The sum of the digits of a two digit number is 14. The difference between the tens digit and the units digit is 2. If x is the tens digit and y is the ones digit, which system of equations represents the word problem?
xy = 14 and x - y = 2

x + y = 14 and x - y = 2

x + y = 14 and y - x = 2

The sampling method used in this case is Self-Selected Sampling (C) and it has bias because those who respond to the survey may overrepresent the number of readers in the community.

The sampling method used in this case is Self-Selected Sampling (C). The magazine invites readers to complete and mail in a survey, therefore the readers themselves choose whether or not to participate. There is no random selection involved in this sampling method.

The sampling method used in this case does have bias. (D) Yes, because the people who respond to the survey may overrepresent the number of readers in the community.

This is because only those who choose to respond will be included in the sample, and those who are more interested in the magazine or have strong opinions about reading may be more likely to respond.

Final answer:

The sampling method used in this situation is Convenience Sampling, and it does have bias because it may underrepresent the number of readers in the community.

Explanation:

The sampling method used in this situation is Convenience Sampling. This is because the magazine invites readers to complete and mail in a survey based on their convenience, rather than using a random or systematic method to select the sample.

The sampling method used in this situation does have bias. The correct answer is B. Yes, because the people who respond to the survey may underrepresent the number of readers in the community. This is because the sample is based on self-selection, meaning that only those who choose to respond to the survey are included. This can result in a biased sample that may not accurately represent the entire community's reading habits.

the answer to this question would be c- 15.6

[tex]\boxed{R_{4}=20\Omega}[/tex]

If resistors are in series, so the current  [tex]I[/tex] is the same in all of them. In this problem we have four resistors. So, we can get a relationship between the Equivalent resistance  of series combination and the four resistors as follows:

[tex]R_{eq}=R_{1}+R_{2}+R_{3}+R_{4}[/tex]

[tex]R_{eq}[/tex] is the total resistance [tex]50\Omega[/tex]. Moreover:

[tex]R_{1}=5\Omega \\ R_{2}=10\Omega \\ R_{3}=15\Omega[/tex]

Therefore:

[tex]50=5+10+15+R_{4} \\ \\ R_{4}=50-(5+10+15) \\ \\ R_{4}=50-30 \\ \\ \boxed{R_{4}=20\Omega}[/tex]

Answer:

4 Small, 6 Large

Step-by-step explanation:

We can start by finding values that would help add our two prices together.

We know that each large umbrella is $25, so if we keep adding until we can add up the umbrellas to 10, then we'll get our answer.

1 Large: $25

2 Larges: $50

3 Larges: $75

4 Larges: $100

5 Larges: $125

6 Larges: $150

Now don't forget, we need 10 umbrellas in total, and we know that we need 4 more umbrellas to get to 10, and we need 40 more dollars to get to 190.

40/10 = 4

6 Larges, 1 Small = $160

6 Larges, 2 Small = $170

6 Larges, 3 Small = $180

6 Larges, 4 Small = $190

Answer 8%, 1/8, 18%, 8/18, 0.8

Step-by-step explanation:

0.8 = 80%

1/8 = 12.5%

8/18 = 44.4%

8% < 12.5% < 18% < 44.4% < 80%

Answer:

pictures 1, 2, 4, and 6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

You need to distribute the 8 to everything in the equation. You need to keep the sign in the middle. So in the end you would get 8x+8y.

Final answer:

Option a), 8x + 8y, accurately represents the total number of erasers Shawn bought since it's obtained by distributing the number of boxes, 8, to both x and y inside the parentheses.

Explanation:

The expression 8(x + y) represents the total number of erasers Shawn bought, where x is the number of pink erasers in each box and y is the number of blue erasers in each box. Since Shawn bought 8 boxes, and each box contains x pink erasers and y blue erasers, we need to multiply the sum of pink and blue erasers in one box by the number of boxes to get the total. Hence, the correct expression that also represents the total number of erasers Shawn bought is option a), 8x + 8y which is obtained by distributing the 8 to both x and y inside the parentheses.

Answer:

11 degrees.

Step-by-step explanation:

"Angles T and U are a linear pair. Angle U measure (9x+6) and Angle T measures(6x+9). What is the value of x, in degrees?"

We know that a linear pair MUST add up to 180 degrees, therefore (9x+6)+(6x+9)= 180

Now for some algebra-

(9x+6)+(6x+9)= 180

6 and nine can both be divided by 3, so we will do that for simplicity:

((9x+6)+(6x+9)= 180)/3=

(3x+2)+(2x+3)=60

We will now separate the parenthesis, as they serve no purpose anymore.

(3x+2)+(2x+3)=60

3x+2+2x+3=60

Combine terms

5x+5=60

Take away the 5 to isolate the variables

5x+5=60

-5

5x=55

Divide by 5

5x=55

/5

x=11

The value of x is 11 degrees.

Answer:

He can make 52 canvases and will have 10 remaining staples

Step-by-step explanation:

1258/24=52 10/24

Answer:

52 canvases can be prepared and 10 staples will be remaining

Step-by-step explanation:

Sweet t has number of staples to create art canvases = 1258

Each canvas requires number of staples = 24

Let n canvases can be prepared by these staples.

Number of staples used in n canvases = 24n

The expression representing this process will be

24n = 1258

n = [tex]\frac{1258}{24}[/tex]

  = 52.42 canvases

Staples used to prepare 52 canvases = 52 × 24

= 1248

Remaining staples = 1258 - 1248

= 10 staples

Therefore, 52 canvases can be prepared and 10 staples will be remaining.

Answer:

the midpoint between (8,5) and (2,-2) is P(5,1.5)

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{2-8}{2}~~,~~\cfrac{-2+5}{2} \right)\implies \left( \cfrac{-6}{2}~,~\cfrac{3}{2} \right)\implies \left(-3~~,~~1\frac{1}{2} \right)[/tex]

ANSWER

The range is

{-1,0,1,3,4,5}

EXPLANATION

The relation is given to us as an ordered pair.

The range is the set of all the y-values of the relation.

We list the set of all the values in ascending order without any repetition.

We then obtain the range as:

{-1,0,1,3,4,5}

Answer:

the answer is a

Step-by-step explanation:

Answer:

37 units

Step-by-step explanation:

The horizontal distance between these two points is 35 and the vertical is 12.

Treat these distances as the lengths of the legs of a right triangle whose hypotenuse we want to determine:

d^2 = 35^2 + 12^2 = 1369, so d  = the distance between these two points = d = sqrt(1369) = 37 units

The difference between the points (15,-17) and (-20,-5) is calculated by subtracting the coordinates, resulting in a difference of (35, -12).

To find the difference between the two points (15,-17) and (-20,-5), we need to subtract the coordinates of the second point from the coordinates of the first point.

For the x-coordinates: 15 - (-20) = 15 + 20 = 35

For the y-coordinates: -17 - (-5) = -17 + 5 = -12

Therefore, the difference between the two points is (35, -12).

During the weekend sale, a total of 360 T-shirts were sold from the initial stock of 800 T-shirts in packs of 4. This resulted in 440 T-shirts leftover in stock after the sale.

In the context of the store scenario, we have an initial stock of 800 T-shirts, which are sold in packs of 4 each. On Saturday, 20 packs are sold, resulting in a reduction of 20 packs times 4 shirts per pack, which equals 80 shirts. On Sunday, 70 more packs are sold, which corresponds to 70 packs times 4 shirts per pack, totaling 280 shirts sold on Sunday. Adding up the shirts sold on both days, we get 80 + 280, which equals 360 shirts sold in total during the weekend. To find the remaining stock, we subtract the total shirts sold from the initial stock: 800 shirts - 360 shirts = 440 shirts remaining after the sale.

Answer:

(6x + 5)(7x² - 6)

Step-by-step explanation:

Factor the first/second and third/fourth term

42x³ + 35x² - 36x - 30

= 7x²(6x + 5) - 6(6x + 5) ← factor out (6x + 5) from each term

= (6x + 5)(7x² - 6)

Answer:

(6x+5)(7x2−6)

Step-by-step explanation:

Factor 42x3+35x2−36x−30

42x3+35x2−36x−30

=(6x+5)(7x2−6)

Let's assume the unknown number is x and as another one is 5 times the number then second number is 5x

》x × 5x = 245

》5x square =245

》x square =245÷5

》x square =49

》x=7

So 5x = 5×7=35

Line AC and Line BD are perpendicular to each other.

In this scenario, we have Line AB parallel to Line CD, and both Line AC and Line BD are perpendicular to Line AB and Line CD. Since two perpendicular lines intersect at a 90-degree angle, we can say that Line AC and Line BD are also perpendicular to each other. This means that Line AC forms a 90-degree angle with Line BD.

Okay so in this question it says to solve f(7). This means to plug in the 7 every where you see an x, so that it looks like this: [tex]\frac{3}{7+2} -\sqrt{7-3}[/tex]Then you'll solve it like a normal equation.

Hope this helped! Let me know if there is anything I need to clarify or explain more in depth!

Answer:

- 1.67

Step-by-step explanation:

To evaluate f(7) substitute x = 7 into the expression

f(7) = [tex]\frac{3}{7+2}[/tex] - [tex]\sqrt{7-3}[/tex]

     = [tex]\frac{3}{9}[/tex] - [tex]\sqrt{4}[/tex]

     = [tex]\frac{1}{3}[/tex] - 2

     = [tex]\frac{1}{3}[/tex] - [tex]\frac{6}{3}[/tex]

     = - [tex]\frac{5}{3}[/tex] ≈ - 1.67

Answer:

1 minute and 40 seconds or 1 2/3 minute

Step-by-step explanation:

If it took Scott 2 miles for 5 minutes, than it took him 2.5 minutes to do 1 mile. For 3 times as fast, we need to divide by 3. 2.5/3= 5/2*1/3=5/6. It is 2 miles, so 5/6*2=10/6=5/3=1 2/3 minute. 2/3 minute=40 seconds. So, the answer is 1 minute and 40 seconds or 1 2/3 minute.

Answer:

1 minute and 40 seconds or 1 2/3 minute(s)

Step-by-step explanation:

Answer:

30 in, 0.5 m, 1.25 ft, 17 cm

30in, 0.5m, 1.25, 17cm

Answer:

C. 58°

Step-by-step explanation:

m∠ACB=(180-138)°

m∠B + m∠A +∠mACB =180

80+ m∠A + (180 -138) =180

80 + m∠A - 138 = 0

m∠A = 58

Answer:

C

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ACD is an exterior angle of the triangle and

∠A and ∠B are the 2 opposite interior angles, hence

∠A + ∠B = 138, that is

∠A + 80 = 138 ( subtract 80 from both sides )

∠A = 58° → C

Answer:

120 degrees aka answer D

Step-by-step explanation:

Answer:

D. 120°.

Step-by-step explanation:

Since the angle is obtuse (greater than 90), it cannot be 30°, since 30° is an acute angle.

The angle cannot be 90° since the angle is obtuse, and red curved line is not a square.

The line would be straight if the angle was 180°, so the most reasonable answer would be D. 120°.

Answer:

  (d)  remains the same as production increases

Step-by-step explanation:

All of the numbers in the Marginal Revenue column are the same. That means we can conclude marginal revenue ...

  remains the same as production increases.

Answer:

 (d)  remains the same as production increases

Step-by-step explanation:

Answer:

3.3

Step-by-step explanation:

3 3/10 = 3 + 3/10 = 3 + 0.3 = 3.3

Answer: $10.40

Explanation:

First, find the cost of 1 box of pasta. 13/5 = 2.6, so $2.60 a box.

Next, find how many boxes there are. 48/12 = 4, so 4 boxes of pasta.

Finally, multiply 4*2.6 to get the final cost.

Answer:

Function 1 has the least minimum value and its coordinates are (2, -7).

Step-by-step explanation:

Two quadratic functions are shown.

Function 1:

[tex]f(x) = 2x^2 - 8x + 1[/tex]

Function 2:

x        g(x)

-2         2

-1         -3

0         2

1         17

LEts find the vertex to get the minimum value

to get the minimum value for function 1 we use formula [tex]x=\frac{-b}{2a}[/tex]

[tex]f(x) = 2x^2 - 8x + 1[/tex], a=2, b=-8

[tex]x=\frac{-b}{2a}=\frac{8}{2(2)}=2[/tex]

when x=2, the value of [tex]f(2) = 2(2)^2 - 8(2) + 1=-7[/tex]

minimum point of function 1 is (2,-7)

For function 2, we find the minimum point using the table

minimum point of function 2 is (-1,-3)

Function 1 has the least minimum -7.

Function 1 has the least minimum value and its coordinates are (2, -7).

The true statement is (b) function 1 has the least minimum value and its coordinates are (2, -7).

The first quadratic function is given as:

Factor out 2 in the above equation

[tex]f(x)= 2(x^2 - 4x) +1[/tex]

Rewrite the expression in the bracket, as follows:

[tex]f(x)= 2(x^2 - 4x + 4 - 4) +1[/tex]

This gives

[tex]f(x)= 2(x^2 - 4x + 4 ) -8+1[/tex]

[tex]f(x)= 2(x^2 - 4x + 4 ) -7[/tex]

Express x^2 - 4x + 4 as a perfect square

[tex]f(x)= 2(x - 2)^2 -7[/tex]

A quadratic function is represented as:

[tex]f(x)= a(x - h)^2 +k[/tex]

Where

[tex]Vertex = (h,k)[/tex]

By comparison, we have:

From the graph, the minimum of function 2 is:

(2,-7) is lesser than (-1,-3).

Hence, the function 1 has the least minimum value at a coordinate of (2,-7)

Read more about quadratic functions at:

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Answer:

$11.00

Explanation:

$60 given - $49 order = $11 change

Answer:

It's 11 because 60-49 equals 11.

Step-by-step explanation:

ANSWER

The swimming pool can hold 1,000,000 cubic feet of water.

EXPLANATION

The capacity of water the pool holds is the volume of water in the swimming pool.

The swimming pool is rectangular, therefore its volume can be calculated using the formula,

[tex]V = l \times w \times h[/tex]

where l=1000ft is the length, w=100ft is the width and h=10ft is the height of the pool.

We substitute all these values into the formula to get:

[tex]V = 1000 \times 100 \times 10 = 1000000 {ft}^{3} [/tex]

The swimming pool can hold 1,000,000 cubic feet of water.

The amount of water the pool can hold is  1,000,000 ft³.

In order to determine the amount of water the pool can hold, we have to determine the volume of the rectangular swimming pool. Since the swimming pool has the shape of a cuboid, the formula for the volume of a cuboid would be used.

Volume = length x width x height

1000 x 100 x 10 = 1,000,000 ft³

To learn more about the volume of a cuboid, please check: https://brainly.com/question/26406747

The solution of the expression (a-b)²/{(1/a)-(1/b)} is ab² - a²b.

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

Given:

An expression,

(a-b)²/{(1/a)-(1/b)}.

Simplifying,

(a-b)²/{(1/a)-(1/b)},

= (a-b)²/{(b-a)/ab},

= -(a-b)² (ab)/(a-b)

= -(a-b)(ab)

= ab² - a²b.

Therefore,  ab² - a²b is the solution.

To learn more about the factorization;

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Final answer:

The expression (a-b)²/(1/a-1/b) simplifies by first finding a common denominator, then multiplying to remove the fraction, resulting in the simplified form -ab(a-b).

Explanation:

To simplify the expression (a-b)²/(1/a-1/b), we can start by finding a common denominator for the terms in the denominator 1/a and 1/b. The common denominator is a × b, so we rewrite the expression as:

((a-b)²) / ((b - a) / (ab))

Now, we can simplify by multiplying both the numerator and the denominator by ab to eliminate the fraction in the denominator:

(a-b)² × (ab) / (b - a)

Note that (a - b) is equal to -(b - a), so:

(a-b)² × (ab) / -(a - b)

Because (a - b)² is (a - b) × (a - b), one (a - b) in the numerator cancels with the (a - b) in the denominator, leaving us with:

-(a - b) × (ab)

Which simplifies to:

-ab(a - b)

Answer:

Part 1) The lateral area is [tex]LA=791.7\ ft^{2}[/tex]

Part 2) The surface area is  [tex]SA=1,244.1\ ft^{2}[/tex]

[tex]LA=791.7\ ft^{2}[/tex], [tex]SA=1,244.1\ ft^{2}[/tex]

Step-by-step explanation:

step 1

Find the lateral area of the cone

we know that

The lateral area of the cone is equal to

[tex]LA=\pi rl[/tex]

we have

[tex]r=12\ ft[/tex]

[tex]l=21\ ft[/tex]

substitute

[tex]LA=(3.1416)(12)(21)=791.7\ ft^{2}[/tex]

step 2

Find the surface area of the cone

we know that

The surface  area of the cone is equal to

[tex]SA=\pi r^{2}+LA[/tex]

we have

[tex]r=12\ ft[/tex]

[tex]LA=791.7\ ft^{2}[/tex]

substitute

[tex]SA=(3.1416)(12)^{2}+791.7=1,244.1\ ft^{2}[/tex]