The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2-foot border of the floor visible on all sides. What should the length (the longer side) of the rug be?

Answer:

5 play Football & Baseball; 22 don't play Football; 11 don't play baseball; 20 don't play either football or baseball. See captures attached. The missing one in your original answer + the one made in Excel.

Step-by-step explanation:

If you fill out the blanks the way explained in the answer, you can prove that the 3 sentences match perfectly. The sum of all of them totals 58.

1. Thirty-one of them said they do not play baseball.

2. Sixteen of them said they play football.

3. Twenty of them said they do not play baseball or football.

By the way, as I mentioned before, I also attached the missing image in your original question.

Have a great day!

Answer:

Here is the answer.

We have been given a system of inequalities and an objective function.

The inequalities are given as:

[tex]y\leq 2x\\ x+y\leq 45\\ x\leq 30\\[/tex]

And the objective function is given as:

[tex]P=25x+20y[/tex]

In order to find the minimum value of the objective function at the given feasible region, we need to first graph the region.

The graph of the region is shown below:

From the graph, we can see that corner points of the feasible region are:

(x,y) = (15,30),(30,15) and (30,60).

Now we will evaluate the value of the objective function at each of these corner points and then we will compare which of those values is minimum.

[tex]\text{At (15,30)}\Leftrightarrow P=25\cdot 15+20\cdot 30=975\\ \text{At (30,15)}\Leftrightarrow P=25\cdot 30+20\cdot 15=1050\\ \text{At (30,60)}\Leftrightarrow P=25\cdot 30+20\cdot 60=1950\\[/tex]

Hence the minimum value of objective function is 975 and it occurs at x = 15 and y = 30

Answer:

The minimum value =

975

and occurs when x =

15

and y =

30

Step-by-step explanation:

Edge. 2020

The simplification of the radical is c/3

Radicals in math refer to expressions containing square roots or higher-order roots.

Represented by the radical symbol (√), they involve finding the root of a number. For example, √9 equals 3, as 3 * 3 equals 9.

Simplifying the surd;

√3c²)/√27

= √3 × √c²)/√9 × √3

= √3c/3√3

= c/3

Therefore the simplification of √3c²)/√27 is c/3.

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Answer:

[tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].

Step-by-step explanation:

According to the factor theorem, if [tex]x-a[/tex] is a factor of [tex]p(x)[/tex], then [tex]p(a)=0[/tex].

Let [tex]p(x)=4x^2-3x+22[/tex]. If  [tex]x-2[/tex] is a factor of [tex]p(x)=4x^2-3x+22[/tex], then [tex]p(2)=0[/tex].

Let us plug in [tex]x=2[/tex] in to the function to see if it will give us zero.

[tex]p(2)=4(2)^2-3(2)+22[/tex]

We simplify to obtain,

[tex]p(2)=4(4)-3(2)+22[/tex]

[tex]p(2)=16-6+22[/tex]

[tex]p(2)=10+22[/tex]

[tex]p(2)=32[/tex]

Since  [tex]p(2)\ne0[/tex], [tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].

According to the Factor Theorem, 'x - 2' is not a factor of the polynomial '4x^2 - 3x + 22'. This determination was made by plugging '2' into the second polynomial and finding that it does not result in zero.

For a polynomial P(x), the Factor Theorem states that if you plug a value 'a' into the polynomial and get zero (P(a) = 0), then x-a is a factor of that polynomial. In this case, you are asked to determine whether 'x - 2' is a factor of the quadratic function '4x^2 - 3x + 22'.

To do so, according to the Factor Theorem, plug the value '2' into the second polynomial function, so we have 4*(2)^2 - 3*(2) + 22 = 16 - 6 + 22 = 32. Because this does not equal zero, we can conclude that 'x - 2' is not a factor of the second polynomial '4x^2 - 3x + 22' based on the Factor Theorem.

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In this mathematical context, the inequality 20 + 6x > 100 can help Adrian find out the number of weeks he needs to continue his weekly addition of 6 cards to his sports card collection to exceed 100 cards in total.

The subject of this question is Mathematics and it appears to be at a Middle School level. The problem involves understanding and using linear equations and inequalities.

In this situation, Adrian starts with 20 cards and adds 6 more each week. So his total number of cards is represented by the equation 20 + 6x, where x is the number of weeks. If he wants to have more than 100 cards, we set up an inequality like this:

20 + 6x > 100

Thus, the inequality 20 + 6x > 100 allows Adrian to calculate the number of weeks x he needs to continue adding cards to his collection in order to exceed 100 cards total.

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To figure out when Adrian's sports card collection will surpass 100 cards given he is adding 6 cards each week, we can set up the inequality [tex]20 + 6x > 100[/tex]. Solving this gives us that Adrian should wait at least 14 weeks to have more than 100 cards.

The subject of this question is Mathematics, specifically, linear algebra and inequalities. Adrian has a sports card collection which began with 20 cards. Every week, he is adding 6 new cards. The statement that relates his ongoing collections would be: 20 + 6x, where x is the number of weeks. Adrian wants to know when his collection will exceed 100 cards. To determine this, we must set up an inequality: [tex]20 + 6x > 100[/tex]. Solving this inequality gives us [tex]x > (100-20)/6[/tex], or [tex]x > 13.33[/tex]. Therefore, Adrian will need to wait at least 14 weeks to have more than 100 cards in his collection given he is adding 6 new cards per week.

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Answer:

[tex]67750.644 ft^2[/tex]

Step-by-step explanation:

Given : A park in a subdivision has a triangular shape two adjacent side of the park are 433 and 520 the angle between the sides is 37

To Find: the area of the park to the nearest square foot

Solution:

Refer the attached figure

Area of triangle = [tex]\frac{1}{2} \times a \times b \times sin c[/tex]

a = 433

b=520

Sin c = Sin 37° = 0.6018

Area of triangle = [tex]\frac{1}{2} \times 433 \times 520 \times 0.6018[/tex]

Area of triangle = [tex]67750.644[/tex]

Hence the area of the park is [tex]67750.644 ft^2[/tex]

Answer:

2nd option

Step-by-step explanation:

On a scatter plot, a positive correlation indicates an increasing relationship between two variables, represented by an upward slope. Negative correlation shows a decreasing relationship, represented by a downward slope. The strength of these relationships is determined by the correlation coefficient.

In a scatter plot, a positive correlation and a negative correlation represent different types of relationships between two variables. A positive correlation suggests that as one variable increases, the other also increases. For example, height and weight are usually positively correlated, as the taller a person is, the more they tend to weigh.

On the other hand, a negative correlation means that as one variable increases, the other decreases. Graphically, this is represented by a downward slope from left to right. An example of this is the relationship between hours of sleep and tiredness, more hours of sleep typically correspond to less tiredness.

The strength of these correlations are determined by the correlation coefficient. A correlation coefficient closer to 1 or -1 indicates a stronger relationship, and a coefficient closer to 0 indicates a weaker relationship.

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Let X be the number of tail when a coin is flipped n number of times. Let n is the number of times a coin is flipped. Let p be the probability of getting tail on any flip of coin.

Here as coin is fair coin the chance of getting head or tail at any flip is 1/2.

n=75, p =0.5

From given information X follows Binomial distribution with n=75 and p=0.5

The probability that getting tail 35 or fewer times is

P(X ≤ 35) = P(X=35) + P(X=34) + P(X=33) + ....+ P(X=2) + P(x=1)

The Binomial probability is calculated using probability function

[tex] P(X=k) = (nCk) p^{k} (1-p) ^{n-k} [/tex]

For given parameters n=75 and p=0.5 the probability of getting X=k is

[tex] P(X=k) = (75Ck) 0.5^{k} (1-0.5) ^{75-k} [/tex]

Using excel function to find cumulative binomial probability for x=1 to 35 is

=BINOM.DIST(35,75,0.5,1) = 0.322

The probability there will be 35 or fewer tails is 0.322

The percentage of getting 35 or fewer tails is 32.2%

Answer:

A.Subtract 3:-7,-10,-13

Step-by-step explanation:

We are given that a sequence

5,2,-1,-4,...

We have to identify  the pattern of the givens sequence and next three terms.

[tex]a_1=5,a_2=2,a_3=-1,a_4=-4[/tex]

[tex]a_2-a_1=2-5=-3[/tex]

[tex]a_3-a_2=-1-2=-3[/tex]

[tex]a_4-a_3=-4-(-1)=-3[/tex]

The difference between two consecutive terms are equal.When the difference between two consecutive terms are equal then the sequence is called arithmetic sequence.Hence, the sequence is arithmetic sequence.

[tex]a_5=a_4-3=-4-3=-7[/tex]

[tex]a_6=a_5-3=-7-3=-10[/tex]

[tex]a_7=a_6-3=-10-3=-13[/tex]

Answer:A.Subtract 3:-7,-10,-13

The solution is, x = -243 is the value of (-3)^-5=1/x.

The algebraic equations are those which are valid for all values of variables in them are called algebraic identities.

Here we have:

Given that,

(-3)^-5=1/x

now, we have to simplify this expression, to get the value o x .

so, we get,

1/(-3)^5=1/x

or, (-3)^5=x

or, x = -243

Hence the value of the expression (-3)^-5=1/x , is x= -243.

(Note the expression asked is different by minus sign, but generally these questions solved as above. It would be a printing mistake)

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Answer:

Abigail could use a 50-foot tape measure to find the length of the classroom.

The dimensions of the rectangle given by the trinomial (x² + x – 42) are 7 and 6, which are derived by factoring the trinomial and applying the quadratic formula.

To find the possible dimensions of the rectangle, we start by factoring the trinomial that represents the area of the rectangle, namely x² + x – 42.

This can be factored as (x + 7)(x - 6), which are the roots of the quadratic equation when set to equal zero.

The roots, or solutions to this equation, can be calculated using the quadratic formula, -b ± √b² - 4ac 2a, which includes squaring the coefficient of the x-term, subtracting four times the product of the remaining coefficients, and dividing the result by twice the leading coefficient.

In this case, the dimensions that correspond to these roots, namely length and width, are 7 and -6. However, since dimensions cannot be negative, we disregard -6. Therefore, the possible dimensions of the rectangle are 7 and 6.

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