A student solved this problem by working backward. Janice went shopping with her mom and at the end of the day she had $59.50 left over. She spent $13.65 on a T-shirt, $22.99 on some new sandals, and $40.75 on a new skirt. How much money did Janice have at the beginning? Student's solution - Janice had $59.50 left. Add up all the amounts she spent ($13.65 + $22.99 + $40.75) and add to the amount she has left over ($77.39 + $59.50). So Janice had $136.89 to begin with. Solve this problem. Dale was fixing his fence. At the end of the day, he had 12.5 feet of wood left over. During the day he had used one 3.5 foot long piece of wood, two 5.9 foot long pieces of wood, and one 10 foot long piece of wood. How many feet of wood did Dale have at the beginning of the day? feet

The perimeter of a triangle is the sum of all sides' lengths.

Thus,

[tex]P=6+4x+(3x+2)=7x+8.[/tex]

Given [tex]P=57\ cm,[/tex] you get

[tex]7x+8=57,\\ \\7x=57-8,\\ \\7x=49,\\ \\x=\dfrac{49}{7},\\ \\x=7\ cm.[/tex]

Answer: x=7 cm.

Using the divison operation, we can conclude that students prefer Basksetball 8.5 times more than soccer.

To obtain the number of times basket ball preference is greater than soccer :

We use the division operation :

(percentage of basketball) ÷ (percentage of soccer)

(25.5) ÷ 3 = 8.5

Therefore, students prefer basketball 8.5 times more than soccer.

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−200+

37

3

(4.5)

=−200+55.5

=−144.5             You can use order of operations or pemdas to solve problems like this. Just remeber to go left to right and multiplaction can be before division and multiplacation can be before divison (same with subtaction and addition)

The diver’s depth is 18.5 feet below from sea level.

Given that, A diver begins at sea level and dives down 200 feet.

He ascends at a steady rate of 121/3 feet per minute for 4.5 minutes.

This depth is represented by the numerical expression is,

                 [tex]=-200 +\frac{121}{3}*(4.5) \\\\=-200+(121*1.5)\\\\=-200+181.5\\\\=-18.5feet[/tex]

Negative sign indicate that below the sea level.

Hence, The  diver’s depth is 18.5 feet below from sea level.

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Answer:

99.7% lies between 76 and 88

Step-by-step explanation:

mean = 82, standard deviation = 2

3 standard deviation has 99.7%

so we need to find 3 standard deviation above and below the mean.

To find 3 standard deviation above the mean , we add standard deviation 2 with mean

82 + 2= 84 first SD

84 + 2= 86 second SD

86 + 2= 88 third SD

88 is the third SD above the mean 82

To find 3 standard deviation below the mean , we subtract standard deviation 2 from mean

82 - 2= 80 first SD

80 - 2= 78 second SD

78 - 2= 76 third SD

76 is the third SD below the mean 82

So , 99.7% lies between 76 and 88

In this situation, we would use something called the vertical line test. In other words, if we can draw a vertical line that passes more than one point on the graph, then the relation is not a function.

If we use the vertical line test in this situation, it is not possible to draw a vertical line that passes through more than one point. Therefore, this does represent a function.

To find the number of male and female cousins Jennifer Lopez met at a family reunion, we can set up a system of equations based on the given information. By solving the system, we can determine the values of the variables and find the answer.

The subject of this question is Mathematics and the grade level is Middle School. The question asks about the number of male and female cousins Jennifer Lopez met at a family reunion. Let's define the number of male cousins as x and the number of female cousins as y. From the given information, we know that x is 2 less than y.

So the equation can be written as: x = y - 2

Since Jennifer met a total of 9 cousins, we can write another equation: x + y = 9

Now we can solve this system of equations to find the values of x and y. Subtracting the first equation from the second equation, we get: (x + y) - (y - 2) = 9 - (y - 2)

Simplifying further, we have: x + 2 = 11 - y

Bringing the variables to one side, we get: x + y = 11 - 2

Combining like terms, we have: x + y = 9

Therefore, the value of x is 4 and the value of y is 5. So Jennifer Lopez met 4 male cousins and 5 female cousins at the family reunion.

88.3-1.8%=86.7 is the answer

The MAD value of the given data set is "3.2".

The average distance between each data value and the mean is defined as the mean absolute deviation of a data set. It is a measure of variation in a data set.

Calculation of the MAD value:

Given:

[tex]\to \{ 13, 6, 3, 7, 11\} \\\\[/tex]

Calculating the sum of the given value:

[tex]\to 13 + 6 + 3 + 7 + 11 = 40\\\\[/tex]

Calculating the average value:

[tex]\to \frac{40}{ 5} = 8\\\\[/tex]

Subtracting the average value from the given set:

[tex]\to 13 - 8 = 5\\\\\to 6 - 8 = | -2 | = 2\\\\\to 3 - 8 = | -5 | = 5\\\\\to 7 - 8 = | -1 | = 1\\\\\to 11 - 8 = 3\\\\[/tex]

Calculated set value:

[tex]\to 5, 2, 5, 1, 3\\\\[/tex]

Adding the set value:

[tex]\to 5 + 2 + 5 + 1 + 3 = 16[/tex]

Calculating the average value of the set:

[tex]\to \frac{16}{5} = 3.2\\\\[/tex]

So, the

[tex]\to \text{MAD} = 3.2[/tex]

Therefore, the final value of MAD is "3.2"

Find out more information about the MAD here:

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Final answer:

Laura is approximately 14.4 units away from the origin after walking 8 units to the right and 12 units up, found by applying the Pythagorean theorem.

Explanation:

The question asks how far Laura is from the origin after walking 8 units to the right and 12 units up. To solve this, we can use the Pythagorean theorem, which is a fundamental principle in geometry that deals with the lengths of sides in a right-angled triangle. Here, we consider Laura's walk as the two perpendicular sides of a triangle, with her movement to the right representing the horizontal side (8 units) and her movement upwards representing the vertical side (12 units).

To find the distance (hypotenuse) from the origin, we apply the Pythagorean theorem as follows:

Hence, Laura is approximately 14.4 units away from the origin, rounded to the nearest tenth.

Final answer:

The greatest common factor of 26n^5 and 12n^2 is 2n^2, as the prime factor 2 and the variable n to the second power are the highest powers common to both monomials.

Explanation:

The greatest common factor (GCF) of two monomials, 26n5 and 12n2, is found by identifying the highest power of each prime factor that is present in both monomials. To find the GCF of 26 and 12, we factor both numbers into their prime factors:

Since 2 is the only common prime factor between 26 and 12, and its lowest power in both numbers is 21, we take this as part of our GCF. For the variable part, we look at n5 and n2 and take the lowest power, which is n2. Hence, the GCF of 26n5 and 12n2 is 2n2.

Final answer:

The length of the line segment connecting points (4, -1) and (9, 7) in the coordinate plane is approximately 9.43 units, when rounded to the nearest hundredth.

Explanation:

To find the length of the line segment that connects the points (4, −1) and (9, 7) in the coordinate plane, we can use the distance formula which is derived from the Pythagorean theorem:

The distance (Δ) between two points (x1, y1) and (x2, y2) is given by:

Δ = √((x2 - x1)² + (y2 - y1)²)

Substituting the given coordinates:

Δ = √((9 - 4)² + (7 - (−1))²)

Δ = √(5² + 8²)

Δ = √(25 + 64)

Δ = √89

Using a calculator, we can find that:

Δ ≈ 9.43

Therefore, the length of the line segment is approximately 9.43 units, rounded to the nearest hundredth.

Answer:

the second one is correct

Step-by-step explanation:

Answer:the second

Step-by-step explanation:

Answer:

Adelaide gave $ 42 to the manicurist.

Step-by-step explanation:

Here, the original price of the manicure = $ 35

Since, 20% tip is given to manicurist,

Thus, the total payment for manicure = Original price of the manicure + 20 % of the original price of the manicure

= 35 + 20 % of 35

[tex]=35+\frac{20\times 35}{100}[/tex]

[tex]=35+\frac{700}{100}[/tex]

[tex]=35+7[/tex]

[tex]=42[/tex]

Hence, Adelaide gave $ 42 to the manicurist.