the following function:
(x) = 3x - 7
The function f translated 6 units up and 2 units rights:
6 units up:
y = 3x - 7 + 6
2 units rigth:
y = 3(x-2) - 7 + 6
y = 3x - 6 - 7 + 6
Finally:
g(x) = 3x - 7
The function f reflected about the y-axis and translated 7 units left:
reflected about the y-axis:
y = 3(-x) - 7
y = -3x - 7
translated 7 units left:
y = -3(x+7) - 7
y = -3x - 21 - 7
y = -3x -28
Finally:
g(x) = -3x - 28
The function f stretched vertically by a factor of 2 and translated up by 5 units:
stretched vertically by a factor:
y = 6x - 14
translated up by 5 units:
y = 6x - 14 + 5
y = 6x - 9
Finally:
g(x) = 6x - 9
The function f stretched vertically by a factor of 4 and translated up by 9 units:
stretched vertically by a factor of 4:
y = 12x - 28
translated up by 9 units:
y = 12x - 28 + 9
y = 12x - 19
Finally:
g(x) = 12x - 19
Thus, the final equations are.:
g(x) = 3x - 7g(x) = -3x - 28g(x) = 6x - 9g(x) = 12x - 19Learn more about function here:
https://brainly.com/question/29633660
#SPJ1
state whether the standardized test statistic t indicates that you should reject the null hypothesis. explain.
No, the standardized test statistic t does not indicate that you should reject the null hypothesis.
The value of the test statistic t only tells you how much of an effect the independent variable has on the dependent variable. To determine whether to reject the null hypothesis, you must compare the value of t to a critical value based on the sample size, the level of significance, and the degrees of freedom.
The standardized test statistic t does not indicate whether you should reject the null hypothesis. To determine this, you must compare the value of t to a critical value based on the sample size, level of significance, and degrees of freedom.
No, the standardized test statistic t does not indicate that you should reject the null hypothesis.
Learn more about test statistics here
https://brainly.com/question/14128303
#SPJ4
A student is trying to identify the composition of a pure metal block by determining its density. The student records the mass to be 20.0g. The rectangular block is 3.00cm x 4.00cm x 1.40cm. Calculate the density (in g/cm^3). Express your answer to the correct number of significant figures.
The block's density can be calculated using the equation d=25g/8.4 cm.
What are equations?Two things are equal, according to an equation.
For instance, 10 + 2 equals 6 + 6.
Simply put, this means that 10 plus 2 equals or is the same as 6 plus 6.
In an equation, the unknown could be present, as in 10 + x = 6 + 6.
So, find the block's volume first:
= Length * Width * Height
= 2 x 3 x 1.4
= 8.4 cm
Now that you know the volume and the mass, you can add them to the density formula, which is as follows:
= Mass / Volume
Assuming density is represented by the symbol b, the formula would be:
d = 25 g / 8.4 cm
Therefore, the block's density can be calculated using the equation d=25g/8.4 cm.
Know more about equations here:
https://brainly.com/question/28937794
#SPJ4
Correct question:
A student is trying to identify the composition of a pure metal block by determining its density. The student records the mass of the sample to be 25.00 g. The rectangular block is 2.0 cm x 3.0 cm x 1.4 cm.
Which equation is necessary to determine the density sample?
Cola Root Beer Lemon-line
Under 21 years of age 40 25 20
Between 21 and 40 35 20 30
Over 40 years of age 20 30 35If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.
The probability of the person over 40 years of age who drinks root beer is equal to 0.1176.
As given in the question,
Total number of people is equal to 255
From the given table :
Number of people who drinks root beer and over 40 years of age is
= 30
Required probability who drinks root beer and over 40 years of age is given by :
= ( Number of favourable outcomes ) / ( total number of outcomes )
= ( 30 / 255 )
= 0.1176
Therefore, the required probability of the people over the age of 40 years and drinks root beer is given by 0.1176.
The above question is incomplete , the complete question is :
Cola Root Beer Lemon-line
Under 21 years of age : 40 25 20
Between 21 and 40 : 35 20 30
Over 40 years of age : 20 30 35 If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.
Learn more about probability here
brainly.com/question/30034780
#SPJ4
Most sports drinks contain minerals. Research shows that the most effective sports drink has a magnesium to calcium ratio of 1: 2. The body absorbs about 87% of magnesium in a drink, and about 44% of calcium in a drink.
One serving of a particular sports drink contains
about 96 mg of calcium and 48 mg of magnesium. About how many milligrams of each mineral will the body absorb?
Answer:
41 mg magnesium
42 mg calcium
Step-by-step explanation:
87% of magnesium; 48 mg of magnesium
44% of calcium; 96 mg of calcium
87% × 48 mg magnesium = 0.87 × 48 mg magnesium = 41 mg magnesium
44% × 96 mg calcium = 0.44 × 96 mg calcium = 42 mg calcium
6.
Simplify. Write in scientific notation. (9 × 10-3)2
08.1 x 10-5
081 x 104
081 × 10-3
08.1 x 10-6
[tex]$\left(9 \times 10^{-3}\right)^2$[/tex] can be wrltten in sclentlflc notation as[tex]$8.1 \times 10^{-5}$[/tex]
What is scientific notation?If a number is too big or too small to be conveniently represented in decimal form, it can be expressed using scientific notation. It might also be known as standard form in the UK, scientific form, or standard index form. A simple approach to write numbers is in scientific notation. Since it is shorter, more efficient, and clearly indicates magnitude, it is particularly helpful when expressing extremely big or extremely small values. Every real number can be expressed as the product of two elements, a decimal portion and an integer power of ten. The default base value ought to be 10. The exponent must be an integer that is not zero; therefore, it may be either positive or negative.A number is written in scientific notation if it can be written as [tex]$p \times 10^x$[/tex]where p has value greater than or equal to 1 and less than 10 and x is an integer.
Given[tex]- $\left(9 \times 10^{-3}\right)^2$[/tex]
Flrst applying [tex]$(a b)^2=a^2 b^2$[/tex]
We get, [tex]$\left(9 \times 10^{-3}\right)^2=9^2 \times\left(10^{-3}\right)^2$[/tex]
using property of exponents [tex]$\left(a^n\right)^m=a^{n m}$[/tex]
[tex]$9^2 \times\left(10^{-3}\right)^2=81$[/tex] times [tex]$10^{-6}$[/tex]
Thus, we have to write 81 times[tex]$10^{-6}$[/tex]In scientific notation,
Multiply and divide by 10 , we get
81 times [tex]$10^{-6}=8.1 \times 10^{-5}$[/tex]
Thus, [tex]$\left(9 \times 10^{-3}\right)^2$[/tex]can be written in scientific notation as [tex]$8.1 \times 10^{-5}$[/tex]
To learn more about scientific notation refer to:
https://brainly.com/question/1767229
#SPJ1
Math Homework Unit 3 Section D
A carpenter has 590) nails in his tool bag. He finds a box with some nails in his truck.
Then, he uses 211 nails at a job site. Now, he has 520 nails. How many nails does the
carpenter find in his truck?
The carpenter finds
My answer is 141
591-211=379
520-379=141
Use drawings, numbers or words. Explain how you can use estimation to make sure your answer makes sense.
I need help on how to use estimation. Thanks!!
Answer:
Please see answer below
Step-by-step explanation:
An estimate is an answer to a problem that is close to the solution, but not necessarily exact. Estimation usually requires rounding
Usually you perform the estimate prior to computing actual values.
Let's look at the numbers
591 can be rounded to 600, 211 can be rounded to 200
Then, in your equations instead of using actual numbers we use the estimates
600 - 200 = 400
500 - 400 = 100
Note this is off quite a bit because we are rounding to the nearest 100
Instead if we round to the nearest tens we get
591 ==> 590
211 ==> 210
520==> 520
So we get
590 - 210 = 380
520 - 380 = 140
A little more work but a more accurate estimate
In the figure below, the segments HI and HJ are tangent to the circle centered at O. Given that OI=8 and OH=11.6, find HJ.
Answer:
HJ = 8.4
Step-by-step explanation:
tangents to a circle from an external point are congruent , then
HJ = HI
the angle between a tangent and a radius of the circle at the point of contact is a right angle.
so Δ OHI is right with ∠ OIH = 90°
using Pythagoras' identity in the right triangle
HI² + OI² = OH² , that is
HI² + 8² = 11.6²
HI² + 64 = 134.56 ( subtract 64 from both sides )
HI² = 70.56 ( take square root of both sides )
HI = [tex]\sqrt{70.56}[/tex] = 8.4
Then
HJ = HI = 8.4
There are 80 pupils in a group. The only languages available for the group to study are Russian and Spanish. 50 pupils study Russian. 31 pupils study Spanish. 23 pupils study neither Russian nor Spanish. Find the probability to select a pupil that studies Spanish and Russian. Probability
3/10
Explanation
The total number of people that are studying neither Russian nor Spanish will be subtracted from the total number of people
i.e 80-23=57
Now let's calculate those that studies both languages (x)
50+31-x=57
-x=57-50-31
-x=-24
x=24
probability of choosing those that studies both Spanish and Russian is
24/80=3/10
Answer:
33 out of 80 pupils
Step-by-step explanation:
Total = 80 pupils
Studying Russian and Spanish = 80 - 23;
= 57 pupils
Out of 57 pupils, 50 pupils study Russian = 7 diff.
Out of 57 pupils 31 pupils study Spanish = 26 diff.
Consider the statements below. Which are not propositions? Mark all that apply.
(a) A delicious chocolate cake.
(b) College students should get more sleep.
(c) 3 + 5 = 8
(d) 5+ 3 = 53
(e) In Idaho, there are 15 temples for the Church of Jesus Christ of Latter-day Saints.
(f) No way!
(g) The great and spacious building.
(h) Will you be my Valentine?
The statements that are listed above that are not propositions include the following:
College students should get more sleep and Will you be my Valentine?. That is option B and H.What is a proposition statement?A proposition statement is defined as the statement that is either a true statement or false statement but can not be both.
From the given statements,the statement that is a true proposition include the following:
A delicious chocolate cake.3 + 5 = 8In Idaho, there are 15 temples for the Church of Jesus Christ of Latter-day Saints.No way!The great and spacious building.The statement that is a false proposition include the following:
5+ 3 = 53The statement will you be my valentine? is not a proposition but a declarative question that needs to be answered.
Learn more about proposition statement here:
https://brainly.com/question/28453782
#SPJ1
Write an equation in the form y = a(x-r)(x-s) to represent the parabola shown.
On solving the provided question, we can say that from the graph we have a equation [tex]y = x^2 - 3x - 4[/tex] => y= x(x+1) - 4(x+1) => y = (x+1)(x-4)
What is graphs?Mathematicians use here graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
from the graph we have a equation
[tex]y = x^2 - 3x - 4[/tex]
y= x(x+1) - 4(x+1)
y = (x+1)(x-4)
To know more about graphs visit:
https://brainly.com/question/11950136
#SPJ1
create the following tables and calculate the average: mean use the additional column to caculate the frequency subtotal
To create the tables and calculate the average mean, we need to have a set of data that we want to organize in a tabular form. The table should have columns for the data values, frequency, and frequency subtotal. The frequency column will show how many times a particular data value appears in the set.
The frequency subtotal column will be used to find the sum of the product of each data value and its corresponding frequency.
The average mean can be calculated by dividing the sum of the frequency subtotal by the total frequency.
Mean = ([tex]f_{1}x_{1}[/tex] + [tex]f_{2}x_{2}[/tex]+ [tex]f_{3}x_{3}[/tex]+ ... + [tex]f_{n}x_{n}[/tex]) / ([tex]f_{1}[/tex]+[tex]f_{2}[/tex]+[tex]f_{3}[/tex]+...+[tex]f_{n}[/tex])
By creating this table, we can easily see the distribution of the data and can calculate the average mean. This method of organizing data in tabular form is commonly used in statistics and data analysis, and it is an efficient way of summarizing and understanding large sets of data.
Read more about Mean:
https://brainly.com/question/26941429
#SPJ4
2x+y=32
x+3y=36
solve the equation by elmination method
Answer: (x,y)=(12,8)
Step-by-step explanation:
Let f: X - Y, where X and Y are the set of all real numbers, and x and h are real numbers. a. Find a function f such that the equation / (x + h) = / (x) + f (h) is not true for all values of x and h. Justify your reasoning. b. Find a function / such that equation / (x + h) = / (x) + / (h) is true for all values of x and h. Justify your reasoning. c. Let /(x) = 2*. Find a value for x and a value for h that makes f(x + h) = f(x) + / (h) a true number sentence.
Answer:
a. A function f such that the equation f(x + h) = f(x) + f(h) is not true for all values of x and h is a function that is not linear. For example, a function f(x) = x^2 is not linear because it does not satisfy the equation f(x + h) = f(x) + f(h).
b. A function f such that the equation f(x + h) = f(x) + f(h) is true for all values of x and h is a linear function. For example, a function f(x) = mx + b, where m and b are constants, is a linear function because it satisfies the equation f(x + h) = f(x) + f(h).
c. Let f(x) = 2x. If we choose x = 3 and h = 2, then f(x + h) = f(3 + 2) = f(5) = 2(5) = 10, and f(x) + f(h) = f(3) + f(2) = 2(3) + 2(2) = 6 + 4 = 10. Therefore, the equation f(x + h) = f(x) + f(h) is true in this case.
Which graph has infinite solutions
The graph that shows a system of equations with infinite solutions is graph C.
Which graph has infinite solutions?Here we have some systems of equations graphed.
A system of equations has infinite solutions when both equations are equivalent (in this case, both equations represent the same line)
Then we we look at the graph of the system of equations we will see a single graph instead of two, like what we can see on option C.
The graph that shows infinite solutions is graph C (the one in the top right side).
Learn more about systems of equations by reading:
https://brainly.com/question/13729904
#SPJ1
At an amusement park, guests have to take either a train or a boat 22 miles from the parking lot to the front entrance and then back when they leave the park. The train goes 10 mph faster than the boat . Abdul takes the train into the park and the boat on his way back. The boat goes an average speed of 20 mph. How long did the round trip take?
Answer:
1 hour 50 minutes
Step-by-step explanation:
Total distance from parking lot to entrance = 22 miles
We will assume that the total distance from entrance to lot is also 22 miles
The average speed of the boat = 20mph
The average speed of the train is 10 mph faster = 20 + 10 = 30 mph
Time taken for travel from parking lot to park by train = 22/30 hours
22/30 hours = 22/30 x 60 minutes = 44 minutes
On the way back, the boat was taken
Distance = 22 miles, speed = 20 mph
Time taken = distance/speed = 22/20 hours
22/20 hours = 22/20 x 60 minutes = 66 minutes
Total round trip time taken = 44 + 66 = 110 minutes
110 minutes = 110/60 hours
= 1 50/60 = 1 hour 50 minutes
GRADES On his first five quizzes, Percy has earned scores of 24, 27, 22, 21, and 18 points. What score must Rachael earn on her sixth and final quiz so that both the mean and median of her quiz scores is 23?
Answer:
26
Step-by-step explanation:
To find the mean score of all six quizzes, you add all the scores and divide by the number of examinations. So if Percy's first five quiz scores are 24, 27, 22, 21, and 18, the total is 112. To find the mean score of all six quizzes, add Rachael's sixth quiz score to the total and divide by 6.
If the mean score of all six quizzes is 23, then the total score of all six examinations is 138 (23 x 6).
To find the score Rachael needs on her sixth quiz, you subtract Percy's score (112) from the total score of all six examinations (138)
Rachael needs to score 26 on her sixth quiz (138 - 112) for the mean and median of her quiz scores to be 23
Why do companies stocks up on extra inventory
Answer:
allows companies to easily and quickly fulfill customer orders as soon as they come in
Step-by-step explanation:
Holding excess inventory will allow companies to easily and quickly fulfill customer orders as soon as they come in, all without having to worry about waiting on their stock to come in to ship an order out.
Determine the point estimator you would use and calculate the value of the point estimate. Tonya wants to estimate what proportion of the seniors in her school plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom
According to the information provided, it should be noted that the 750 seniors in her school make up the population of interest, and the parameter of interest is the percentage of seniors who intend to attend the prom.
Given,
Additionally, a strictly random sample is required in order to create a confidence interval. Additionally, the sample size should be examined to see if it adequately represents the population.
Using the z critical of 1.645, a 90% confidence interval will be built. The sample proportion in this case will be:
= 36/50 = 0.72
Q = 1 - 0.72 = 0.28
n = 50
As a result, the standard error will be equal to 50 squared times the multiplication of 0.72 and 0.28. This amounts to 0.0635.
For a big sample randomly selected among 750 seniors, the interval on the context suggests that we are 90% confident that the fraction of those who desire to attend the prom falls within the interval.
Learn more about population here;
https://brainly.com/question/14456358
#SPJ4
brainstorm consider what kind of program you would like to build. as you do, think about how your program can fulfill the coding requirements the college board outlines. remember, you need a list, an algorithm that uses sequencing, selection and iteration and a procedure that uses parameters.
The total score will be used to determine the student’s final admissions status.
I would like to build a program that calculates a student's score for a college admissions test. The program will be based on the coding requirements outlined by the college board, which include a list, an algorithm that uses sequencing, selection and iteration and a procedure that uses parameters.
The list will contain the student’s scores for each section of the admissions test. The algorithm will use sequencing to add the scores of each section together. Selection will then be used to determine whether the student has met the minimum requirements, and iteration will be used to keep track of any sections that were not completed. The procedure will be used to calculate the student’s total score, using parameters such as the number of sections completed and the scores for each section. The total score will be used to determine the student’s final admissions status.
Learn more about total score here;
https://brainly.com/question/29109498
#SPJ4
Find the volume of this cylinder. Give your answer to 1 decimal place 20 cm 9 cm
The volume of the given cylinder is 11304 cm³.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, radius of a cylinder is 20 cm and depth of a cylinder is 9 cm.
We know that, the volume of a cylinder is πr²h.
Now, volume = 3.14×20²×9
= 3.14×400×9
= 11304 cm³
Therefore, the volume of the given cylinder is 11304 cm³.
To learn more about the volume visit:
https://brainly.com/question/13338592.
#SPJ1
Answer:
5089.4cm
Step-by-step explanation:
9² x pi x 20 =5089.3800
Find the general solution to
1/ln(t)(5e^t c) Enter your answer as y=…y=… .
Use C to denote the arbitrary constant in your answer.
y = c * 5e^t / ln(t) is the general solution to 1/ln(t)(5e^t c) .We can simplify this expression by applying the chain rule of differentiation. The chain rule states that if y = f(u) and u = g(x), then
dy/dx = dy/du * du/dx.
The given expression is 1/ln(t)(5e^t c) .
In this case, we can let y = 5e^t c and u = ln(t).
Taking the derivative with respect to t, we get:
dy/dt = 5e^t c * (du/dt) / u
Since u = ln(t), we can use the chain rule again to find du/dt:
du/dt = 1/t
Plugging this back into the original expression, we get:
dy/dt = 5e^t c * (1/t) / ln(t)
Now we can factor out the constant c, which is an arbitrary constant of integration, giving us the final answer:
y = c * 5e^t / ln(t)
So the final answer is: y = c * 5e^t / ln(t)
It's important to note that this is only the general solution of the function, if we have an initial condition then we can find the specific solution for the function
To know more about differentiation ,click here:
brainly.com/question/24062595
#SPJ4
tion. Then. determine how many books she will have after 4 years.
Answer:2x3x4
Step-by-step explanation:
What is BD?
In triangle ABC, the length of side AB is 12 and the length of side AD is 27. The line AC started from point A and cuts the side BD a point C. The length of BC is x and the length of CD is x + 5.
The procedures below can be used to determine a triangle's length BD.
In th that is presented;
The holding ratio is, therefore, as follows:
12 : x = 27 : x + 5
12 / x = 27 / (x + 5 )
When we cross multiply these, we obtain:
12 ( x + 5 ) = 27x
12x + 60 = 27x
Taking the x values on one side, we obtain:
27x - 12x = 60
15x = 60
x = 60/15
x= 4
The length of line BD is:
= BC + CD
= x + x + 5
After entering the value of x, we get
= 4 + 4 + 5
= 13
As a result, the length of the line BD is 13.
Learn more about how to find side of a triangle here:
https://brainly.com/question/30241889
I need help solving this
Answer:
110 cm^2 & 39 cm^3
Step-by-step explanation:
Volume = Length x Width x Height. With that in mind, volume is 39 cm^3
Surface Area = Area of all the shapes
2(13 x 1) + 2(13 x 3) + 2(3 x 1) =110 cm^
in one or two well-crafted paragraphs, summarize how neurons communicate at the synapse. your paragraph must include each of the following terms. underline each term in your paragraph. synapse action potential neurotransmitters vesicles axon dendrites axon terminal receptors
Dendrites first receive electrical signals from other neurons, after which an action potential is sent down the axon until it reaches the axon terminal. The vesicles then set the neurotransmitters in motion. Neurotransmitters will then travel to the synapse, where receptors will begin to transmit the signal.
What is neurotransmitters?A neurotransmitter is a signaling molecule that a neuron secretes to affect another cell across a synapse. The cell receiving the signal, which could be any major body part or target cell, could be another neuron or a gland or muscle cell. Neurotransmitters are chemical messengers required by your body to function. They are in charge of moving chemical signals (called "messages") from one neuron (nerve cell) to the next target cell. The next target cell might be another nerve cell, a muscle cell, or a gland.
To know more about neurotransmitters,
https://brainly.com/question/9725469
#SPJ4
Neeedd helpppp !!!! I only have a little bit of time
The value of m∠1 is 50°. The solution is obtained using properties of angle and triangle.
What is an angle?
When two rays are brought together at a single point, an angle is created. The two rays in this instance are referred to as the arms of the angle, while the common point is known as the node or vertex. The symbol "∠" stands for an angle. Angle is a derivative of the Latin word "Angulus."
In the figure, we are given a right-angled triangle which means that one angle in the triangle measures 90°.
We are given an exterior angle equal to 140°.
We know that angles on a straight line form a linear pair which means that their sum is 180°.
Let the angle on the straight line be 'x'.
So, we get
⇒x + 140° = 180°
⇒x = 40°
Now, we know that in a triangle, the sum of all the angles is 180°.
Therefore,
⇒m∠1 + 90° + 40° = 180°
⇒m∠1 + 130° = 180°
⇒m∠1 = 50°
Hence, the value of m∠1 is 50°.
Learn more about angle from the given link
https://brainly.com/question/25770607
#SPJ1
Sample surveys show that fewer people enjoy shopping than in the past.
A recent survey asked a nationwide random sample of 2577 adults if they agreed or disagreed that "I like buying new clothes, but shopping is often frustrating and time-consuming."
The population that the poll wants to draw conclusions about is all U.S. residents aged 18 and over.
Suppose that in fact 62% of all adult U.S. residents would say "Agree" if asked the same questions.
What is the probability that 1610 or more of the sample agree?
The likelihood that at least 1610 members of the sample agree is 0.3385.
What is meant by probability?How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes how likely they are when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. The quantity of possible outcomes is known as probability. all events that could possibly occur. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail). P(heads) = 12 is the formula.Probability is a measure of how likely it is for a given event to take place.Given,
sample std = sqrt[0.62 × 0.38/2577]
= 0.0096
sample proportion = 1610/2577
= 0.6240
z(0.6240) = (0.6240-0.62)/0.0096
= 0.4167
P(x >= 1610) = P(z >= 0.4167)
Then we get,
= 0.3385
Hence, The likelihood that at least 1610 members of the sample agree is 0.3385.
To learn more about probability, refer to:
https://brainly.com/question/24756209
#SPJ4
. let x denote the annual salary of scientists in the united states, measured in thousands of dollars. suppose that e[x]
The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8. and The mean is the average. So the average, measured in thousands of dollars, is 56.
Average salary: 56
Standard deviation of the salary: 8
$56,000 dollars is 56 thousand dollars.
$8,000 is 8 thousand dollars.
The mean is the average. So the average, measured in thousands of dollars, is 56.
The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8.
complete question
Let X denote the average starting salary for 2014 U.S. college graduates, measured in dollars. Suppose that the average annual salary is $56,000 dollars, with a standard deviation of 8,000. Find the mean and standard deviation when salary is measured in thousands of dollars.
learn more about of average here
https://brainly.com/question/13606063
#SPJ4
دین
-10
26. The drama club is selling tickets for the upcoming play. Each student ticket costs $5.50 and each adult
ticket costs $9.50. If the Drama Club sold 98 tickets and raised $703, write a system of equations to figure out
how many of each ticket was sold. Find how many of each ticket was sold.
A total of 57 student tickets and a total of 41 adult tickets were sold to generate a total revenue of $703.
What is the definition of an equation?A mathematical statement known as an equation is composed of two expressions joined together with the equal sign. A formula would've been 3x - 5 = 16, for illustration.. When this equation is solved, we discover that the quantity of the variables x is 7.
The following response has been produced in a straightforward, step-by-step manner.
Step: 1
Price of each student ticket = $ 5.50
Price of each adult ticket = $ 9.50
If x Equals the quantity of student tickets sold
If y Equals the quantity of adult tickets sold,
Step: 2
(i). It is given that a total of 98 tickets were sold.
Therefore, we can write as -
(Number of student tickets sold) + (Number of adult tickets sold) = 98
x+y =98 -----------equation (1)
Step: 3
(ii). The total revenue earned from the sale of tickets was $703.
Therefore, we can write as -
(Revenue earned from selling student tickets) + (Revenue earned from selling adult tickets) = 703
(Price of each student ticket×Number of student tickets sold) + (Price of each adult ticket ×Number of adult tickets sold) = 703
(5.50 × x)+ (9.50 × y) =703
5.50x+9.50y =703 ----------equation 2
Step: 4
System of Equations :
1) x+y =98
2) 5.50x + 9.50y =703
On performing (eq 2) - 5.50(eq 1), we get -
(5.50x +9.50y) - 5.50(x+y)=703-5.50(98)
5.50x + 9.50y - 5.50x-5.50y=703-539
4y=164
y=164/4
y=41
The operation was performed to reduce the equation in a single variable.
Step: 5
On substituting the value of y=41 in eq 1 , we get-
x+41 =98
x= 98-41
x=57
Thus, a total of 57 student tickets and a total of 41 adult tickets were sold to generate a total revenue of $703.
To Learn more about equation visit :
https://brainly.com/question/12788590
#SPJ1
