Answer: Frank owes $212 on his credit card and then charges $105 more, so the new balance on Frank's credit card is:
$212 + $105 = $317
So the new balance on Frank's credit card is $317.
Step-by-step explanation:
Here are ingredients from recipes for two different banana cakes.
First recipe is in the table shown.
Second recipe is shown in the relationship cups of flour y and cups of sugar x in the second recipe is y=7/4x.
1.if you used 4 cups of sugar, how much flour does each recipe need? Type your answer in the boxes below.
2. What is the constant of proportionality for each situation and what does it mean?
1. The amounts of flour, considering 4 cups of sugar for each recipe, are given as follows:
First recipe: 6 cups.Second recipe: 7 cups.2. The constant for each recipe is given as follows:
First recipe: 3/2, meaning that for each cup of sugar, 3/2 cups of flour are needed.Second recipe: 7/4, meaning that for each cup of sugar, 7/4 cups of flour are needed.How to model the proportional relationship?A proportional relationship is modeled as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
Input x: amount of sugar.Input y: amount of flour.From the table, the constant is given as follows:
k = (3/4)/(1/2)
k = 3/2.
Meaning that for each cup of sugar, 3/2 cups of flour are needed.
Hence the relation is:
y = 3x/2.
The amounts of flour, considering 4 cups of sugar for each recipe, are obtained as follows:
First recipe: 3 x 4/2 = 6 cups.Second recipe: 7 x 4 / 4 = 7 cups.More can be learned about proportional relationships at brainly.com/question/10424180
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1) b^2 -4=0
2)2x^2 =21+11x
3)5x^2 =3x+92
Answer:
1. b1=-2, b2=2
2. x1= -3/2, x2=7
3. x1=-4, x2= 23/5
Follow formula
b = -b [+][-] sq| b^2-4ac/ 2a
Determine algebraically whether the given function is even, odd, or neither. f(x) = -9x3 O Even O Odd O Neither
The function f(x) = -9x^3 is odd because it is not at the initial state after replacing x by -x.
By taking a function, replacing each x with an equal value, simplifying it, and then comparing the outcomes to what you had initially, you can "determine algebraically" whether it is even, odd, or neither.
If the function is identical to what you started with that is, if f(-x) = f (x), with all the signs remaining the same then the function is even. If the function is exactly the opposite of what you started with (i.e., if f(-x) = -f(x), with all the signs switched this is known as an odd function.
The function is f(x) = -9x^3
Now substitute -x in place of x.
f(-x) = -9(-x)^3
f(-x) = -9 × -(x)^3
f(-x) = 9x^3
As we can see that the function is not in the initial position so the function is odd.
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The table shows the number of laps jogged by Cameron last weekend. Day Number of Laps Saturday 21 Sunday 16.5 What was the percent of decrease in the number of laps jogged from Saturday to Sunday? Round the percent to the nearest tenth if necessary.
Answer: To find the percent of the decrease in the number of laps jogged from Saturday to Sunday, we can use the following formula:
percent decrease = (change in value / original value) x 100
In this case, the original value is the number of laps jogged on Saturday, which is 21 laps. The change in value is the difference in the number of laps jogged from Saturday to Sunday, which is 21 - 16.5 = 4.5 laps.
So, substituting these values into the formula:
percent decrease = (4.5 / 21) x 100
percent decrease = 0.214 x 100
percent decrease = 21.4%
Rounded to the nearest tenth, the percent of decrease in the number of laps jogged from Saturday to Sunday is 21.4%.
Step-by-step explanation:
mj supply distubutes bags of dog food to pet stores its markup rate is 28% which eqaution represents the new price of a bag of dog food y given an orignal price x?
Answer:
Step-by-step explanation:
You didn't post any answer choices, but the answer should be:
y = x + (0.28)x = 1.28x
angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
solve an equation to determine the measure of angle x.
Applying the sum of angles on a straight line, we have:
Equation = x + 70 + 60 = 180
Measure of x = 50°.
What is angle ?In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.
A straight line angle equals 180 degrees.
Therefore, the sum of all the angles on a straight line = 180 degrees.
Thus, the equation to solve for x would be:
x + 70 + 60 = 180
Solving for x
x + 130 = 180
x = 180 - 130
x = 50°
Hence, 50° is the measure of angle x.
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Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply
The quadratic equation 4 · x² - 7 · x = 3 · x + 24 has the following roots: x₁ = 19 / 4 and x₂ = - 9 / 4.
How to solve a quadratic equation
In this question we find the case of a quadratic equation, whose form is defined below:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficientsx - Independent variabley - Dependent variableThe procedure find the solutions to the quadratic equations:
Modify the polynomial into standard form.Complete the square.Simplify part of the expression into a perfect binomial.Clear the variable x by algebra properties.Now we proceed to determine the solutions to the quadratic equation:
4 · x² - 7 · x = 3 · x + 24
4 · x² - 10 · x - 24 = 0
4 · [x² - (5 / 2) · x - 6] = 0
4 · [x² - (5 / 2) · x + 25 / 4] = 4 · 6 + 4 · (25 / 4)
4 · (x - 5 / 4)² = 49
(x - 5 / 4)² = 49 / 4
x - 5 / 4 = ± 7 / 2
x = 5 / 4 ± 7 / 2
The solutions to the quadratic equation 4 · x² - 7 · x = 3 · x + 24 are x₁ = 19 / 4 and x₂ = - 9 / 4.
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Colton puts geapes in plastic bags to sell at the farmer's market. He weighs each bag and records the weights in a line plot. What is the difference between the lightest bag of grapes?
The difference between the lightest bag of grapes that has been recorded by Colton will be 3/2 or 1 - 1/2.
[tex]2 - \frac{1}{2} [/tex]
[tex] = \frac{4}{2} - \frac{1}{2} [/tex]
[tex] = \frac{3}{2} or \: 1 - \frac{1}{2} [/tex]
Data gathering, analysis, interpretation, presentation, and organization are all topics covered in the study of statistics. In other words, gathering and summarizing data is a mathematical discipline. Additionally, statistics can be considered a subfield of applied mathematics.
Uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can be used to determine the uncertainty and variation in various fields. Probability, which has a significant impact on statistics, essentially determines these uncertainties.
Note that the graph for the following question is: (check the attached image).
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Figure 2 is a scale image of Figure 1, as shown below.
What is the scale factor applied to Figure 1 to produce Figure 2?
A.
The scale factor is equivalent to {k} = 4/3.
What is scale factor?Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically - {K} = y/x = constantScale factor is a dimensionless quantity that tells by how much time a specific dimension of a figure is enlarged or reduced. Mathematically, it is the ratio of two similar quantities.Scaling is defined as the process of changing the dimensions of the original figure as per some specific proportional rule.In case of length scaling, we can write -{K} = L{final}/L{initial}
Given is that figure 2 is a scale image of figure 1.
We can write the scale factor as -
K = {y}/{x} = 8/6 = 4/3
Therefore, the scale factor that is applied to figure {1} to get figure {2} is equivalent to {k} = 4/3.
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what is the shift
y = log(x+4) -3
The shift of the function y = log(x+4) -3 is 4 units left and 3 units down
How to determine the shiftFrom the question, we have the following parameters that can be used in our computation:
y = log(x + 4)
The above equation is a logarithmic equation
So, the parent function is
y = log(x)
When the parent function is compared to the given function, we have
3 units down and 4 units left
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people with type o-negative blood are universal donors. that is, any patient can receive a transfusion of o-negative blood. only 7.2% of the american population have o-negative blood. if we choose 10 americans at random who pg 327 pg 329 gave blood, what is the probability that at least 1 of them is a universal donor?
The probability that at least one of 10 randomly chosen Americans has O-negative blood is 0.722.
The probability that at least one of 10 randomly chosen Americans has O-negative blood can be calculated by first determining the probability that none of them have O-negative type blood. Since 7.2% of the population has O-negative blood, the probability that one of 10 randomly chosen Americans has O-negative blood is (1 - 0.072)^10. To determine the probability that at least one of 10 randomly chosen Americans has O-negative blood, we subtract this value from 1. Therefore, the probability that at least one of 10 randomly chosen Americans has O-negative blood is 1 - (1 - 0.072)^10, which is equal to 0.722.
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Work out the value of g in the following equation:
g sin 34° =3.5
The value of g in the following equation is 6.25. The solution has been obtained using trigonometry formula.
What is trigonometry?
The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. Therefore, applying the trigonometric formulas, functions, or trigonometric identities aids in locating the unknown or missing angles or sides of a right triangle. In trigonometry, angles can be stated in either degrees or radians. For calculations, the most common trigonometric angles are 0, 30, 45, 60, and 90 degrees.
We are given g sin 34° =3.5
⇒ g = 3.5/sin34° (Dividing both sides by sin34°)
Now, value of sin34° = sin(30+4)° = 0.5592
So, we get
⇒ g = 3.5/0.5592
⇒ g = 6.25
Hence, the value of g in the following equation is 6.25.
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In the equation below, g has a value of 6.25. The trigonometric formula has been used to arrive at the solution.
What is a triangle?The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry." In order to find the unknown or missing angles or sides of a right triangle, one can apply the trigonometric formulae, functions, or identities. Angles can be expressed in radians or degrees in trigonometry. The most frequent trigonometric angles used in computations are 0, 30, 45, 60, and 90 degrees.
Given is g sin 34° = 3.5.
g = 3.5/sin34° (both sides divided by sin34°)
The cost of sin today
34° = sin(30+4)° = 0.5592
So, we obtain
⇒ g = 3.5/0.5592
⇒ g = 6.26
Thus, the importance of g in the following equation is 6.26.
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(n^3+3n^2-15n+19)/(n-2) Synthetic Division
The quotient is n^2+5n-5 and the remainder is 9. The solution has been obtained by using the synthetic division.
What is synthetic division?
Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1."
We are given the expression as (n^3+3n^2-15n+19)
The expression is to be divided by (n-2)
So, by using the synthetic division, we get
2 | 1 3 -15 19
- 2 10 -10
1 5 -5 9
Quotient = n^2+5n-5
Remainder = 9
Hence, the quotient is n^2+5n-5 and the remainder is 9.
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alfred and bonnie play a game in which they take turns tossing a fair coin. the winner of a game is the first person to obtain a head. alfred and bonnie play this game several times with the stipulation that the loser of a game goes first in the next game. suppose that alfred goes first in the first game, and that the probability that he wins the sixth game is m n , where m and n are relatively prime positive integers. what are the last three digits of m n ? (1993,
So, the last three digits of m*n is 001.
Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.
Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:
p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2
Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.
Therefore, the last three digits of m*n is 001.
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The veterinarian orders 15 mg of Vitamin K. The vial is labeled 10mg/mL how many mL is needed?
please explain how to do it
Each ml of the vial contains 10 mg of Vitamin K. So to obtain 15 mg of Vitamin K, we needs a volume 1.5 ml of the solution.
We can calculate the required amount in two ways. We can use either proportions, or we can use the unit value determination.
By using proportions.In 1 ml we have 10mg , to get 15 mg we can use x ml
[tex]\frac{1}{10} = \frac{x}{15}[/tex]
[tex]x = \frac{15* 1}{10}[/tex]
x = 1.5
So, to get 15 mg of Vitamin K, we need 1.5 ml of solution.
By finding the unit valueVolume required to get 10 mg of vitamin K = 1 ml
Volume required to get 1 mg of vitamin K = [tex]\frac{1}{10}[/tex] ml = 0.1 ml
Volume required to get 15 mg of Vitamin K = 15 × 0.1 = 1.5 ml
So volume required to get 15mg = 1.5 ml
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4 of 54 of 5 Items
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Question
The two lines graphed on the coordinate grid each represent an equation.
Which ordered pair represents a solution to both equations?
Responses
A (2, 2)(2, 2)
B no solution solution
C (2, 1)(2, 1)
D (1, 2)
Answer:
Step-by-step explanation:
in every there w234e
A ring is now reduced to 840 this is saving 40%of the original price .work out the original price of the ring
Answer: 1400
Step-by-step explanation: If it is saving 40% of the original price than it is 60% of the original price. 840=60/100*x, and so we divide both sides by 60/100. 840*100/60=1400. Therefore, 1400 is the original price.
what is the distance from y to wx
Step-by-step explanation:
this distance YZ is the height of the triangle WXY.
it splits the main triangle into 2 right-angled triangles WYZ and XYZ.
we can use Pythagoras
c² = a² + b²
with any of the 2 smaller right-angled triangles to get YZ.
remember, "c" is the Hypotenuse (the side opposite to the 90° angle). a and b are the legs.
so, when picking the larger one :
26² = 24² + YZ²
676 = 576 + YZ²
100 = YZ²
YZ = sqrt(100) = 10 = distance of Y to WX.
Ben is considering purchasing a new home. His banker has presented a 10-year mortgage at a fixed rate of 7.6%. The cost of the home is $196000 and Ben will be required to provide a 25% down
payment. If we use Sheets to determine his monthly payment, which of the following Sheets commands could be used to determine his payment? (Choose all that apply!)
-PMT(0.076/12,120,-147000)
PMT(0.076/12,10 12,-$147000)
PMT(7.6,10,-196000)
PMT (7.6% / 12,12 10,-147000)
PMT(7.6/12,12 10,-147000)
-PMT(0.076/12,120,-196000+49000)
Answer: The PMT function in Sheets is used to calculate the monthly payment for a loan. The syntax of the function is PMT(rate, nper, pv, [fv], [type]).
Rate: the interest rate per period
Nper: the total number of payments
Pv: the present value (the total amount of the loan)
Fv: the future value of the loan (optional)
Type: the number 0 or 1 indicating when payments are due (0 = end of period, 1 = beginning of period)
Given the information in the problem, Ben's mortgage is for 10 years, so the total number of payments is 10*12 = 120. The present value of the loan is $196000 and the down payment is 25% of the home's cost so 25%*196000 = $49000. Therefore, the present value of the loan is $196000 - $49000 = $147000
Based on this information, the following commands would be used to determine the monthly payment:
PMT(0.076/12,120,-$147000)
PMT(0.076/12,120,-196000+$49000)
The first command uses the annual interest rate divided by 12 to convert it to a monthly rate, and the total number of payments is 120 (10 years * 12 months/year). The second command also uses the same monthly rate and total payments and the present value which is $147000
The other commands
Step-by-step explanation:
Triangle BCD has vertices B(-8,3), C(-4, 6), and D(2, 0). If the triangle is reflected across the x-axis and dilated by a scale factor of 0. 5 with respect to the origin, what are the coordinates of the vertices of triangle B"C"D"?
If the vertices of the triangle BCD with vertices B(-8,3), C(-4, 6), and D(2, 0) , and if they are reflected across x axis and dilated by a scale factor of 0.5 then the coordinates of B"C"D" are B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0) .
If the point (x,y) is reflected across the x axis , then the reflected points are (x,-y) .
the vertices of the triangle BCD are : B(-8,3), C(-4, 6), and D(2, 0) ;
So , the reflected vertices are : B'(-8,-3) , C'(-4,-6) and D'(2,0) ;
if the point (x,y) is dilated by a scale factor of "k" , then the dilated vertices are written as : (kx , ky) .
the dilation factors is = 0.5 ;
So , the vertices B'(-8,-3) , C'(-4,-6) and D'(2,0) after dilation will be written as :
⇒ B''(-8×0.5 , -3×0.5) , C"(-4×0.5 , 6×0.5) and D"(2×0.5 , 0) ;
After simplifying further ,
we have ;
⇒ B''(-4 , -1.5) , C"(-2 , 3) and D"(1 , 0) ;
Therefore , the coordinates of the triangle B"C"D" are B''(-4,-1.5) , C"(-2,3) and D"(1,0) .
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Courtney has $12 to spend at the concession stand. She
wants to buy a combination of air heads, x, and popcorn, y.
An air head costs $. 25 and popcorn costs $2. Which
inequality represents this situation?
The inequality representing Courtney's situation to buy air heads and popcorn is 0.25x + 2y ≤ 12.
Based on the situation of Courtney, we can conclude that she must get the combination in such quantity of each that it's total is less than or equal to 12. Creating the expression according to this statement.
Number of air heads × cost of one air head + number of popcorn × cost of one popcorn ≤ 12
Keep the values in formula to find the inequality
x×0.25 + y×2 ≤ 12
Performing multiplication between the constant and variable
0.25x + 2y ≤ 12
Thus, inequality representing this situation is 0.25x + 2y ≤ 12.
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The surface area of a cylinder is 28π m². The distance around the base of the cylinder is 7π meters and the diameter of a base of the cylinder is 4 meters.
What is the height of the cylinder?
Enter your answer, as a simplified fraction, in the box.
m
Answer:
5
Step-by-step explanation:
diameter = 4 so radius =2
open up the cylinder so its top & bottom circle's circumference = 2πr =4π
top & bottom circle's area = πr² = 4π each, 8π for both
total surface = 28π
so lateral surface = 28π - 8π = 20π
so 20π = 4π* height
so height is 5
Deshaun must choose a number between 49 and 95 that is a multiple of 4, 7 , and 14 . Write all the numbers that he could choose. If there is more than one number, separate them with commas.
Answer: To find the numbers that Deshaun could choose, we need to find the least common multiple (LCM) of 4, 7, and 14. The LCM is the smallest number that is a multiple of all the given numbers.
We can find the LCM using the prime factorization method:
4 = 2^2
7 = 7
14 = 2 * 7
The least common multiple of 4, 7, and 14 is 2^2 * 7 = 28
So, the numbers Deshaun could choose are multiples of 28, which means they must be in the form of 28n, where n is a positive integer.
The numbers between 49 and 95 that are multiples of 28 are: 56, 84
So the numbers that Deshaun could choose are 56, 84.
Step-by-step explanation:
suppose a survey of women in the united states found that more than % are the primary investor in their household. which part of the survey represents the descriptive branch of statistics? make an inference based on the results of the survey.
A. 549 women were surveyed B. There is an association between U.S. women and being the primary investor in their household C. There is an association between the 549 women and being the primary investor in their household. D. 62% of women in the sample are the primary investor in their household.
D. 62% of women in the sample are the primary investor in their household.Inference: Women in the United States are likely to be the primary investors in their households.
The answer to this question is D. 62% of women in the sample are the primary investor in their household. This is an example of the descriptive branch of statistics because it summarizes the data collected in the survey. The inference based on the results of the survey is that women in the United States are likely to be the primary investors in their households.
62% of women in the sample are the primary investor in their household.
Inference: Women in the United States are likely to be the primary investors in their households.
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If the trend continued, about how many cds were sold in 2019?
If the trend continued, the number of CDs that were sold in 2019 is approximately equal to: D. 2,000.
How to determine the line of best fit?In order to write a linear function that models the data point contained in the table and determine the slope, we would have to use the point-slope form to determine the line of best fit based on the data points provided on the scatter plot (see attachment).
Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
y represents the number of CDs.x represents the number of years.m represents the slope.y - 800 = (700 - 800)/(2005 - 2002)(x - 2002)
y = 33.33(x - 2002) + 800
y = 33.33x - 65,266
When x = 2019, the number of CDs sold is given by:
y = 33.33(2019) - 65,266
y = 2,027 ≈ 2,000 million CDs.
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Complete Question:
The scatter plot shows a number of CD's (in millions) that were sold from 1999 to 2005. If the trend continued, about how many CDs were sold in 2019?
A. 3000
B. 8500
C.3500
D. 2,000
A kettle holds
4
44 liters of magic potion. There are
11
1111 liters of potion.
About how many kettles can we fill with magic potion?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Between
0
00 and
1
11 kettles
(Choice B)
B
Between
1
11 and
2
22 kettles
(Choice C, Checked)
C
Between
2
22 and
3
33 kettles
Which equation tells us exactly how many kettles we can fill?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
11
÷
4
=
4
11
11÷4=
11
4
11, divided by, 4, equals, start fraction, 4, divided by, 11, end fraction
(Choice B)
B
4
÷
11
=
4
11
4÷11=
11
4
4, divided by, 11, equals, start fraction, 4, divided by, 11, end fraction
(Choice C)
C
11
÷
4
=
11
4
11÷4=
4
11
The correct option regarding the number of kettles that can be filled with the potion is given as follows:
C. Between 2 and 3.
How to obtain the number of kettles?The number of kettles is obtained applying the proportions in this problem, dividing the total number of litters by the number of liters of each kettle.
The parameters for this problem are given as follows:
Total of 11 liters.Capacity of 4 liters per kettle.Hence the number of kettles is obtained as follows:
11/4 = 2.75.
Meaning that the correct option is given by option C.
Missing InformationA kettle holds 4 liters of magic potion. There are 11 liters of potion.
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Please help with the question below
The area of the given image design is; 15 in²
How to find the area of a triangle?The formula to find the area of a triangle is;
Area = ¹/₂(base * height)
Let us divide the image into two triangles and as such;
Area of biggest triangle = ¹/₂(14 * 15)
= 85 in²
We will now deduct the rectangle that was removed by finding its' area to get;
Area of rectangle = length * width
= 10 * 7 = 70 in²
Thus;
Area of image = 85 - 70
Area of image = 15 in²
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Choose all the multiplication sentences that have 5/6 as the missing part
PLEASE ANSWER ASP
If the value be 5/6 then the equation be [tex]$x \times \frac{2}{3}=\frac{5}{9}$$[/tex].
What is meant by fraction?A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
A fraction is a piece of a whole number and a means to divide a number into pieces that are each equal. The numerator, also known as the number of equal parts being counted, is expressed as being greater than the denominator, also known as the number of parts in the entire.
Let the value be 5/6 then
simplifying the equation as
[tex]$x \times \frac{2}{3}=\frac{5}{9}$$[/tex]
Multiply both sides by 3
[tex]$3 x \frac{2}{3}=\frac{5 \cdot 3}{9}$$[/tex]
Simplifying the above equation, we get
2x = 5/3
Divide both sides by 2, we get
[tex]$\frac{2 x}{2}=\frac{\frac{5}{3}}{2}$$[/tex]
x = 5/6
Therefore, the correct answer is option a.
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Of the 6 vacant positions to be filled at a company, 3 must be given to men, 2 to woren and can be ether gender. In how many ways can these different positions be filled given that 5 men and o women have applied for these positions?
There are a total of 6 vacant positions to be filled at a company, with 3 of those positions being given to men, 2 to women and 1 being either gender.
How many ways can these different positions be filled given that 5 men and o women have applied for these positions?Given that there are 5 men and 0 women who have applied for these positions, there are a total of 150 ways to fill the 6 positions.Firstly, the 3 positions that must be given to men can be filled in a total of 5 ways, as there are 5 men applying for those positions.Secondly, the 2 positions that must be given to women cannot be filled in this instance, as there are no women applicants for these roles.Finally, the position that must be given to either gender can be filled by any of the 5 men who have applied. This can be done in a total of 5 ways.Combining these three scenarios, the total number of ways to fill the 6 positions is 5 x 5 x 1, or 5 x 5, which is equal to 150.In conclusion, there are a total of 150 different ways to fill the 6 vacant positions at the company, given that 5 men and 0 women have applied for the positions.To learn more about the gender-neutral position refer to:
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Let A1, A2, A3, and A4, be events from a common sample space. these events are pairwise mitially exclusive, with the exception tha A1 and A2 occur simultaneously with a probability of 0.1. if events A1, A2, and A3 each occur with probability 0.3, what is the largest possible value for the probability of A4?
this is my work:
P(A1) = P(A2) = P(A3) = 0.3
sum of the probabilities of all events must be equal to 1, so we have:
P(A1) + P(A2) + P(A3) + P(A4) = 1
the probability of both A1 and A2 is 0.1
P(A1 and A2) = 0.1
the probability of the intersection of two events is given by P(AnB) = P(A) + P(B) - P(AuB)
So, we can write:
P(A1) + P(A2) - P(A1 and A2) = 0.3 + 0.3 - 0.1 = 0.5
we have:
P(A1) + P(A2) + P(A3) + P(A4) = 1
0.3 + 0.3 + 0.3 + P(A4) = 1
P(A4) = 1 - 0.9 = 0.1
The largest possible value for the probability of A4 is 0.3.
If events A1, A2, A3, and A4 are pairwise mutually exclusive with the exception that A1 and A2 occur simultaneously, then the probability of A1 and A2 occurring together is 0.1. This means that the probability of A1 occurring separately is 0.3 - 0.1 = 0.2, and the same is true for A2.
Since A1, A2, A3, and A4 are pairwise mutually exclusive, the probability that they all occur together is 0. Therefore, the sum of their individual probabilities is also 0. Therefore, the probability of A4 is the remaining probability after accounting for the probability of A1, A2, and A3. The largest possible value for the probability of A4 is the total probability minus the probability of A1, A2, and A3.
So, the largest possible value for the probability of A4 would be:
1 - (0.2 + 0.2 + 0.3) = 1 - 0.7 = 0.3
Therefore, the largest possible value for the probability of A4 is 0.3.