The probability of selecting a person who is either a Democrat or a woman is 0.8, or 80%.
Probability is a branch of mathematics that deals with the study of random events. It is used to predict the likelihood of an event occurring.
Let's start by finding the probability of selecting a Democrat. We are given that there are 60 Democrats in the group of 100 people. Therefore, the probability of selecting a Democrat at random is:
P(Democrat) = 60/100 = 0.6
Next, let's find the probability of selecting a woman. We are given that there are 60 women in the group of 100 people. Therefore, the probability of selecting a woman at random is:
P(Woman) = 60/100 = 0.6
Now, we need to find the probability of selecting both a Democrat and a woman. We are given that 40 of the Democrats are women. Therefore, the probability of selecting a woman who is also a Democrat is:
P(Democrat and Woman) = 40/100 = 0.4
To find the probability of selecting a person who is either a Democrat or a woman, we add the probabilities of selecting a Democrat and selecting a woman, and then subtract the probability of selecting both a Democrat and a woman. Therefore, the probability of selecting a person who is either a Democrat or a woman is:
P(Democrat or Woman) = P(Democrat) + P(Woman) - P(Democrat and Woman)
= 0.6 + 0.6 - 0.4
= 0.8
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among the cast aluminum parts manufactured on a certain day, 80% were awless, 15% had only minor aws, and 5% had ma jor aws. find the probability that a randomly chosen part (a) has a aw and (b) has no ma jor aw.
Probability that a randomly chosen part (a) has a P(flaw) = 0.2 and
has no major flaws b) P(No major flaws) = 0.95
The probability that an event will occur is determined by probability: P(A) = f / N. Probability and odds are related, but probability determines what the odds are. Probability is required before calculating the likelihood that an event will occur.
To find the probability of flaws, we can find the probability of no flaws first by dividing by 100:
P(no flaw) = 80/100 = 0.8
So then:
P(flaw) = 1 - P(no flaw) = 1 - 0.8 = 0.2
P(flaw) = 0.2
B) First, we need to find the probability of major flaws:
P(major flaws) =
P(Major flaws) = 0.05
So to find the probability of no major flaws:
P(No major flaws) = 1 - P(major flaws) = 1 - 0.05 = 0.95
P(No major flaws) = 0.95
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Lauren and Aidan left their offices at 6:15 P.M. and drove to meet at a restaurant the same
distance away from their offices for dinner. Lauren drove at a constant speed of 39 miles
per hour. Aidan drove at a constant speed of 42 miles per hour. Aidan reached the restaurant
away was Lauren from the restaurant when Aidan reached?
at 6:35 P.M. How far away
Lauren was 13 miles away from the restaurant when Aidan reached it.
What is travel?
Travel refers to the act of moving from one place to another, often over a distance or by means of transportation.
Lauren and Aidan both left their offices at 6:15 P.M. and traveled for 20 minutes (from 6:15 P.M. to 6:35 P.M.) before Aidan arrived at the restaurant. During this time, Lauren traveled at a speed of 39 miles per hour, so she covered a distance of:
distance = speed x time
distance = 39 miles/hour x (20 minutes / 60 minutes/hour) = 13 miles
After 20 minutes, Aidan arrived at the restaurant, having traveled for 20 minutes at a speed of 42 miles per hour. The distance he covered during this time is:
distance = speed x time
distance = 42 miles/hour x (20 minutes / 60 minutes/hour) = 14 miles
Since they both traveled the same distance to the restaurant, but Aidan arrived there first, Lauren must have been 1 mile behind him when he arrived at the restaurant.
Therefore, Lauren was 14 - 1 = 13 miles away from the restaurant when Aidan reached it.
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Sydney drives 45 miles in 90 minutes. If she drove three hours in total at the same rate, how far did she go?
Before you try that problem, answer the question below.
How many minutes did Sydney drive in total?
180
180
How far would Sydney drive in 180 minutes?
Answer: 90 miles in 180 minutes
Step-by-step explanation: Since 90 minutes is two times 45, there would be 2 miles in one minute. Then, you multiply 2 times 45 so therefore you get 90 miles in 180 minutes.
The table shows how much money Earl's grandmother gave him each birthday.
Age Birthday Money
5 15
8 24
10 30
17 ?
At this rate, how much money should Earl receive from his grandmother when he turns 17?
$35
$45
$48
$51
Answer:
$51
Step-by-step explanation:
At each age his grandmother gives him three times his age in money.
3 x 5
3 x 8 ...
Find the value of x that makes the quadrilateral a parallelogram. 4x + 2 5x - 6
The required value of x for the diagonals of parallelogram is 8.
What is relation between diagonals of parallelogram?Let ABCD be the parallelogram, and let the diagonals AC and BD intersect at point E.
We know that in a parallelogram, the diagonals bisect each other. So, we have:
AC = 2AE and BD = 2BE
We are given that AC = 4x + 2 and BD = 5x - 6. Substituting in the above equations, we get:
2AE = 4x + 2 and 2BE = 5x - 6
Dividing both sides by 2, we get:
AE = 2x + 1 and BE = (5x - 6)/2
Since AE and BE are the same length (they are both half the length of the diagonals), we have:
2x + 1 = (5x - 6)/2
Multiplying both sides by 2, we get:
4x + 2 = 5x - 6
Subtracting 4x from both sides, we get:
8 = x
Therefore, the value of x is 8.
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Trigonometry question
Step-by-step explanation:
[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]
So let find cos
We know that
[tex] \tan {}^{2} (x) + 1 = \sec {}^{2} (x) [/tex]
We know the value of tan
[tex]( \frac{8}{5} ) {}^{2} + 1 = \sec {}^{2} (x) [/tex]
[tex] \frac{64}{25} + 1 = \sec {}^{2} (x) [/tex]
[tex] \frac{89}{25} = \sec {}^{2} (x) [/tex]
[tex] \frac{ \sqrt{89} }{5} = \sec(x) [/tex]
Sec is the reciprocal of cosine so cosine is
[tex] \cos( \alpha ) = \frac{5}{ \sqrt{89} } [/tex]
Which becomes
[tex] \cos( \alpha ) = \frac{5 \sqrt{89} }{89} [/tex]
So since we know cos a, let's find sin
[tex] \sqrt{ \frac{1 - \frac{5 \sqrt{89} }{89} }{2} } [/tex]
[tex] \sqrt{ \frac{89 - 5 \sqrt{89} }{2} } [/tex]
solve the equation abbc for​ a, assuming that​ a, b, and c are square matrices and b is invertible.
Considering AB=BC, the matrices A, B, and C are square matrices such that matrix B is invertible.
Now, post-multiply both sides of
[tex]AB=BC by {B}^{−1} [/tex]
[tex] {ABB}^{−1} = {BCB}^{−1} [/tex]
Solving the obtained equation for A by using the properties
[tex]AI= {BCB}^{−1} \\ A= {BCB}^{−1} [/tex]
Therefore, the required matrix A is BCB−1
A matrix, also known as matrices, is a rectangular array or table of letters, numbers, or other symbols arranged in rows and columns that is used to represent a mathematical object or a characteristic of one.
In linear algebra, matrices represent linear maps and enable explicit computations. Since most properties and operations of abstract linear algebra can be expressed in terms of matrices, the study of matrices constitutes a significant portion of linear algebra.
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Write as an algebraic expression: five times the difference between six less than a number
The algebraic expression is,
⇒ 5 (6 - n)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ five times the difference between six less than a number.
Now, Let a number = n
Hence, We can formulate;
⇒ 5 (6 - n)
Thus, The value of expression is,
⇒ 5 (6 - n)
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Ms. Reynold's sprinkler system has 9 stations that water all parts of her front and back lawn. Each station runs for an equal amount of time. If it takes 49 minutes for the first 7 stations to water, how long does it take to water all parts of her lawn?
The amount of time it require to water all the parts of her lawn is, 63 minutes
What is division?Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.
We denote division by '÷' this symbol.
Given that,
Ms. Reynold's sprinkler system has 9 stations that water all parts of her front and back lawn.
Each station runs for an equal amount of time
it takes 49 minutes for the first 7 stations to water
The amount of time it require to water stations = ?
First, we need to calculate time required to water 1 station,
t = Total time taken / Total station watered
= 49 / 7
= 7 minutes/station
So
Time for water all parts = 7 x 9
= 63 minutes
Hence, the required time is 63 minutes
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1. 5x^-10 * -2x^4 (Simplify)
2.-4x^2 * 3y^-5 * 2y^7 * x^-6 (Simplify)
(Show Your Work)
Answer: 5x^-10 * -2x^4
To simplify this expression, we will multiply the coefficients (the numbers in front of the variables) and add the exponents of x.
5 * -2 = -10
-10x^(-10 + 4) = -10x^-6
So, the simplified expression is:
-10x^-6
2.-4x^2 * 3y^-5 * 2y^7 * x^-6
To simplify this expression, we will multiply the coefficients and add the exponents of x and y.
-4 * 3 * 2 = -24
-24x^2 * y^(-5 + 7) * x^(-6)
-24x^2 * y^2 * x^-6
-24x^(2 - 6) * y^2
-24x^-4 * y^2
So, the simplified expression is:
-24x^-4 * y^2
Step-by-step explanation:
- If Andrea does 5 more hours of community service, she will have at least the 12
hours of service required by her school. This can be represented by the
inequality below, where x stands for the number of hours of community service
that Andrea has already done.
1+52 12
Which number line BEST represents all values of x that satisfy this inequality?
Answer:
The first/top option
Step-by-step explanation:
First, we can find the inequality that the line is representing. X is the number of hours she has already done, and she has five hours more to do to fulfill the 12 or more hours of required service. The inequality would be x+5≥12.
The minimum that X has to be is 7 because any value lower than 7 would make the inequality false[ ex. 6 + 5 ≠ 12 ]. The arrow would be pointing to the right, because 7 is the minimum value, not the max, so any value higher than 7 would still make the inequality true. Lastly, the circle would be filled, because 7 is included in the set of values that make the inequality true[ 7 + 5 = 12 ].
So, the answer would be the first option.
6 unit squares each have 3/5 of their area shaded. What is 3/5 of 6?
Answer: 3.6
Step-by-step explanation:
3/5 is equal to 20% (3 divided by 5 times 100)
1.2 is 20% of 6
So, 3.6 is 3/5 of 6
for each of the following variables, determine whether the variables is categorical or numerical and determine its measurement scale. if the variable is numerical, determine whether the variable is discrete or continuous.a. name of internet service providerb. time in hours, spent surfing the internet per weekc. whether the individual uses a mobile phone to connect to the internetd. number of online purchases made in a monthe. where the individual uses social networks to find sought -after information
(a). Name of internet service provider is categorical variable because it cannot be quantified or measured. It can be divided into different categories according to the service they provide.
A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.
Measurement scale used for determination is nominal scale, also called the categorical variable scale.
(b). Time in hours, spent surfing the internet per week is continuous numerical variable because time can be measured over an infinite number of real values within a given interval.
A variable is said to be continuous if it can assume an infinite number of real values within a given interval.
Measurement scale used for determination is ratio scale.
(c). Whether the individual uses a mobile phone to connect to the internet is categorical variable because the answer can only be yes or no and it cannot be measured numerically.
A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.
Measurement scale used for determination is nominal scale, also called the categorical variable scale.
(d). Number of online purchases made in a month is discrete numerical variable because it is a value that arises through a counting process.
A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation.
Measurement scale used for determination is interval scale.
(e). Where the individual uses social networks to find sought -after information is categorical variable because the answer can only be yes or no and it cannot be measured numerically. It can be either he/she uses or he/she do not.
A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.
Measurement scale used for determination is nominal scale, also called the categorical variable scale.
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1.) distinguish between the null hypothesis and the research hypothesis. when does the researcher decide to reject the null hypothesis?
A hypothesis that there is some sort of relationship between the variables is where scientists start their inquiry. The alternative, or null hypothesis, asserts that there is no such relationship. Although the null hypothesis may not appear fascinating, it is a crucial component of research.
The claim can be supported by either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is the same as the value specified in the claim. If the null hypothesis is the assertion, then the alternative hypothesis statement is the antithesis of the null hypothesis. A hypothesis is a well-informed, logically-supported guess about the answer to a scientific question. Although it is the experiment's anticipated outcome, it does not constitute experimental proof. The information obtained may or may not be supported, depending on the information received. Simple hypotheses simply state the relationship between two independent and dependent variables. Examples: If you stay up late, you will feel fatigued the next day.
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Indicate the method you would use to prove the two 's . If no method applies, enter "none".
None
SSS
AAS
ASA
SAS
With given features we can definably say that Both triangles are congruent under ASA Criteria.
What is a congruent triangle?A triangle is a closed polygon made up of three line segments that intersect at three different angles.
If the sides and angles of two triangles are the same length, the triangles are said to be congruent. As a result, two triangles can be superimposed side by side and angle by angle. Congruence is the term used to describe the relationship between an object and its mirror image. When two objects or shapes superimpose on one another, they are said to be congruent. They are identical in terms of shape and size. Line segments of the same length and angles of the same measure are congruent in the context of geometric figures.
Given far opposites angle are same = 25°
Given intersected line makes equal line
Intersecting angles are equal due to vertically opposite angle theorem.
Then we have,
Angle = Angle
Side = Side
Angle = Angle
With this features we can definably say that Both triangles are congruent under ASA Criteria.
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I don’t understand this can someone help
Answer:
f(-2) = 2
Step-by-step explanation:
Using the graph, we can determine the y value when x = -2.
When x = -2, the y value is 2.
f(-2) = 2
The helmet Clare plans to buy is on sale for 20% less than the original price. The original price is $5 more than the sale price. What is the original price of the helmet
The Original Price of helmet is $20.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The helmet Clare plans to buy is on sale for 20% less than the original price.
let the sale price be x.
So, the Original price is (x+5).
Also, Sales price = Original price - 20% of Original price
x= x+ 5 - 0.20(x+5)
x = x+ 5 - 0.20x - 1
0.20x = 4
x= 4/ 0.20
x= $20
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solve the system of equations, with a complete solution
Answer: Solutions for x - 4,4,-5 and for y - 3,-3, 0
Step-by-step explanation: I wrote the solutions in order. To solve this question I combined both equations to eliminate the y variable to solve for x. It looked like this : [tex]x^2+x=20[/tex]. I brought the 20 to the other side and got [tex]x^2+x-20=0[/tex]. Then I factored and got [tex](x+5)(x-4)[/tex] which means x = -5 and x = 4. Finally I plugged in these values into the equation to find the possible y values.
what is the number of times a variable appears in a data set?
The number of times a variable appears in a data set is Known as Frequency.
Frequency
The frequency of a particular data is the number of times the data value appears. Denote the frequency of a data value by f. For example, if 5 students got an A in science, the frequency of an A score is considered to be 5.
Frequency distributions are used to tabulate the collected data. Data can be scores given by students, temperatures in different cities, scores scored in volleyball matches, and so on. After data is collected, it needs to be presented in a meaningful way for better understanding. Organize your data so that all characteristics are summarized in a table. This is called a frequency distribution.
Types of Frequency distribution:
1. Group frequency distribution: Use group frequency distribution tables to organize large numbers of observations or data. By doing so, we create class intervals to calculate the frequency of data belonging to a particular class interval.
2. Ungrouped Frequency Distribution: In an ungrouped frequency distribution table, we record the exact frequency of individual data without classifying them.
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What would you pay for 2 1/2 kg of tomatoes at 1. 50 each per kg
Answer: To find out how much you would pay for 2.5 kg of tomatoes at $1.50 per kg, we need to multiply the weight of the tomatoes by the price per kg:
Cost = 2.5 kg x $1.50/kg
= $3.75/kg x 2.5 kg
= $9.38
So, you would pay $9.38 for 2.5 kg of tomatoes at $1.50 per kg.
Step-by-step explanation:
8. Gianna is making bows for her cheerleading squad. She has 4 yards of ribbon to make the
bows. If each bow requires 1/5 a yard of ribbon, will she have enough ribbon to make 18 bows?
Using the concept of proportion, Gianna will have enough yards to make 18 bows
Will she have enough ribbon to make 18 bowsTo solve this problem, we need to apply the concept of proportions.
In order to make 1 bow, she needs 1/5 yard of ribbon
Representing this in an equation form will be;
1 bow = 1/5 yard
18 bow = x yard
cross multiply both sides and solve for x
x * 1 = 18 * (1/5)
x = 3.6 yards
From the above, there will be enough yards to make 18 bows.
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Write 60.9% as a decimal.
A. 0.0609
B. 0.609
C. 0.00609
D. 6.0900
Answer:
0.609
Step-by-step explanation:
convert to a fraction then convert to a decimal by dividing the numerator and denominator :)
question 5
pls help me as soon as possible
i'm being timed i only have a hour
Answer:
CD = 36°
Step-by-step explanation:
the measure of secant angle BFE is half the difference of the measures of the intercepted arcs , that is
[tex]\frac{1}{2}[/tex] (BE - CD) = ∠ BFE
[tex]\frac{1}{2}[/tex] (128 - x) = 46 ( multiply both sides by 2 to clear the fraction )
128 - x = 92 ( subtract 128 from both sides )
- x = - 36 ( multiply both sides by - 1 )
x = CD = 36°
Solve for y
x-3/2y=-12
The equation x-3/ 2y=-12 when solved for the variable y is y = x-3/-24
How to solve for the variableWe have to make 'y' the subject from the equation, we have;
x-3/2y=-12
By solving for the variable, we need to work it out.
Also, we have to make it stand alone on one end of the equality sign.
cross multiply the values
x - 3(1) = -12(2y)
multiply the values
x-3 = -24y
Make 'y' the subject by dividing both sides by the coefficient of y
y = x-3/-24
Hence, the equation is y = x-3/-24
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Acellus
Find the equation of the axis of
symmetry for this function.
f(x) = 4x² - 8x + 5
-b
Hint: To find the axis of symmetry, use the equation: x =
2a
Simplify your answer completely. Enter
the number that belongs in the green box.
x = [?]
Answer:Rewrite the equation in vertex form.
Tap for more steps...
y
=
4
(
x
−
1
)
2
−
9
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
4
h
=
1
k
=
−
9
Since the value of
a
is positive, the parabola opens up.
Opens Up
Find the vertex
(
h
,
k
)
.
(
1
,
−
9
)
Find
p
, the distance from the vertex to the focus.
Tap for more steps...
1
16
Find the focus.
Tap for more steps...
(
1
,
−
143
16
)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x
=
1
Step-by-step explanation:
Grace was born on January 1, 2020. Thomas was born on December 31, 2018. How many days older is Thomas than Grace?
Answer:
I think it’s 730 days
Step-by-step explanation:
Step-by-step explanation: 2 years = 730 + the 10 months+ 740
please help asap thankyou
Answer:
A = 648π cm²
Step-by-step explanation:
the area (A) of a semicircle is half the area of a circle , then
A = [tex]\frac{1}{2}[/tex] πr² ( r is the radius ) , then
A = [tex]\frac{1}{2}[/tex] × π × 36² = [tex]\frac{1}{2}[/tex] × π × 1296 = 648π cm²
what is the value of the y-intercept of the graph of f(x)= 57(3.2)x
The y-intercept of the graph of a function is the point at which the graph intersects the y-axis. In other words, it's the value of the function when x=0.
So to find the y-intercept of f(x) = 57(3.2)x, we can substitute x=0 into the function:
f(0) = 57(3.2)(0)
f(0) = 0
So the y-intercept of this function is (0,0).
PLS HELP ASAP!
in ABC, mC=90, mA=50, and AB=35. find the length of the altitude CH
Answer:
Step-by-step explanation:
no idea sorry :/
The length of the altitude CH is 17.234.
What is Altitude of a Triangle?Altitude of a triangle is defined as the perpendicular line segment joining the vertex to the opposite side.
The figure for the triangle is given below.
Here the area of a triangle can be found in two ways.
Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
Consider the triangle ABC given below.
Area of the triangle when considered base as BC and altitude as AC is,
Area, A = [tex]\frac{1}{2}[/tex] × BC × AC
BC = AB Sin (50) = 35 sin(50)
AC = AB Sin (40) = 35 sin(40)
A = [tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40))
Area of the triangle when considered base as AB and altitude as CH is,
Area, A = [tex]\frac{1}{2}[/tex] × AB × CH
A = [tex]\frac{1}{2}[/tex] × 35 × CH
Area of the same triangle will be equal when find in different ways.
[tex]\frac{1}{2}[/tex] × (35 sin(50)) × (35 sin(40)) = [tex]\frac{1}{2}[/tex] × 35 × CH
Cancelling the terms which are on both sides,
CH = 35 sin(50) sin(40)
CH = 35 × 0.766 × 0.643
CH = 17.234
Hence the length of the altitude is 17.234.
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4. Triangle WXY with vertices W(-4, 8),
X(10, 0), and Y(-2, -8): k = 1
itblib
Slot
blib
brit d
W': C
X': (85
Y':
piqot
OM
The dilated points are:
W': (-1, 2)
X': (2.5, 0)
Y': (-0.5, -2).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.
Given:
Triangle WXY with vertices W(-4, 8), X (10, 0), and Y(-2, -8).
And the scale factor is 1/4.
So, the image points are,
W': (-4/4, 8/4) = (-1, 2)
X': (10/4, 0/4) = (2.5, 0)
Y': (-2/4, -8/4) = (-0.5, -2)
Hence, the image points are given above.
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