A wire 18 cm long is cut into two pieces. The longer piece is 6 cm longer than the shorter piece. Find the length of the shorter piece of wire

Answer:

4 times 6= 24

she will lose 24 pounds over a period of 6 months.

Reasoning:

If she loses 4 pounds EACH month and you have 6 months. You would multiply.

Answer:

she will lose 24 pounds

Step-by-step explanation:

she will lose 4 pounds every month and she does it for 6 months so

4 x 6 = 24

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Answer:

plot at least 10 points whose x-coordinate is 3.

The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

From the question, we have the following parameters that can be used in our computation:

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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Answer:

Tens:11,410

Ten thousand :10,000

Hundred : 11,400

Answer:

The answer is $2,732,728

Step-by-step explanation:

You start subtracting by aligning the numbers by place value. You subtract and get 28 then you have to subtract 0 - 3 which you can’t do and next to it are 2 other 0’s the only number you can carry is 7. You cross out the 7 and put a 6 in its place. The zero next to it becomes a 9. The one next to it also becomes a 9. Then the one on top of the three becomes a 10. You then do 10 - 3. Which equals 7. Then you do 9 - 7 = 2. 9 - 6= 3. You can’t do 6 - 9. so you cross out the 3 make it a 2 and turn the 6 into a 16. 16 - 9 =7. 2 - 0 =2 so then you get. $2,732,728.

Answer: 500 + 20 + 3 + 0.1 + 0.05

Step-by-step explanation: This 5th grade math

Answer: 500+20+3+.1+.05

Step-by-step explanation:

The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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The system of inequalities are : C + D ≤ 1300 ; C≥500 and D≥650

The graph can be made using these three inequalities.

How do you describe linear inequality with two variables?

The solution(s) of a linear inequality in two variables like mx + ny > p is value in pair (x, y) that satisfies the inequality when the values of x and y are substituted into that inequality. The graph of that inequality in two variables is the set of points that represents all roots to the inequality.

Let the commercial units be represented by C and Domestic units by D,

Given that both units are not more than 1300.

Means, C + D ≤ 1300

Also Given that, Commercial units are atleast 500 i.e, C≥500

Similarly, for domestic D≥650

a)The system of inequalities are:

C+D ≤1300

C≥500

D≥650

b)Graph for the above inequalities

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Refer to the graph attached with solution.

The worker earns $10 an hοur, and works for 10 hours a day for 10 days. So the total amount earned befοre the vacation is \(10^3$.\)

What is the coefficient?

In algebra, a coefficient is a numerical factοr that is placed in front of a variable οr a term. It is the number that is being multiplied by the variable or term. For example, in the expressiοn 4x, the coefficient is 4.

1) The worker earns $10 an hour, and wοrks for 10 hours a day for 10 days. So the total amount earned befοre the vacation is:

\(10 \cdot 10 \cdot 10 = $1000\)

Therefore, the correct answer is \($$103$\), which is \(10^3$.\)

2) \($3^4$\) is equal to 81, since \(3^4=3\times3\times3\times3=81$.\)

Therefore, the answer is 4.

3) The variables in the equation y=3x−4 are x and y.

Therefore, the answer is x and y.

4)The expression for the total area of the sign that needs to be painted is

\($$3S^2 - 2s^2$$\)

5)We substitute a = 2, b = 3, and c = 8 in the given expression:

\(a^5 - bc + 4a/c\)

\(= 2^5 - (3)(8) + (4)(2)/8\)

\(= 32 - 24 + 1/2\)

= 8.5

Therefore, a5 − bc + 4a ÷ c, when a = 2, b = 3, and c = 8, is 8.5.

6)The expression is t = 1m + 24, where m is the number of miles driven.

To find the total cost when 135 miles are driven, we substitute m = 135 into the expression:

t = 1(135) + 24 = 135 + 24 = $159

Therefore, the total cost of renting the truck for 135 miles is $159.

7)The expression 5p translated into words is "the product of 5 and a number p".

8)In the equation 9c=18, 9 is the coefficient of the variable c. A coefficient is a numerical factor that is placed in front of a variable or a term in an algebraic expression.

It indicates how many times the variable or the term is being multiplied. In this case, 9 is being multiplied by the variable c to produce 18. Therefore, 9 is the coefficient of c.

9)The coefficient is the numerical factor that is multiplying the variable in a term. In the given expression, there is only one term with a variable, which is 8b.

Therefore, the coefficient of 8b is simply 8.

10)We can simplify the expression using the order of operations (PEMDAS):

First, we need to evaluate 4 ÷ 4, which equals 1.

So, the expression becomes:12 - 1 + 3 + 1

Next, we add and subtract from left to right:

12 - 1 equals 11, then 11 + 3 equals 14, and finally 14 + 1 equals 15.

Therefore, the simplified expression is 15.

11) The correct pairing of a property of operations and its example is:

2(a+3) = 2a+6; Distributive Property.

12) To simplify the expression, we first use the distributive property to remove the parentheses: 2(x+3) + 4(x+1) = 2x + 6 + 4x + 4

Then, we combine like terms:2x + 4x + 6 + 4 = 6x + 10

Therefore, the expression 2(x+3) + 4(x+1) is equivalent to 6x+10.

Answer: 6x+10

13) Starting with the expression: 2(a+5)+4(2a+3)−10

We can apply the distributive property to simplify the expression inside the parentheses: 2a + 10 + 8a + 12 - 10

Then, we can combine like terms: 10a + 12

So the expression equivalent to the original expression using the associative and commutative properties is: 10a + 12

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Answer:

e. a and b only

Step-by-step explanation:

Question - A lambda expression is typically used ?

Solution -

The correct option is - e. a and b only

Reason -

As we know that, lambda expression is used to define anonymous function object.

So,

It is used when the function is short or the function is simple.

And it is used for the functions that are only used once.

So,

a. for functions that are only used once

b. for simple functions

a and b both parts are correct.

So,

The correct option is - e. a and b only

Answer:

9.    \(35^{2}\) or 1225

12.    \(15^{2}\)  or  225

Step-by-step explanation:

Put 5 instead of b

9.   \((7b)^{2}\)

   = \((7 * 5)^{2}\)

  = \(35^{2}\) or 1225

12.  \((3b)^{2}\)

    = \(( 3 * 5)^{2}\)

    = \(15^{2}\)  or  225

is simply changing from percentage form to a decimal form usually, but the fractional form works the same.  Check the picture below.

From the given box plot, it is found that:

The minimum height is of 156 cm, the first quartile Q1 is 168.1 cm, the second quartile Q2(or the median) is of 173.7 cm, the third quartile Q3 is of 181.4 cm, and the maximum height is of 192 cm.

A box and whisker plot shows five things:

The measures are shown in order, from left to right, hence:

The minimum height is of 156 cm, the first quartile Q1 is 168.1 cm, the second quartile Q2(or the median) is of 173.7 cm, the third quartile Q3 is of 181.4 cm, and the maximum height is of 192 cm.

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Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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It can be seen that x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.

To find x using the sine rule, we need to solve the equation:

sine(45) / x = sine(30) / (2x + 2√3)

Simplifying this equation, we have:

(2x - 1) / x = 1 / (2x + 2√3)

Cross-multiplying and simplifying further, we get:

(2x - 1)(2x + 2√3) = x

Expanding the brackets, we have:

\(4x^2 + 4\sqrt3x - 2x - 2\sqrt3 = x\)

Rearranging the terms and simplifying, we get:

\(4x^2 - 3x - 2\sqrt3 = 0\)

Using the quadratic formula, we can solve for x:

x = (-(-3) ± √((-3)^2 - 4(4)(-2√3))) / (2(4))

x = (3 ± √(9 + 32√3)) / 8

Therefore, x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.

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Answer:

(X<-25) or -oo, -25

Step-by-step explanation:

because max is -25

Answer:

Step-by-step explanation:

a, e, f

From the information below, we draw the conclusion that there is insufficient evidence to support the claim that alcohol use is more frequently associated with automobile deaths.

In statistical hypothesis testing, null and alternate hypotheses are utilized. The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables. The alternative or research hypothesis is the claim that, if true, is strongly supported by the evidence provided by the data, according to the criterion for the proper construction of a hypothesis test. Usually, the alternative hypothesis complements the null hypothesis.

Null Hypothesis: The typical dosage offered under this brand is 50 mg (mean dosage for population = 50 mg). Alternative Hypothesis: The typical dosage for this brand is lower than 50 mg (the population mean dosage).

Here n=92

let x: number of automobile accident =45

p: percentage of alcohol related automobile fatalities

alcohol related is 41% = 0.41

So. total =45/92 =0.49g

Now Null Hypotheses : p= 0.49

alternative hypotheses: p >0.49

test:

\((p-P)/(\sqrt{\frac{pq}{n} }) \\(0.49-0.41)/(\sqrt{\frac{0.41*0.59}{92})\)

= 1.56

Since \(\alpha\) must be 0.5 <1,5 So, we accept null hypotheses.

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Answer:

9/4

Step-by-step explanation:

Answer:

-(11/4)

Step-by-step explanation:

The required angle is 24.5°.

Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,

To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.

In this case, the perpendicular side is 16 and the base is 35.

Let's denote the acute angle as θ.

Using the tangent function, we can set up the equation:

tan(θ) = perpendicular side / base

tan(θ) = 16 / 35

To find the value of θ, we can take the inverse tangent of both sides:

θ = tan⁻¹(16 / 35)

θ = 24.5°

Hence the required angle is 24.5°.

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1. Suppose you are pouring two solutions and they react to each other and form another product that is undesirable or the reaction of these two are exothermic (liberation of heat) and results in an explosion. Hence not pour at the same time.

2. Number of grams present = (% strength × total volume ) ÷ 100

3. % strength depend on amount of solute and total amount of solution.

Since here the amount of solute silver nitrate is 20ml and total volume of solution is 80+20=100 ml.

Hence % strength will not change.

4. % strength of the solution is important because it tells about relative amount of solute present in solution, hence it play a great role to define the definite composition.

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Answer:

B. 25

Step-by-step explanation:

The computation of the no of adult tickets sold is shown below;

let us assume the number of child ticket be x

And, for adult ticket be y

Now as per the questions

x + y = 100

7.50x + 10y = 812.50

Multiply by 7.50x in equation 1

7.50x + 7.50y = 750

7.50x + 10y = 812.50

-2.50y = -62.50

y = 25

Hence, the number of adult ticket sold is 25

Step-by-step explanation:

To convert equations from polar form to rectangular form, we can use the following conversions:

1. For the equation r = tan(θ):

In rectangular form, we can express r in terms of x and y using the relationships:

r = √(x² + y²)

tan(θ) = y / x

Substituting these values into the equation r = tan(θ), we get:

√(x² + y²) = y / x

Squaring both sides of the equation, we have:

x² + y² = y² / x²

Multiplying both sides by x², we get:

x⁴ + x²y² = y²

Therefore, the rectangular form of the equation r = tan(θ) is:

x⁴ + x²y² - y² = 0

2. For the equation r = 2 / (1 - sin(θ)):

Using the same conversions as above, we have:

r = √(x² + y²)

1 - sin(θ) = 1 - y / r

Substituting these values into the equation r = 2 / (1 - sin(θ)), we get:

√(x² + y²) = 2 / (1 - y / √(x² + y²))

Squaring both sides of the equation, we have:

x² + y² = 4 / (1 - y / √(x² + y²))

Multiplying both sides by (1 - y / √(x² + y²)), we get:

(x² + y²)(1 - y / √(x² + y²)) = 4

Expanding and simplifying the equation, we have:

x² + y² - y = 4 - 4y / √(x² + y²)

Multiplying both sides by √(x² + y²), we get:

(x² + y² - y)√(x² + y²) = 4√(x² + y²) - 4y

Therefore, the rectangular form of the equation r = 2 / (1 - sin(θ)) is:

(x² + y² - y)√(x² + y²) = 4√(x² + y²) - 4y

Answer:

Step-by-step explanation:

40/30=409

Answer:

24 months

Step-by-step explanation:

Given :

Mean = 48

Standard deviation = 8

Zscore = - 3

Using the relation :

Zscore = (x - mean) / standard deviation

Where, x = score

-3 = (x - 48) / 8

-3 * 8 = x - 48

-24 = x - 48

-24 + 48 = x

24 = x

Score = 24

Answer:

52/15

Step-by-step explanation:

1 3/10 = 33/10 + 1/6 = 198/60 + 10/60

208/60 = 52/15

We are given the data of basketball tournament appearance of schools.

We are asked to draw a box-and-whisker plot of the data.

Recall that a box-and-whisker plot provides us the following five statistical measures.

1. Minimum value

2. Lower quartile

3. Median

4. Upper quartile

5. Maximum value

Let us calculate the above five statistical measures for the box-and-whisker plot.

First of all, arrange the data in ascending order (from least to greatest)

1, 1, 1, 2, 2, 2, 4, 5, 5, 7, 8, 8, 9

Please note that 24 and 34 seem to be outliers that's why we are not considering these two values.

As you can see from the above data,

Minimum value = 1

Maximum value = 9

The median value is located in the middle of the data set.

There are a total of 13 values.

The value at the 7th position is 4

Median = 4

The lower quartile is

The value at the 4th position is 2

Lower quartile = 2

The upper quartile is

The value at the 10th position is 7

Upper quartile = 7

Therefore, the five statistical measures are

1. Minimum value = 1

2. Lower quartile = 2

3. Median = 4

4. Upper quartile = 7

5. Maximum value = 9

From the given options, option C exactly matches with the given statistical measures.

Therefore, the correct box-and-whisker plot is option C

Answer: The length is 8 yards

Step-by-step explanation: First, take the volume of the prism (115 cubic yards), divide it by the width (2 1/2), the divide that by the height (5 3/4) getting you the length: 8 yards

we must replace the value of the variable x on 82

the rounded weight of the player is 242

Answer:

From your selections of answers, It's B: 12 x^3 - 21 b^5, but it's not completely simplified.

Step-by-step explanation:

Simplify the following:

3 (3 x^3 - 7 b^5) + 3 x^3

3 (3 x^3 - 7 b^5) = 9 x^3 - 21 b^5:

3 x^3 + (9 x^3 - 21 b^5)

Grouping like terms, 9 x^3 + 3 x^3 - 21 b^5 = (3 x^3 + 9 x^3) - 21 b^5:

(3 x^3 + 9 x^3) - 21 b^5

3 x^3 + 9 x^3 = 12 x^3:

12 x^3 - 21 b^5

Factor 3 out of 12 x^3 - 21 b^5:

Answer:  (3 (4 x^3 - 7 b^5)) = 12 x^3 - 21 b^5