Here, we are given;
P(A)=0.6
P(B)=0.42
P(B/A)=0.63
We have to find;
[tex]P(A\cap B)[/tex]Now,
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]This is the formula for finding conditional probability.
From here,we can see that we have values of P(B/A) and P(A) and we can easily find P(Aand B) from here.
Since P(A)>0 so we can use this formula.
Therefore,
[tex]\begin{gathered} P(A\cap B)=P(A)\times P(\frac{B}{A}) \\ P(A\cap B)=0.6\times0.63 \\ P(A\cap B)=0.378 \end{gathered}[/tex]Rebecca wants to prove that if the diagonals in a parallelogram are perpendicular, then it is a rhombus.
It is shown that if a parallelogram's diagonals are perpendicular, the parallelogram is a rhombus.
In mathematics, what is a parallelogram?A parallelogram is a quadrilateral with two parallel sides (and therefore opposite angles equal).
What exactly is a rhombus?A rhombus is a quadrilateral with all of its sides equal. Because opposite sides of a parallelogram are equal, a rhombus is a type of parallelogram in which all sides are equal.
We must demonstrate that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Let ABCD be a parallelogram .
Consider Δ AOD and Δ COD
Since, a parallelogram's diagonals bisect each other we can say that,
AO = CO
∠AOD = ∠COD = 90°
DO = OD
Δ AOD ≅ Δ COD [SAS rule]
∴ AD = CD
Because the parallelogram's adjacent sides are equal, we can conclude that all four sides are equal.
As a result, it is demonstrated that if the diagonals of a parallelogram are perpendicular, the parallelogram is a rhombus.
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Which of the following is the best estimate of the slope of the best -fit line for the graph at the right?
The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.
What is the slope?The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope. A line that is moving up will have a positive slope, and a line that is moving down will have a negative slope if you view the line from left to right. A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x₁,y₁) and (x₂,y₂), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
Given Data
x coordinate = 4
y coordinate = 7
Slope = y-coordinate/ x-coordinate
Slope = 7/4
The best estimate of the slope of the best-fit line for the graph at the right will be 7/4.
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Find the value of p in the inequality.
three fourths times p plus 8 is greater than or equal to 3
The value of p that we get by solving the inequality given in the question is [tex]p\geq \frac{-20}{3}[/tex]
The given inequality is
[tex]\frac{3}{4}p+8\geq 3[/tex]
⇒[tex]\frac{3}{4}p\geq 3-8[/tex] (subtracting 8 on both sides)
⇒[tex]3p\geq -5*4[/tex] (multiplying both sides by 4)
⇒[tex]p\geq \frac{-20}{3}[/tex] (dividing both sides by 3)
⇒[tex]p\geq -6.667[/tex]
Therefore the value of p must be greater than or equal to -20/3 or -6.667
That is, [tex]p\geq -6.667[/tex]
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-5w/9 = 30 solve for w and simplify your answer as much as possible
After simplification of the given expression -5w /9 =30 , value of w is equal to -54.
As given in the question,
Given expression is equal to :
-5w / 9 = 30
Simplification of the given expression to get the value of w is :
-5w / 9 = 30
Multiply both the side of the given expression by 9 we get ,
-5w = 30 × 9
Divide both the side of the given expression by -5 we get,
-5w /-5 = ( 30 × 9 ) / -5
⇒ w = -(6 × 9 )
⇒ w = -54
Therefore, after simplification of the given expression -5w /9 =30 , value of w is equal to -54.
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write the equation of the line in a fully simplified slope-intercept form.
Slope intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptWe can identify two points on the given graph and solve for the slope and the y-intercept.
Solving the QuestionTwo clear points on the graph are (6,0) and (0,6).
First, we can solve for the slope by using the slope equation:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
⇒ Plug in the points (6,0) and (0,6):
[tex]m=\dfrac{0-6}{6-0}\\\\m=\dfrac{-6}{6}\\\\m=-1[/tex]
Therefore. the slope of the line is -1. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-x+b[/tex]
Now, we can find the y-intercept. It is the value of y when the line crosses the y-axis.
In this case, we can see on the graph that this is 6.
[tex]y=-x+6[/tex]
Answer[tex]y=-x+6[/tex]
Two quarters of the basketball game are complete. Now it is half time. Explain how this could be
Using proportions, the explanation for this is that a basketball game has four quarters, hence half-time is at the end of the second quarter.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the basic arithmetic operations, especially multiplication and division with the unit rates in the problem.
The entirety of a basketball game is composed by:
4 quarters.
Hence the mid-point of the game is calculated as follows:
0.5 x 4 quarters = 2 quarters.
This means that the end of the second quarter is the mid-point of the game, which is why the halftime is positioned at the end of the second quarter.
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-2
-3
S
y = -2|x|
2
X
The function is positive when
The function is negative when
The function is increasing when
The function is decreasing when
Answer: Never, All real numbers, x<0, x>0
Step-by-step explanation:
The function is positive when it is above the x-axis.
The function is negative when it is below the x-axis.
The function is increasing when the graph is going up.
The function is decreasing when the graph is going down.
What is the
domain?
Help me plssss
60 cents as percent of $3
60 cents is 20% of $3.
What is the percentage?In essence, percentages are fractions with 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). The value of a number out of 100 is the percentage of that number. The terms "percent" and "cent" combine to make the word "percentage." Having Latin and French roots, the term "cent" means "hundred," while the word "percent" means "per hundred."
Given Data
60 cents as a percent of $3
1 dollar = 100 cents
$3 dollar = 300 cents
Percentage:
[tex]\frac{Value}{Total value}[/tex] × 100
[tex]\frac{60}{300}[/tex] ×100
20%
60 cents in 20% of $3.
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The complete question is:
"60 cents is what percent of $3."
k (x)=6x-12 ; k(x)=15
The input value x in the function k( x ) = 6x - 12 when k( x ) = 15 is 9/2.
What is the input value (x) in the given function?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the data in the question;
k( x ) = 6x - 12k( x ) = 15x = ?To determine the value of x, equate the function to 15 and solve for x.
k( x ) = 6x - 12
k( x ) = 15
15 = 6x - 12
Rearrange the equation
6x - 12 = 15
Collect like terms
6x = 15 + 12
6x = 27
Divide but sides by 6
6x/6 = 27/6
x = 27/6
x = 9/2
Therefore, the input value (x) is 9/2, this forms an ordered pair of ( 9/2, 15 ).
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find the values of a,b,c, and d so that h(x)=a|bx+c|+d is a translation 7 units up and 1 unit right, followed by a reflection in the y-axis of the graph of g(x)=1/3|x+3|-4
The translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.
What is translation and reflection?
In mathematics, the translation shift the coordinates either on the horizontal axis or on the vertical axis. It compress the expression also. Similarly, in reflection, the expression get reflected on the coordinate axis either on the upper side or downward side.
According to the question, the given expression for the translation as well as for the reflection are as follows:
h(x)=a |b(x) + c| + d
g(x)=1/3 | x + 3| - 4
And the given condition state that the translation is for 7 units and reflection is on the y-axis. Translation shift the expression and reflection reflects the expression.
Translation expression: h(x+7)=a |b(x+7) + c| + d
Reflection expression: g(-x)=1/3 | -x + 3| - 4 = 1/3 | x + 3| - 4
Therefore, the translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.
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Ryan has a deck that measures 3 feet by 8 feet. He wants to increase each dimension
by equal lengths so that its area is increased by 50%. By how much should he increase each dimension?
The dimensions of the deck would be increased by 1 feet.
How much should he increase each dimension?Area of a rectangle = length x width
Initial area of the deck = 3 x 8 = 24 feet²
Area of the deck when it is increased = (1 + 0.50) x 24 = 36 feet²
Length of the deck after it is increased = 3 + x
Width of the deck after it is increased = 8+ x
Area of the new deck : (3 + x) + (8 + x) = 36
24 + 3x + 8x + x² = 36
x² + 8x + 3x + 24 - 36 = 0
x² + 11x - 12 = 0
The solutions of the quadratic equation are -1 and 12
-1 + x = 0
x = 1
or
12 + x = 0
x = -12
Thus, the dimension of the deck would be increase by 1 feet.
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your ethics professor decides to conduct a survey in your class about whether voluntary euthanasia should be legal in the united states. for her survey, she takes all 30 students' names and assigns them each a number. then she has a computer program indiscriminately choose 15 students. we could say that her survey will be:
Hence, the survey of professor will be representative survey.
What is survey?A survey is a technique for acquiring data from a sample of people by asking pertinent questions with the goal of comprehending populations as a whole.
Everyone involved in the information economy, from corporations to the media to the government and academia, relies on surveys as a vital source of information and insights.
The survey of professor will be representative survey.
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help me with this please!!
y -intercept #4 the starting value
(1 , 7.5) #3 the value after 1 year
because the x axis is the time (in years). When x = 0 (at the y-intercept) time = 0 or beginning time. When x = 1 one year has passed.
Which of these shapes are a trapezoid?
Answer: The Pink one
Step-by-step explanation: Trapezoids have 2 parallel sides and 2 non-parallel sides.
I need helping finding out the answers … I’m confused.
To solve this problem, we will use the following formula for the area of a trapezoid:
[tex]A=\frac{a+b}{2}h,[/tex]where a, and b are the lengths of the bases and h is the height.
Now, we are given that ( we will omit the units to simplify the calculations):
[tex]\begin{gathered} h=\frac{1}{4}(a+b), \\ h=2\frac{1}{2}. \end{gathered}[/tex]Therefore:
[tex]\frac{(a+b)}{2}=2(\frac{a+b}{4})=2h=2(2+\frac{1}{2})=4+1=5.[/tex]Substituting in the above formula, we get:
[tex]A=\frac{5}{2}\times(2\frac{1}{2}).[/tex]Simplifying the above result, we get:
[tex]A=\frac{25}{4}ft^2.[/tex]Answer:
[tex]\begin{gathered} A=\frac{1}{2}(2\frac{1}{2})(2\frac{1}{2}\cdot2) \\ =\frac{1}{2}(\frac{5}{2})(\frac{5}{2}\cdot2) \\ =\frac{50}{8}=\frac{25}{4}=6.25ft^2. \end{gathered}[/tex]5
8
of the staff are male. 5
12
of the staff works part time at
the aquarium. What fraction of the staff is female?
The fraction that are female in the company is 227/256
How to determine the fraction that are female?The given parameters are
Male staff = 58
Total number of staff = 512
Start by calculating the number of female staffs
So, we have
Female staff = Total number of staff - Male staff
Substitute the known values in the above equation
So, we have
Female staff = 512 - 58
Evaluate the like terms
Female staff = 454
The fraction that are female is
Fraction = Female staff/Total number of staff
This gives
Fraction = 454/512
Simplify
Fraction = 227/256
Hence, the fraction is 227/256
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Solve the equation for the given variable. (type "no solution" if the equation has no solution and type "all
real numbers" if the equation is valid for all possible x-values)
4(4x + 2) + 2(9x + 4) + 3 = 34x + 19
Answer:
all real numbers
Step-by-step explanation:
4(4x+2)+2(9x+4)+3=34x+19
16x+8+18x+8+3=34x+19
34x+19=34x+19
all real numbers
:]
A string measures 30 cm about how many lnches long is the string
Find the quotient of.(4.617 × 10 ^3 ) ÷ (5,700 ÷ 10^ 2 )
The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The expression is;
(4.617 × 10³ ) ÷ (5,700 ÷ 10² )
Now, Solve the expression by using BODMAS rule;
= (4.617 × 10³ ) ÷ (5,700 ÷ 10² )
= 4,617 ÷ 57
= 81
Thus, The quotient of the expression (4.617 × 10³ ) ÷ (5,700 ÷ 10² ) is 81.
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What is the lowest common multiple of six and nine
Answer: 18
Step-by-step explanation: it is the smallest one in both tables.
1x6=6 2x6=12 3x6=18
1x9=9 2x9=18
hope this helped
Evaluate the arithmetic series described:
a (subscript 1) = 12
a (subscript n) = 64
Find S (subscript 14)
Answers:
541
532
1082
1064
...the subscript thing isn't working for some reason
Answer:
532
Step-by-step explanation:
Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac{n}{2}(a_1+a_n)}[/tex]
Where:
aₙ is the nth term.a₁ is the first term.n is the position of the term.Given terms:
[tex]a_1=12[/tex][tex]a_n=64[/tex]Substitute the given terms into the formula to create an equation for the nth term:
[tex]\implies S_n=\dfrac{n}{2}(12+64)[/tex]
[tex]\implies S_n=\dfrac{n}{2}(76)[/tex]
[tex]\implies S_n=38n[/tex]
To find S₁₄, substitute n = 14 into the found equation:
[tex]\begin{aligned}n=14 \implies S_{14}&=38(14)\\ & = 532\end{aligned}[/tex]
The figures below are congruent. Name the corresponding sides.
Answer:
KM
KL
LM
Step-by-step explanation:
(Inv. 1)*30. Multiple Choice Tika's math class began 18 minutes ago. Theclass will end in 37 minutes. Which equation can be used to find thelength in minutes of Tika's math class?A 18 + m = 37Bm – 37 = 18C 37 - m = 18D 18 – m = 37
Step 1
Let the length in minutes of Tika's class be m
His class had lasted already for 18 minutes
His class had 37 more minutes to end.
Step 2
Get the equation
[tex]\begin{gathered} 18\text{ + 37 = m} \\ To\text{ suit the options} \\ 18\text{ = m-37} \\ \text{Therefore,} \\ m-37\text{ = 18} \end{gathered}[/tex]Hence the answer is option B ------ ( m - 37 = 18)
what’s the inequality
17 < 9 + x
Answer:
x > 9
Step-by-step explanation:
HELP ME PLEASE! THIS IS URGENT!!
For what value of x will the line passing through the following pairs of points be veritcal? F(3-2x, 12) and G(x+9, 7)
By solving a linear equation, we will see that the points are vertical only if the value of x is -2.
For which value of x are the points vertical?
We say that two points (x₁, y₁) and (x₂, y₂) are vertical if the points have the same x-component and different y-component, so we must have:
x₁ = x₂
y₁ ≠ y₂
In this case, the two points are:
F(3-2x, 12) and G(x+9, 7)
The y-component is different, so we only need to have:
3 - 2x = x + 9
This is a linear equation, below I will solve it:
3 - 2x = x + 9
3 - 9 = x + 2x
-6 = 3x
-6/3 = x
-2 =x
The points are vertical if x = -2.
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The start of an arithmetic sequence is
17, 21, 25, 29,
21,
The rule for the sequence can be written in the form
In
= en + d, where c and d are numbers.
a) By first calculating the values of c and d, work out the rule
for the sequence.
b) What is the value of 211?
The equation of the sequence is xₙ = 4n + 17 and the 11th term is 61
The equation of the sequenceFrom the question, we have the sequence to be
17, 21, 25, 29, 21
The form of the sequence is given as
xₙ = cn + d
From the question, we have the first term to be 17
This means that
d = 17
So, we have
xₙ = cn + 17
When n = 1, we have x = 21
So, we have
21 = c + 17
Evaluate
c = 4
Substitute c = 4 in xₙ = cn + 17
xₙ = 4n + 17
The value of x₁₁This means that
n = 11
So, we have
x₁₁ = 4 * 11 + 17
Evaluate
x₁₁ = 61
Hence, the value is 61
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A restaurant chain is measuring the levels of arsenic in chicken from its suppliers. The question is whether there is evidence that the mean level of arsenic is greater than 80 ppb, so we are testing vs , where represents the average level of arsenic in all chicken from a certain supplier. It takes money and time to test for arsenic so samples are often small. A sample of chickens from one supplier is tested, and the resulting sample mean is . Subtracting 11 from the sample data to move the mean down to the null mean of results in the following data: . 62, 78, 89, 95, 95, 137
The p-value of the test is 0.1515 which concludes that the average amount of arsenic in chicken from suppliers is 80 ppb.
The test hypothesis is as follows:
H₀: The mean amount of arsenic is 80 ppb, i.e. μ= 80.
Hₐ: The mean amount of arsenic is more significant than 80 ppb, i.e.μ > 80.
We will apply a t-test for a single mean because the population standard deviation is unknown,
It is assumed that the sample means [tex]\bar{x}[/tex] = 91.
The adjusted sample presented is:
S = { 62, 78, 89, 95, 95, 137}
Calculate the sample standard deviation as follows:
[tex]\bar{x}[/tex] = 62 + 78 + 89 + 95 + 95 + 137 =80
[tex]s =\sqrt{\frac{1}{6-1} \times [(62-80)^2 + (78-80)^2 + (89-80)^2 + (95-80)^2 + (95-80)^2 + (137-80)^2]}[/tex]
s =28.66
[tex]t =\dfrac{\bar{x}-\mu}{s/ \sqrt{n} } = \dfrac{{91}-80}{28.6/ \sqrt{6} }=0.94[/tex]
Thus, the test statistic value is 0.94.
Compute the p-value of the test as follows:
p-value = p(tₙ₋₁ < t)
p-value = p(t₆₋₁ < t)
p-value = p(t₅ < t)
*Make use of a t-table.
As a result, the test has a p-value of 0.1515.
Rule of decision:
The null hypothesis will be rejected if the p-value of the test is less than the significance threshold, and vice versa.
p-value = 0.1515 > α = 0.05
At 5% significance, the null hypothesis will not be rejected.
As a result, we may conclude that the average amount of arsenic in chicken from suppliers is 80 ppb.
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I'm doing linear equations and one if the things says y = -x so do i plug in the x that i have already and just switch it to the opposite integer????
To solve for y we will have to simply replace the value of x and the solution we write it in the equivalent palce for y, that is:
For x = -5:
[tex]y=-(-5)\Rightarrow y=5[/tex]For x = -2:
[tex]y=-(-2)\Rightarrow y=2[/tex]For x = 0:
[tex]y=0[/tex]For x = 3:
[tex]y=-3[/tex]Solve the system of linear equations using the substitution method.
4x + 7y = 19 and y = x + 9
A. (-4, 5)
B. (-6, 4)
C. (-1, 2)
D. (-4, 3)
Answer:D
Step-by-step explanation: