if lines ax-2y=5 and 2x-by =8 intersect at point (11,3), find the value of a and b
​

The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2

Experimental probability of 3

From the table of values, we have

n(3) = 1

Total = 12

So, we have

P(3) = 1/12

Experimental probability of 6

From the table of values, we have

n(6) = 3

Total = 12

So, we have

P(6) = 3/12

P(6) = 1/4

Experimental probability of less than 4

From the table of values, we have

n(Less than 4) = 6

Total = 12

So, we have

P(Less than 4) = 6/12

P(Less than 4) = 1/2

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Answer:

x= 7

Step-by-step explanation:

Answer:

P=40 and y was decreased by 40%

Step-by-step explanation:

Let's set up an equation as follows. In this case, we will set y will be equivalent to 1, as the number can be any value for this equation in the other fraction as the original number. Let us then represent the new number, 0.6y, or 0.6*1 which will be equivalent to 0.6 itself, and we will set that equal to 100-p as p will be the amount of percent it was decreased by. Here is the equation as follows:

We can use a method of solving fractions that is known as the Cross-multiplication property, which demonstrated in the image attached below this answer. Using this property, we can determine and simplify the equation to as follows:

[tex]1*(100-p)=0.6(100)[/tex], which can be simplified to [tex]100-p=60[/tex], and then solving the equation gives us the answer:

[tex]p=40[/tex]

P=40

The correct answer is: No, because for each input there is not exactly one output.

In mathematics, a function is a relation between two sets, where each element in the first set (called the domain) is associated with exactly one element in the second set (called the codomain or range). A function assigns a unique output value (dependent variable) to each input value (independent variable) from the domain.

The given relation does not represent a function because for some inputs there are multiple outputs, violating the "one-to-one" or "vertical line test" rule.

The correct answer is: No, because for each input there is not exactly one output.

In this relation, we can see that x = 1 has two different outputs, y = 5 and y = -1/2. Therefore, the relation does not meet the criteria of a function as it violates the requirement of having exactly one output for each input.

Therefore, The correct answer is: No, because for each input there is not exactly one output.

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According to the infographic, women constitute approximately 15-19% of members of Congress, less than 15% of state legislators, and 25-50% of statewide executives and mayors in the top 100 cities.

According to the information provided in the infographic, the following options apply:

Women constitute approximately 25-50% of statewide executives and mayors in the top 100 cities.

Women constitute approximately 15-19% of members of Congress.

Women constitute less than 15% of state legislators.

Therefore, the correct options are:

15-19%

Less than 15%

25-50%

The infographic presents data on the percentage of women overall in elected office and the share of Latinas in elected office. The data indicates that women constitute less than 15% of state legislators, approximately 15-19% of members of Congress, and 25-50% of statewide executives and mayors in the top 100 cities. This suggests that women are underrepresented in elected office at all levels of government, with the exception of statewide executives and mayors in the top 100 cities. The infographic underscores the need for greater gender diversity in elected office, and the importance of supporting and encouraging women to run for political office at all levels of government.

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Complete question:

The infographic shows percentages of women overall in elected office as well as the share of Latinas in elected office. Women constitute approximately what percentage of members of Congress, statewide executives, state legislators, and mayors in the top 100 cities? Check all that apply.

19-25%

Less than 15%

15-19%

25-50%

The length of the pole is approximately 412.7 feet.

What is the tangent function?

The tangent function is a mathematical function that relates the ratio of the length of the side opposite to an acute angle in a right triangle to the length of the adjacent side. It is defined as the ratio of the sine of the angle to the cosine of the angle.

We can solve this problem using trigonometry. Let's call the length of the pole "x". We can then use the tangent function to relate the angle that the pole makes with the vertical to the length of the shadow cast by the pole.

The tangent of the angle between the pole and the vertical is equal to the opposite side (length of the shadow) divided by the adjacent side (length of the pole).

tan(7°) = opposite / adjacent

tan(7°) = 49 / x

We can solve for x by multiplying both sides by x and then dividing both sides by tan(7°):

x = 49 / tan(7°)

Now we know the length of the pole is:

x = 49 / tan(7°) = 412.7 ft (rounded to one decimal place)

Therefore, the length of the pole is approximately 412.7 feet.

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The quarterly dividend fοr οne share οf Bοοtle is $12.52.

A divisiοn is οne οf the fundamental mathematical οperatiοns that divides a larger number intο smaller grοups with the same number οf cοmpοnents. Hοw many tοtal grοups will be established, fοr instance, if 20 students need tο be separated intο grοups οf five fοr a spοrting event?

The divisiοn οperatiοn makes it simple tο tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the οutcοme. There will therefοre be 4 grοups with 5 students each. By multiplying 4 by 5 and receiving the result 20, yοu may cοnfirm this value.

Tο find the quarterly dividend fοr οne share οf Bοοtle, we can divide the tοtal quarterly dividend payment by the number οf shares Leslie οwns:

Quarterly dividend per share = Tοtal quarterly dividend payment / Number οf shares

Quarterly dividend per share = $1,490 / 119

Quarterly dividend per share = $12.52 (rοunded tο twο decimal places)

Therefore, the quarterly dividend for one share of Bootle is $12.52.

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For the the inequality –3(2x – 5) < 5(2 – x) the correct options are: x < 5, –6x + 15 < 10 – 5x

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

x < 5 (obtained by simplifying the inequality and solving for x)

–6x + 15 < 10 – 5x (obtained by distributing the terms and simplifying the inequality)

Therefore, the correct options are:

x < 5

–6x + 15 < 10 – 5x

The options that describe number lines are not applicable to this inequality since they represent a single value, whereas an inequality represents a range of values that satisfy the inequality.

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Answer:

[tex]\boxed{\frac{1}{12}}[/tex]

Step-by-step explanation:

The multiplication of fractions satisfies the following rule:

[tex]\displaystyle{\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]

applied to our exercise, it looks like this

[tex]\displaystyle{\frac{5}{14}\times\frac{7}{30}=\frac{5\times 7}{14\times 30}[/tex]

also, we can "decompose" denominator numbers as follows:

[tex]14=7*2[/tex]

[tex]30=5*6[/tex]

Therefore:

[tex]\displaystyle\frac{\not{5}\times \not{7}}{2 \times \not{7}\times \not{5}\times 6}= \frac{1}{12}[/tex]

In this way, only one multiplication was necessary.

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer:41,328

Step-by-step explanation:

18+7+11=36 36%

100-36=64 64%

25,200 x 164%=41,328

Answer: r = 45°

Step-by-step explanation:

All triangles angles add up to 180 degrees.

With that said we can use the given information and create an equation to solve.

55° + 80° + r = 180°

Lets solve for r.

55° + 80° + r = 180°

first lets combine like terms.

135° + r = 180°

now lets subtract 143° from both sides

135° + r = 180°

-135°       -135°

r = 45°

Total area of shaded region in trapezoid is 54.4in²

A trapezoid is a four-sided, quadrilateral shape with two parallel sides, which are called the bases, and two non-parallel sides, which are called the legs.

The formula for the area of a trapezoid is:

Area = (1/2) × (sum of the bases) × (height)

The Shaded region in trapezoid form right angled triangle.

Area of 1st shaded region=area of right triangle

=1/2×b×h

=1/2×6.8×7.4

=25.16in²

Area of 2nd shaded region=area of right triangle

=1/2×b×h

=1/2×6.8×8.6

=29.24in²

Hence, total area of shaded region in trapezoid is 54.4in²

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To graph g(x), we must replace x with x + 1 in the function f(x) = 2x - 5: g(x) = f(x + 1) = 2(x + 1) - 5 = 2x - 3 (a) To display the g of x line that passes through the coordinates 0, -4, and 2, 0, we replace x = 0 and x = 2 in the equation g(x) = 2x - 3:

g(0) = 2(0) - 3 = -3

g(2) = 2(2) - 3 = 1

Hence the line's points are (0, -3) and (2, 1):

yaml Copy code | 5 |- * (2,1) | 4 |- | 3 |- * (0,-3) | 2 |- | 1 |- | 0 |—————————— 0 1 2 3 4 5\s(b) (b) To display the g of x line that passes through points 0, -3, 4, 5, we replace x = 0 and x = 4 in the equation g(x) = 2x. - 3:

g(0) = 2(0) - 3 = -3

g(4) = 2(4) - 3 = 5

Hence the line's points are (0, -3) and (4, 5):

Copy code in yaml | 5 |- * (4,5)

|\s4 |-\s |\s3 |- * (0,-3)\s |\s2 |-\s |\s1 |-\s |\s0 |

————————-\s 0 1 2 3 4 5\s(c) (c) To display the line labeled g of x that goes through points -5, -3, and 0, 7, we use the equation g(x) = 2x - 3:

g(-5) = 2(-5) (-5) - 3 = -13\sg(0) = 2(0) - 3 = -3

Thus the line points are (-5, -13) and (0, -3):

| 5 |- | 4 |- | 3 |- | 2 |- | 1 |- | 0 |- * (0,-3) | -1 |- (-5,-13)

\ \s ——————-\s -5 -4 -3 -2 -1 0\s(d) To draw the g of x line that passes between points 0, -7, and 5, 3, In the equation g(x) = 2x - 3 we substitute x = 0 and x = 5:

g(0) = 2(0) - 3 = -3

g(5) = 2(5) (5) - 3 = 7

Hence the line's points are (0, -3) and (5, 7):

| 7 |- * yaml Copy code (5,7)

|\s6 |-\s |\s5 |- \s | * (0,-3) (0,-3)

4 |-\s |\s3 |-\s |\s2 |-\s |\s1 |-\s |\s0 |

————————-\s 0 1 2 3 4 5.

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Answer: they are adding 30 each time

Step-by-step explanation:

in 320 to 350, it adds 30 because 20 plus 30 equals 50 then you can add 300 which is 350 then 350 plus 30 is 380 which is also the next number which means you are adding 30 each time and for the first box you subtract 30 from 350 which is 320 and for the last box you add 30 which is 380 + 30 which is 410 so that is your answer.

There are 2,139,792,767,488,000 ways to assign scores to the problems if the sum of the scores is 100 and each question is worth at least 5 points.

To solve this problem, we will use the concept of combinations with repetition.

First, let's subtract 5 points from each question, since each question is worth at least 5 points. Now, we need to distribute the remaining 50 points (100 - 10*5) among the 10 questions.

Imagine that we have 50 identical balls (points) to distribute among 10 distinct boxes (questions). To do this, we can use a technique called "stars and bars". We need to place 9 dividers (bars) between the 50 balls (stars) to divide them among the 10 questions.

We will have a total of 59 positions (50 stars + 9 bars). We need to choose 9 of these positions for the bars, and the stars will fill the remaining positions.

The number of ways to do this is given by the combination formula:

C(n, k) = n! / (k! * (n - k)!)

In our case, n = 59 (total positions) and k = 9 (dividers). So, we need to calculate C(59, 9):

C(59, 9) = 59! / (9! * (59 - 9)!)
C(59, 9) = 59! / (9! * 50!)
C(59, 9) = 2,139,792,767,488,000

Therefore, there are 2,139,792,767,488,000 ways to assign scores to the problems if the sum of the scores is 100 and each question is worth at least 5 points.

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A scatter plot would be more appropriate to construct for the data, given the context of the problem. The reason is that the marine biologist is interested in seeing the relationship between a manatee's weight and food consumption.

A scatter plot is a type of graph that displays the relationship between two variables, where each variable is plotted along one axis, and a point is placed at the intersection of the two values. In this case, weight would be plotted along one axis and food consumption along the other axis.

A scatter plot allows the researcher to see if there is a relationship between the two variables, and if so, what type of relationship it is (positive, negative, or no correlation). Therefore, a scatter plot is the most appropriate way to display the relationship between a manatee's weight and food consumption.

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a) The probability that more than 180 customers will take your free sample is approximately 0.9999.

b) The probability that fewer than 200 customers will take your free sample is approximately 0.0119.

c) Therefore, the probability that a customer will take a free sample and buy the product is 0.21.

d) The probability that between 60 and 80 customers will take the free sample and buy the product is approximately 0.043

a) Let X be the number of customers who take the free sample.

We know that X follows a binomial distribution with n = 327 and p = 0.58. To find the probability that more than 180 will take free sample, we need to find P(X > 180).

Using a binomial calculator or software, we get:

P(X > 180) = 1 - P(X ≤ 180) = 1 - binomial distribution (180, 327, 0.58, TRUE) ≈ 0.9999

Therefore, the probability that more than 180 customers will take your free sample is approximately 0.9999.

b) To find the probability that fewer than 200 will take your free sample, we need to find P(X < 200).

Using a binomial calculator or software, we get:.

P(X < 200) = binomial distribution (199, 327, 0.58, TRUE) ≈ 0.0119

Therefore, the probability that fewer than 200 customers will take your free sample is approximately 0.0119.

c) Let A be the event that a customer takes a free sample, and B be the event that the customer buys the product.

We are given P(B|A) = 0.35 and P(A) = 0.60.

Using the multiplication rule for dependent events, we get:

P(A ∩ B) = P(B|A) × P(A) = 0.35 × 0.60 = 0.21

Therefore, the probability that a customer will take a free sample and buy the product is 0.21.

d) Let Y be the number of customers who take the free sample and buy the product. We know that Y follows a binomial distribution with n = 327 and p = 0.21 (from part c). .

To find the probability that between 60 and 80 customers will take the free sample and buy the product, we need to find P(60 ≤ Y ≤ 80).

Using a binomial calculator or software, we get:

P(60 ≤ Y ≤ 80) = binomial distribution (80, 327, 0.21, TRUE) - binomial distribution (59, 327, 0.21, TRUE) ≈ 0.0434

Therefore, the probability that between 60 and 80 customers will take the free sample and buy the product is approximately 0.0434.

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Question: Do You Take The Free Samples Offered In Supermarkets? About 58 % Of All Customers Will Take Free Samples.

Furthermore, Of Those Who Take The Free Samples, About 37% Will Buy What They Have Sampled. Suppose You Set Up A Counter In A Supermarket Offering Free Samples Of A New Product. The Day You Were Offering Free Samples, 327Customers Passed By Your

Do you take the free samples offered in supermarkets? About 58% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 312 customers passed by your counter.(round your answers to four decimal places.)

a.) What is the probability that more than 180 will take your free sample?

b.) What is the probability that fewer than 200 will take your free sample?

c.) What is the probabilty that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample)=0.35, while P(sample)=0.60

d.) What is the probability that between 60 and 80 customers will take the free sample and buy the product? HInt: Use the probability of success calculated in part(c).

Answer:

Step-by-step explanation:

f=133

a=93

c=140

The function g(-7) * f(-7) is approximately equal to *-8056.5*.

What is a function?

A function is a mathematical rule that assigns a unique output value to each input value from a given set. It represents a relationship between two sets of numbers in which each input has exactly one output. A function can be expressed symbolically, graphically, or verbally and is used to model real-world phenomena, solve equations, and make predictions in various fields of study.

According to the given information

To find g(-7) and f(-7), we need to substitute -7 for y in the function g(y) = -2ᵇ - 4b + 13 and x in the function f(x) = -2x² - 4x + 13.

g(-7) = -2⁻⁷ - 4⁻⁷ + 13

Simplifying this expression gives:

g(-7) = -1/128 + 28 + 13

g(-7) = 141 - 1/128

Therefore, g(-7) is approximately equal to 140.9922 .

f(-7) = -2(-7)² - 4(-7) + 13

Simplifying this expression gives:

f(-7) = -98 + 28 + 13

f(-7) = -57

Therefore, f(-7) is equal to -57.

So, g(-7) * f(-7) is approximately equal to -8056.5.

The correct question is

g(y ) = − 2ᵇ − 4b + 13 and f(x)=−2x² −4x+13, find g( − 7 ) f(−7)

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Step-by-step explanation:

Area of a triangle = 1/2 * base * height

 For this triangle   base =  9 m   height =  8 m

1/2 ( 9 ) ( 8) = 36 m^2

The aggregate functions that can be used with grouped data include:
COUNT(), SUM(), AVG(),  MIN().,MAX().

1. COUNT(): This function counts the number of rows in a group.
2. SUM(): This function adds up the values of a specified column within a group.
3. AVG(): This function calculates the average of a specified column within a group.
4. MIN(): This function finds the minimum value of a specified column within a group.
5. MAX(): This function finds the maximum value of a specified column within a group.
These functions can be used in combination with the GROUP BY clause in SQL to perform calculations on grouped data.

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Answer:

$30

Step-by-step explanation:

6x3=18

        +

4x3=12

=30

The correct equation for the hanger balance is:= w = 2

How to balance equations?

The hanger balance equation is typically used in physics experiments to determine the weight of an object by comparing it to known weights on the other side of a balance. The equation is based on the principle of equilibrium, which states that the sum of the forces acting on an object must be zero for it to remain stationary.

The correct equation for the hanger balance is:

w = 2

This equation simply states that the weight of the object being measured (represented by "w") is equal to a known weight of 2 units. This indicates that the object being measured has a weight of 2 units.

The other equations provided, such as "6 = w + 2" and "6 = w - 2", do not accurately represent the hanger balance equation because they do not take into account the known weight on the other side of the balance. In order to determine the weight of an object using a hanger balance, it is necessary to have a known weight on the other side of the balance to compare it to.

In summary, the correct equation for the hanger balance is w = 2, which represents the weight of the object being measured as 2 units.

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If the sample size is large and the probability of success is not too close to 0 or 1, using the normal distribution to approximate the binomial probability will generally give a more accurate answer than using the binomial tables. However, if the sample size is small or the probability of success is very close to 0 or 1, using the binomial tables may be more accurate.

If the sample size is large (typically, n ≥ 30) and suppose that the probability of success (p) is not too close to 0 or 1, then we can use the normal distribution. As it gives more approximate value to the binomial probability which will generally give a more accurate answer than using the binomial tables.

This is because the normal distribution provides a more precise approximation of the binomial distribution as the sample size increases.

However, if the the probability of success is very close to 0 or 1 or sample size is small then using the binomial tables to calculate the probability directly may be more accurate. In general, it's important to check the conditions for using the normal approximation before using it and to use good judgment in deciding which method is more appropriate for a given problem.

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Answer:

True

Step-by-step explanation:

Since C has to add up to 180 and we already have 150 we can assume that that other angle is 30. The sum of angles in a triangle always has to equal 180. 120+30=150 meaning B also equals 30. B+A=150 therefore making it true.

The data set as there are some large residuals, such as 4 and -7, indicating that the actual fares are not well-predicted by the linear equation.

In statistics, residuals refer to the differences between the observed values of a variable and the values predicted by a statistical model. They are calculated by subtracting the predicted values from the observed values.

To calculate the residuals, we first need to find the predicted fares for each distance using the equation y = 0.1 x + 12;

Miles        Fares $          Predicted Fares $              Residuals $

50               14                          17                                     -3

40               16                          16                                     0

60               16                          18                                     -2

30               14                          15                                     -1

60               22                         18                                     4

70               12                          19                                     -7

80               24                         20                                     4

To find the residuals, we subtract the predicted fare from the actual fare. If the predicted fare is greater than the actual fare, the residual is negative, and if the predicted fare is less than the actual fare, the residual is positive. We can see that a linear model may not be appropriate for the data set as there are some large residuals, such as 4 and -7, indicating that the actual fares are not well-predicted by the linear equation.

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10 to the 9th power is 10 times 10 to the 8th power.

Answer:

To solve the equation |x+3|=9, we need to split it into two separate equations, one for the positive value and one for the negative value of the absolute value:

For the positive value:

x+3=9

Solving for x, we get x=6

For the negative value:

-(x+3)=9

Multiplying both sides by -1, we get:

x+3=-9

Solving for x, we get x=-12

Therefore, the solutions to the equation |x+3|=9 are x=6 and x=-12.

Hope This Helps!

After answering the presented question, we can conclude that As a equation result, Emily's automobile will be valued roughly $19,105.25 after 8 years.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the phrase "[tex]2x + 3[/tex]" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "[tex]x2 + 2x - 3 = 0[/tex]." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Emily's car will be worth 100% - 18% = 82% of its original value after one year, or 0.82 times its initial value.

After two years, the car is worth 0.82 times its initial value, or 0.822% of its original value.

Similarly, the car will be worth 0.828% of its initial value after 8 years.

Hence, after 8 years, Emily's automobile will be worth:

In 8 years, the value is $55,000 x 0.82.

After 8 years, the value is $19,105.25. (rounded to the nearest cent)

As a result, Emily's automobile will be valued roughly $19,105.25 after 8 years.

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The cosine of angle X is 0.75 of triangle WXV.

In a right-angled triangle, the cosine of an angle is equal to the adjacent side divided by the hypotenuse. Therefore, to find cos(X) in triangle XWV, we need to find the adjacent and hypotenuse sides that correspond to angle X.

We know that WV = 72, which is the length of the side opposite the right angle. To find the length of the hypotenuse XV, we can use the Pythagorean theorem: [tex]XV^{2}[/tex] = [tex]WV^{2}[/tex] + [tex]WX^{2}[/tex], where WX is the length of the side adjacent to angle X.

Solving for WX, we get:

[tex]WX^{2}[/tex] = [tex]XV^{2}[/tex] - [tex]WV^{2}[/tex]

[tex]WX^{2}[/tex]= [tex]90^{2}[/tex] - [tex]72^{2}[/tex]

[tex]WX^{2}[/tex] = 2916

WX = 54

Now we can find cos(X):

cos(X) = adjacent/hypotenuse

cos(X) = WX/WV

cos(X) = 54/72

cos(X) = 0.75

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