A ladder leans against the wall of a building. The ladder measures 47 inches and forms an angle of 51 degrees with the ground. How far from the ground, in inches, is the top of the ladder? How far from the wall, in inches, is the base of the ladder? Round to two decimal places as needed.

Ground to top in inches:
Base to wall in inches:

y= 2x+1 y = -3x-4

2x-y+1 = 0. 3x+y+4 = 0

a1 + b1 + c1 = 0 a2+ b2 + c2 = 0

x,y = b1c2- b2c1/ a1b2-a2b1 , a2c1-a1c2/a1b2-a2b1

x,y = -1×4 - 1×1 /2×1 - 3×-1 , 3×1-2×4 / 2×1 -3×-1

x,y = -5/-1 , -5/2

x,y= 5, 5/2

The angles of the triangle are A=146.8°,B=22.3° and C=10.9°

The cosine rule states that for any triangle with sides of length a, b, and c and angles A, B, and C (with the side opposite each angle labeled with the corresponding lowercase letter), the following equation holds:

a² = b² + c²- 2bc cos(A)

b² = a² + c² - 2ac cos(B)

c² = a² + b² - 2ab cos(C)

Using the cosine rule,

a²=b²+c²-2bcCosA

2bcCosA=b²+c²-a²

A=cos⁻¹(b²+c²-a²/2bc)

A=cos⁻¹(18²+9²-26²/2×18×9)

A=cos⁻¹(-0.83642)=146.8°

Also from b²=a²+c²-2acCosB

B=cos⁻¹(a²+c²-b²/2ac)

B=cos⁻¹(26²+9²-18²/2×26×9)

B=cos⁻¹(0.925)=22.3°

The total angle of the triangle is 180°

A+B+C=180°

C=180°-146.8°+22.3°=10.9°

Thus, the angles of the triangle are A=146.8°,B=22.3° and C=10.9°

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The compelte question is;

Image is attached below

Answer:

a. lines intersecting at a single point

b. one solution

Step-by-step explanation:

a. The equations can be rewritten as:

y = -5x+23 and y = -1/6x+1

Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.

Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.

b. The equation will have one solution as below.

The equations can be rewritten as:

5x+y=23

5x+30y=30

Subtracting both equation will result in,

29y=7

=> y=7/29

Hence x= 660/29

a sample size of at least 73 is needed to estimate the mean of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas with 98% confidence and an error of 0.25 mpg.

How to solve questions?

A. To estimate the standard deviation of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas, we can use the empirical rule for normal distribution. The empirical rule states that for a normally distributed random variable, about 68% of the values fall within one standard deviation of the mean, about 95% of the values fall within two standard deviations of the mean, and about 99.7% of the values fall within three standard deviations of the mean.

The range of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas is 21 mpg to 26 mpg. We can estimate the mean by taking the average of the range:

Mean = (21 + 26) / 2 = 23.5 mpg

We can estimate the standard deviation by using the empirical rule. Since we know that about 68% of the values fall within one standard deviation of the mean, we can estimate the standard deviation as half the range that covers about 68% of the values:

Standard Deviation ≈ (26 - 21) / 4 = 1.25 mpg

B. To find the sample size needed to estimate the mean with 98% confidence and an error of 0.25 mpg, we can use the formula for the sample size:

n = (zα/2 * σ / E)²

where:

n is the sample size

zα/2 is the z-score corresponding to the desired confidence level, which is 2.33 for 98% confidence (from the standard normal distribution table)

σ is the population standard deviation, which we estimated in part A to be 1.25 mpg

E is the desired margin of error, which is 0.25 mpg

Substituting the values, we get:

n = (2.33 * 1.25 / 0.25)²

n = 72.96

Since we cannot have a fraction of a person in our sample, we round up to the next integer and get:

n = 73

Therefore, a sample size of at least 73 is needed to estimate the mean of the combined City/Highway fuel economy of the 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas with 98% confidence and an error of 0.25 mpg.

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The equation of the given quadratic equation through which it satisfied the relation are y =

What about quadratic equation?

In mathematics, a quadratic equation is a polynomial equation of the second degree, meaning it has the highest power of the variable x as 2. The standard form of a quadratic equation is:

ax^2 + bx + c = 0

where a, b, and c are constants, and x is the variable. The coefficient a cannot be zero, or else the equation would reduce to a linear equation.

The quadratic equation can be solved using the quadratic formula:

x = [tex]( b + \sqrt{(b^2 - 4ac)) / 2a[/tex]

where the ± sign means that there are two possible solutions for x, one obtained by adding the square root term and the other obtained by subtracting it.

The solutions of a quadratic equation may be real or complex numbers, depending on the discriminant (b^2 - 4ac) of the equation. If the discriminant is positive, the equation has two real solutions. If the discriminant is zero, the equation has one real solution (which is a double root). And if the discriminant is negative, the equation has two complex solutions (which are conjugates of each other).

Quadratic equations are used in various branches of mathematics and physics to model a wide range of phenomena, such as motion, acceleration, gravity, and electromagnetic fields.

According to the given information:

The normal form of the equation are y = [tex]a(x-h)^{2} + k[/tex]

(h,k) = ( -1,2)

When we put the value in the equation we have that,

y = [tex]a(x+1)^{2} + 2[/tex]

As, we see it intercept at (-2,0)

y = 0 and x = -2

0 = [tex]a(-2+1)^{2} + 2[/tex]

a = -2

So y  = [tex]-2(x+1)^{2} + 2[/tex]

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P(X ≤ 2.39)= 0.9967, P(X ≥ -2.39) = 0.3808, P(|X| ≥ 2.39)  = 0.0388 ,P(|X + 3| ≥ 2.39) can be rewritten as P(X + 3 ≤ -2.39) + P(X + 3 ≥ 2.39)=  0.0388,  P(X < 5) = 1 AND P(|X| < 5) =  0.34 with X is a normal random variable .

To solve the given problems, we need to standardize the normal random variable X using the formula Z = (X - μ)/σ, where μ is the mean and σ is the standard deviation.

a) P(X ≤ 2.39) = P(Z ≤ (2.39 - (-3))/2) = P(Z ≤ 2.695) = 0.9967

b) P(X ≥ -2.39) = P(Z ≥ (-2.39 - (-3))/2) = P(Z ≥ 0.305) = 0.3808

c) P(|X| ≥ 2.39) = P(X ≤ -2.39) + P(X ≥ 2.39) = P(Z ≤ (-2.39 - (-3))/2) + P(Z ≥ (2.39 - (-3))/2) = P(Z ≤ -1.805) + P(Z ≥ 2.695) = 0.0354 + 0.0034 = 0.0388

d) P(|X + 3| ≥ 2.39) can be rewritten as P(X + 3 ≤ -2.39) + P(X + 3 ≥ 2.39)

= P(Z ≤ (-2.39 - (-3))/2) + P(Z ≥ (2.39 - (-3))/2) = P(Z ≤ -1.805) + P(Z ≥ 2.695) = 0.0354 + 0.0034 = 0.0388

e) P(X < 5) = P(Z < (5 - (-3))/2) = P(Z < 4) = 1

f) P(|X| < 5) = P(-5 < X < 5) = P((-5 - (-3))/2 < Z < (5 - (-3))/2) = P(-4 < Z < 4) = 0.9987

g) Let the value that X exceeds with a probability of 0.33 be x. Then, we need to find the value of x such that P(X > x) = 0.33. Using the standard normal distribution table, we can find that the z-score for the 0.33 probability is 0.44. So, we can solve for x as follows:

0.33 = P(X > x) = P(Z > (x - (-3))/2) = P(Z > (x + 3)/2)

0.44 = 1 - P(Z ≤ (x + 3)/2)

P(Z ≤ (x + 3)/2) = 1 - 0.44 = 0.56

Using the standard normal distribution table, we can find that the z-score for the 0.56 probability is 0.17. So, we can solve for x as follows:

0.56 = P(Z ≤ (x + 3)/2) = P(Z ≤ (x + 3)/2)

0.17 = (x + 3)/2

x = 0.34

Therefore, with a probability of 0.33, variable X exceeds the value of 0.34.

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The first statement given is not a random sample because athletes leaving practice are not representative of all athletes.

A random sample is a sample in which every member of the population being studied has an equal chance of being selected. In the given statement, the sample is not random because the athletes leaving practice are not representative of all athletes, as they may have different preferences or levels of skill in their favorite sport.

Additionally, the sample is not chosen through a random selection process, but rather through a convenience sampling method, in which participants are chosen based on their availability and willingness to participate.

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You would need to buy 4 liters of stain to cover a wheelchair ramp with an area of 100 square feet.

The answer to this question depends on the dimensions of the wheelchair ramp and how much area needs to be covered with stain.

Assuming that the wheelchair ramp has an area of 100 square feet, and that the stain coverage is similar to the area covered by paint, then the amount of stain required can be estimated by using the following formula:

Amount of stain (in liters) = Area to be covered (in square feet) ÷ Coverage per liter (in square feet per liter)

If the stain coverage is 25 square feet per liter, then the amount of stain required to cover 100 square feet would be:

Amount of stain = 100 ÷ 25 = 4 liters

Therefore, you would need to buy 4 liters of stain to cover a wheelchair ramp with an area of 100 square feet.

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Answer:

The missing values to complete the diagram are:

4 → 6

2 → 5

-1 → -3

To find the missing values, we need to follow the pattern of the given arrows.

Starting with 4 and going to 6, we add 2 to get to the next number. So, starting with 2, we add 3 to get the missing value of 5.

Going from 2 to 5, we add 3 once again. So, to get from 5 to the next number, we add 3 to get 8.

To find the missing value that goes from an unknown number to -3, we need to subtract 3. Since we have already used the numbers 2 and 4, we can try a negative number. Starting with -1 and subtracting 3 gives us the missing value of -3.

Therefore, the completed diagram would look like this:

4 → 6

2 → 5

-1 → -3

Here's the completed diagram with the missing values filled in based on the pattern:

```

4 → 6

2 → 4

-1 → -3

```

The pattern seems to be that for each input value (x), the output value (y) is x + 2.

Answer:

Let's call the number of packs of red flyers Taylor gave out "r" and the number of packs of blue flyers she gave out "b". We know that each pack contains 13 red flyers and 20 blue flyers. So the total number of red flyers is 13r and the total number of blue flyers is 20b.

We also know that Taylor gave out the same number of red and blue flyers. In other words:

13r = 20b

To find the minimum number of flyers of each color, we want to find the smallest integer values of r and b that satisfy this equation. One way to do this is to find the least common multiple (LCM) of 13 and 20, and then divide by 13 and 20 to get r and b, respectively.

The prime factorization of 13 is 13, and the prime factorization of 20 is 2 x 2 x 5. The LCM of 13 and 20 is 2 x 2 x 5 x 13 = 520.

So:

13r = 20b

13r = (13/4) x (80b)

r = (13/4) x (80b) / 13

r = 20b

We can see that r = 20b is the smallest integer value that satisfies the equation. Therefore, Taylor distributed a minimum of:

13r = 13 x 20b = 260 red flyers

20b = 20 x 20b = 400 blue flyers

So Taylor distributed a minimum of 260 red flyers and 400 blue flyers.

Answer:

Answer:

Let's call the number of packs of red flyers Taylor gave out "r" and the number of packs of blue flyers she gave out "b". We know that each pack contains 13 red flyers and 20 blue flyers. So the total number of red flyers is 13r and the total number of blue flyers is 20b.

We also know that Taylor gave out the same number of red and blue flyers. In other words:

13r = 20b

To find the minimum number of flyers of each color, we want to find the smallest integer values of r and b that satisfy this equation. One way to do this is to find the least common multiple (LCM) of 13 and 20, and then divide by 13 and 20 to get r and b, respectively.

The prime factorization of 13 is 13, and the prime factorization of 20 is 2 x 2 x 5. The LCM of 13 and 20 is 2 x 2 x 5 x 13 = 520.

So:

13r = 20b

13r = (13/4) x (80b)

r = (13/4) x (80b) / 13

r = 20b

We can see that r = 20b is the smallest integer value that satisfies the equation. Therefore, Taylor distributed a minimum of:

13r = 13 x 20b = 260 red flyers

20b = 20 x 20b = 400 blue flyers

So Taylor distributed a minimum of 260 red flyers and 400 blue flyers.

Step-by-step explanation:

Answer: Slope: 6y-intercept:(0,−1)

x= 0,1

y= -1,5

Step-by-step explanation:

The value of the expression 12 ÷ {[(6 × 5) ÷ (4 + 1) ÷ 2] + 1} is 3.

We can simplify the expression using the order of operations (also known as PEMDAS)

Which dictates that we perform the operations inside the parentheses first, then any exponents or roots,

Then multiplication and division from left to right, and finally addition and subtraction from left to right.

Applying this rule, we get:

12 ÷ {[(6 × 5) ÷ (4 + 1) ÷ 2] + 1}

= 12 ÷ {[(30) ÷ (5) ÷ 2] + 1}

= 12 ÷ {[6 ÷ 2] + 1}

= 12 ÷ {3 + 1}

= 12 ÷ 4

= 3

Therefore, the value of the expression is 3.

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a. You would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000

b. The present value of $100,000 when your child is born is $100,000.

Compound interest is interest that is calculated on the initial principal and also on the accumulated interest of previous periods. This results in exponential growth of the investment over time.

a. To calculate the amount that needs to be invested each year, we can use the formula for the future value of an annuity:

[tex]FV = PMT*((1 + r)^n - 1)/r[/tex]

where FV is the future value, PMT is the annual payment, r is the interest rate per period (which is 5% in this case), and n is the number of periods (which is 18 years).

Plugging in the values, we get:

$100,000 = PMT*((1 + 0.05)^18 - 1)/0.05

Solving for PMT, we get:

PMT = $3,436.76

Therefore, you would need to invest approximately $3,436.76 each year, starting now, to reach your goal of $100,000 for your child's college education in 18 years, assuming continuous compounding at a 5% annual interest rate.

b. To calculate the present value of $100,000 when your child is born, we need to discount it back to the present time using the formula:[tex]PV = FV/(1 + r)^n[/tex]

where PV is the present value, FV is the future value ($100,000), r is the interest rate per period (which is 5%), and n is the number of periods (which is 0 since the money is being received now).

Plugging in the values, we get:

PV = $100,000/(1 + 0.05)^0

Solving for PV, we get:

PV = $100,000

Therefore, the present value of $100,000 when your child is born is $100,000.

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We can give the proof to class with certainty that 1+1=2 and not 11.

A statement that has been shown to be true based on a collection of axioms or presumptions is known as a theorem. This fact can be used to support other claims using mathematics. On the other hand, a proof is a logical argument that shows a theorem or claim to be true. In other terms, a proof is the procedure used to demonstrate a theorem's validity. A theorem may be true even in the absence of a proof, but it is not regarded as established until a proof is provided.

The basic properties of arithmetic can be used to prove 1 + 1 = 2.

The symbol "+" represents addition, thus 1 + 1 represents addition of 1 with 1 which is 2.

For 11 the 1 needs to be different place values which is not possible for 1 + 1.

Hence, we can give the proof to class with certainty that 1+1=2 and not 11.

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The bearing from A to F is 38

Volume of given two cylinders are 115.52π m³ and 350π in³

What is the formula for the volume of a cylinder?

[tex]V = π {r}^{2} h[/tex]

where r is the radius of the cylinder, h is the height of the cylinder, and π is a constant approximately equal to 3.14.

4) Given, radius =3.8 m and height = 8 m

Substituting the given values into the formula, we get:

[tex]V = π × (3.8)^2 × 8 \\ V = 115.52\pi \: cubic \: meters[/tex]

Therefore, the volume of the cylinder is approximately 361.984 cubic meters.

5) Given, radius = 5 in and height = 14 in

Substituting the given values:

[tex]V = π(5²)(14) \\ V = π(25)(14) \\ V = 350π[/tex]

Therefore, the volume of the cylinder is 350π cubic in (or approximately 1099.56 cubic meters if you want to use a numerical approximation for π).

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When the slope is an integer the best answer would be a. the rise number is one.

Any number, including zero, positive numbers, and negative numbers, is an integer. An integer can never be a fraction, a decimal, or a percent, it should be observed. Integers include things like 1, 3, 4, 8, 99, 108, -43, -556, etc.

When the slope is an integer, it means that the rise over run is also an integer, and the rise and run are relatively prime. Therefore, the best answer would be:

Therefore, the correct answer is a. the rise number is one.

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Answer:

∀x(D(x)→P(x))→(∃y∃z(St(y) ∧ St(z) ∧ R(y) ∧ R(z) ∧ y≠z))

Answer:

  3 times the second equation, plus the first

Step-by-step explanation:

You want a strategy for eliminating x-terms in the system of equations ...

You can eliminate x-terms by making their coefficients opposites. We observe that the coefficient of x in the first equation is -3 times the coefficient of x in the second equation.

Multiplying the second equation by 3 will make the x-coefficient -9, the opposite of that in the first equation. Doing that makes the system ...

Adding these two equations together will eliminate the x-terms:

  (9x -7y) +(-9x +15y) = (-3) +(27)

  8y = 24 . . . . . . . simplify; x-terms are gone

You can eliminate x-terms by multiplying the second equation by 3, then adding the two equations together.

1. ∠EAD ≅ ∠EBC (Given) 2. ∠AEB ≅ ∠AEB (Common angle) 3. AD- ≅ BC- (Given) 4. ∆AED ≅ ∆BEC (AAS) 5. CE- ≅ DE- (CPCT)

According to the concept of corresponding parts of congruent triangles, or cpct, corresponding sides and corresponding angles of two congruent triangles are identical. The corresponding sides and angles of two triangles that are congruent to one another according to any of the following principles of congruency must be equal. When the corresponding sides and corresponding angles of two triangles are the same, two triangles are said to be congruent.

In the given figure given that, ∠EAD ≅ ∠EBC; AD- ≅ BC.

Thus,

1. ∠EAD ≅ ∠EBC (Given)

2. ∠AEB ≅ ∠AEB (Common angle)

3. AD- ≅ BC- (Given)

4. ∆AED ≅ ∆BEC (AAS)

5. CE- ≅ DE- (CPCT)

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Answer:

5) 120.3

6) 57

Step-by-step explanation:

5)9x8=72(area)

π(4)²=50.3(area)

total area= 72+50.3=120.3

6) 12x4=48(area)

7-4=3

12-9=3

3x3=9(area)

total area = 48+9=57

It's important to note that the effective interest rate takes into account the Compounding effect, which means that Antonio's savings will grow faster than if the interest was only applied annually.

Antonio has saved 10,000 soles in the bank, and the bank is offering him an annual interest rate of 16% which is compounded monthly. To find out the effective interest rate that Antonio will receive, we need to calculate the annual percentage yield (APY).

The formula for APY is (1 + (interest rate/number of compounding periods))^number of compounding periods - 1.

In this case, the interest rate is 16% and the number of compounding periods is 12 (since the interest is compounded monthly). Plugging these values into the formula, we get:

APY = (1 + (0.16/12))^12 - 1
APY = 0.1728 or 17.28%

So, the effective interest rate that Antonio will receive is 17.28%. This means that at the end of the year, he will have earned 1,728 soles in interest (assuming he doesn't withdraw any money from the account). It's important to note that the effective interest rate takes into account the compounding effect, which means that Antonio's savings will grow faster than if the interest was only applied annually.

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Answer:

Yes, the data is an example of numerical data.

1. This is about data, which means information that we can measure and count.

2. There are two types of numerical data: continuous and discrete.

3. Continuous numbers CAN have fractions, like 3.5, 4.2, or 5.0. 4. like show sizes

4. Discrete data CANNOT have fraction. only whole numbers, like 0, 1, 2, 3, and so on. like number of students in a class

7. "range" formula used to find the difference between discrete & continuous numerical data

8.  "range" formula is largest value minus smallest value

Step-by-step explanation:

chatgpt

Answer: yes because it records the shoe sizes and you can calculate average, median, mode and range from this

Step-by-step explanation:

There are three possible cases for the number of solutions to an absolute value equation:

One solution: In this case, the absolute value of the expression equals a positive number. For example, the equation |x - 3| = 5 has one solution: x = 8 or x = -2.

Two solutions: In this case, the absolute value of the expression equals zero. For example, the equation |x - 3| = 0 has two solutions: x = 3.

No solution: In this case, the absolute value of the expression equals a negative number. However, the absolute value of any expression is always non-negative, so there can be no solutions. For example, the equation |x - 3| = -2 has no solutions.

The reason why there are differences in the number of solutions is because the absolute value function takes any input and returns a non-negative output. When we set an absolute value expression equal to a number, we are essentially splitting the equation into two parts: one where the expression is positive, and one where it is negative. Depending on the value that the absolute value expression is set equal to, we may get only one of these two parts (the positive part), both of them (the zero part), or none of them (the negative part).

For example, let's consider the absolute value equation |2x - 6| = 4. To solve this equation, we can split it into two cases:

Case 1: 2x - 6 = 4. Solving for "x", we get x = 5.

Case 2: -(2x - 6) = 4. Simplifying, we get -2x + 6 = 4, which gives us x = 1.

Therefore, the equation has two solutions: x = 1 and x = 5.

Answer:

Absolute value equations can have three possible cases based on the value within the absolute value brackets:

One solution: If the value within the absolute value brackets equals zero, there is only one solution. For example, |x| = 0 has the solution x = 0.

Two solutions: If the value within the absolute value brackets is positive, there are two solutions: one positive and one negative. For example, |x| = 3 has two solutions: x = 3 and x = -3.

No solutions: If the value within the absolute value brackets is negative, there are no solutions. For example, |x| = -2 has no solution because the absolute value of any real number is non-negative.

The differences in the number of solutions depend on the nature of the equation and the value within the absolute value brackets. If the value within the absolute value brackets equals zero, there is only one solution; if it is positive, there are two solutions; and if it is negative, there are no solutions.

For example, consider the absolute value equation |x - 5| = 7. If we subtract 5 from both sides, we get |x - 5| - 5 = 7 - 5, which simplifies to |x - 5| = 2.

Since the value within the absolute value brackets is positive, we know that there are two solutions. We can solve for both solutions by setting x - 5 equal to 2 and -2:

x - 5 = 2 => x = 7 x - 5 = -2 => x = 3

Therefore, the solutions to the absolute value equation |x - 5| = 7 are x = 3 and x = 7.

So to summarize, the number of solutions for an absolute value equation depends on the value within the absolute value brackets and can be one, two or zero, depending on the nature of the equation.

Mary Lou Mason's total taxes on her purchase would be $1.37.

Taxes are mandatory payments to the government that are used to fund public services such as infrastructure, education, and health care. Taxes can be direct, such as income taxes, or indirect, such as sales taxes.

Mary Lou Mason's total purchase was $19.14.

To calculate the total taxes for her purchase, we can use the following formula:

Tax = (State Sales Tax %) x (Total Purchase) + (County Tax %) x (Total Purchase)

Therefore, the total taxes for Mary Lou Mason's purchase would be:

Tax = (6.5%) x ($19.14) + (1.5%) x ($19.14)

Tax = (0.065 x 19.14) + (0.015 x 19.14)

Tax = 1.24 + 0.13

Tax = $1.37

Mary Lou Mason's total taxes on her purchase would be $1.37.

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Answer:

a

Step-by-step explanation:

The statement that is true about the ranges of the data sets is "The range of ages at Table 2 is 1 year greater than the range of ages at Table 1."

In statistics, a data set is a collection of observations or measurements that are typically organized into rows and columns. Each row in a data set represents a single observation or individual, while each column represents a variable or characteristic that has been measured.

The range of a data set is the difference between the maximum and minimum values in the set.

For table 1, the minimum age is 31 and the maximum age is 43, so the range is 43 - 31 = 12.

For table 2, the minimum age is 29 and the maximum age is 42, so the range is 42 - 29 = 13.

Therefore, the statement that is true about the ranges of the data sets is:

"The range of ages at Table 2 is 1 year greater than the range of ages at Table 1."

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Complete question:

The ages of the people at two tables in a restaurant are shown in the chart.

Which statement about the range of the data sets is true?