The polling results show the ratio of votes for Candidate A to Candidate B.


Candidate A Candidate B
12 20
18 30
27 45
36 ?


At this rate, if Candidate A received 36 votes, how many votes did Candidate B receive?
36
50
60
72

The mother must drive at a speed of 6 mph to reach Anna in ten minutes.

To find the speed required for the mother to reach Anna in ten minutes, you need to calculate the distance between them and the time it takes to close the gap.

Let x be the speed of the mother's car in mph.

In one hour, Anna will have covered 6 miles.

In ten minutes, the mother will have covered x * 10/60 miles.

The total distance between them is 6 + x * 10/60 miles.

The mother must cover this distance in ten minutes, so:

x * 10/60 = 6 / (10/60)

x = 6 * (10/60) / (10/60)

x = 6 mph

Therefore, the mother must drive at a speed of 6 mph to reach Anna in ten minutes.

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Answer: i think y =  x + 5

Step-by-step explanation:

Step-by-step explanation:

To solve this problem, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c,

c² = a² + b² - 2abcos(C)

In this problem, we can consider the man's starting point as the origin, and the distance he travels in the first leg as the first side of the triangle (a = 4km). The distance he travels in the second leg is the second side of the triangle (b). The angle between the two legs is the angle opposite side c, which is 90 degrees since the man changes direction from due west to southwest.

Therefore, we can use the law of cosines to find the distance he traveled in the second leg:

c² = a² + b² - 2abcos(90)

c² = 4² + b²

c = √(4² + b²)

c = √(16 + b²)

We know that the bearing of the second leg is 197 degrees, which is equivalent to a bearing of -163 degrees, since bearing measurements are taken clockwise from due north.

So we can use the law of cosines to find the distance he traveled in the second leg:

b = √(c² + a² - 2ac cos (-163))

We can now plug in the values we know:

b = √(c² + 4² - 24c*cos(-163))

We can now solve for c:

c = √(b² + 16 - 8bc)

The man is then southwest of his starting point, so the distance from his starting point to the final point is c.

The simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate is $280.

It is the interest calculated on the principal at a given rate for a time period.

We have,

P = $2800

T = 5 years

R = 2%

Now,

The formula for simple interest.

SI = PRT/100

Now,

SI = (2800 x 2 x 5) / 100

SI = 28 x 10

SI = $280

Thus,

Simple interest is $280.

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The number of days before she mows the lawn and washes her window on the same day is 60 days.

The day she would mow the lawn and wash her window on the same day would be the least common multiple of 12 and 20.

A multiple of a number is the product of an integer and that number. A common multiple is a multiple that two or more numbers share. The least common multiple is the smallest multiple that two or more numbers share.

Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 120

Multiple of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200

Least common multiple = 60

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The Centers for Disease Control and Prevention (CDC) states that the average height for men and women in the United States is around 5 feet, 9 inches and 5 feet, 4 inches, respectively.

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(a) The area of the space shuttle is:2.07x10⁻⁹km²

(b) $11.0321 is the cost of the patch.

Area of the patch of the space shuttle = 21.9cm²

a) 1 cm=0.00001 km

1cm²=(0.00001 km)²=10⁻¹⁰km²

21.9cm²=21.9x10⁻¹⁰km²=21.9x10⁻⁹km²

the patch's area =21.9x10⁻⁹km²

b) 1 cm = 0.393701 inch

1cm²=0.1550inch²

21.9cm²=21.9x0.1550inch²=3.3945inch²

The cost of patching area = 3.3945inch²

The cost of patching is are: 3.3945inch²

3.25inch²x3.3945inch²=11.0321

the cost of the patch to the nearest cent=11.0321

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

[tex]\int p(t)dt = \int\frac{1}{400}dt[/tex][tex]\int p(t)dt = \frac{1}{400}t[/tex]

[tex]\mu=e^{\int p(t)dt}[/tex]

[tex]\mu=e^{\frac{t}{400}}[/tex]

So, S(t) = [tex]\frac{\int\mu q(t)dt+C}{\mu}[/tex]

S(t) = [tex]\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)[/tex]

Now solving the bracket

S(t) = 4000 + [tex]e^{\frac{-t}{400}}[/tex]C.....(1)

At S(0) = 100

100 = 4000 + [tex]e^{\frac{-0}{400}}[/tex] C

100 = 4000 + [tex]e^{0}[/tex] C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

C. 5/4

Step-by-step explanation:

Let s = the scale factor

4s = 5  divide both sides by 4

s = 5/4

Answer:

Step-by-step explanation:

35

Answer:

70

Step-by-step explanation:

you divide the intergert and div8de its easy

Answer: 70

Step-by-step explanation:

An open circle is at 5 and a bold line starts at 5 and is pointing to the right. Therefore, option B is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -3(2x - 5) < 5(2 - x).

Here, -6x+15<10-5x

Add 5x on both the sides of an inequality, we get

-x+15<10

Subtract 15 on both the sides of an inequality, we get

-x<10-15

-x<-5

Multiply -1 on both the sides of an inequality, we get

x>5

Therefore, option B is the correct answer.

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The time taken by the submarine to make the descent when the equation of descent is given is 0.677 hours.

Submarine's descent can be represented by the equation, y = -3100 x

where,  

y is elevation

x is time in hours

We need to determine how long it will take this submarine to travel 2,100 feet below the surface of the ocean.

Since the submarine to make the descent to the seafloor 2,100 feet below the surface

So, y = - 2100

y = - 3100x gives

- 2100 = - -3100 x

Divide both sides by -3100,

x = 2100/3100 = 0.677 hours

As a result, the submarine will need 0.677 hours to complete the descent.

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12 students do not play any of the games. Number of students who do not play any of the games = 60 - 82 = 12

A group of 60 students, 25 play table tennis, 16 do swimming and 22 play cricket, 8 play table tennis and do swimming, 6 play cricket and do swimming, 5 play table tennis and cricket.

25 play table tennis

16 do swimming

22 play cricket

8 play table tennis and do swimming

6 play cricket and do swimming

5 play table tennis and cricket

Find the number of students who do not play any of the games

Total number of students = 60

Number of students who play any of the games = 25 + 16 + 22 + 8 + 6 + 5 = 82

Number of students who do not play any of the games = 60 - 82 = 12

12 students do not play any of the games.

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The order in which they performed be

14 + 16 . . . . add 5 + 9  

30 . . . . . . . add 14 + 16

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. There are four possible math operations here: addition, subtraction, multiplication, and division.

Given: 40/8 + 3² + (15 - 7) × 2

The order of operations instructs you to begin by assessing parenthesized expressions. This is done by deducting 7 from 15.

40/8 + 3² + 8 × 2 . . . . (15 - 7) = 8

Then you evaluate exponential terms.

 40/8 + 9 + 8 × 2 . . . . . 3² = 9

Next, multiply and divide from left to right. In this case, division comes before multiplication.

 5 + 9 + 8 × 2 . . . . . divide 40/8 = 5

 5 + 9 +16 . . . . . . multiply 8 × 2 = 16

The order in which they performed be

14 + 16 . . . . add 5 + 9  

30 . . . . . . . add 14 + 16

The complete question is:

Using the order of operations, what are the steps for solving this expression?

40/8+3^2+(15-7)*2

Arrange the steps in the order in which they are performed.​

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Tyson has (30-2x) hours left after x days .

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).

A first-degree polynomial is described as the sum of a collection of terms, each of which is the product of a constant and the first power of a variable in a linear equation.

She works out for two hours per day for a total of x days.

She has thus worked for two hours.

She has 30 hours left to accomplish, of which she has already worked for two of them.

She now has 30 2 hours to finish the task.

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A linear equation giving the value of the equipment in terms of the time t is calculated to be v = 117000 - 16714.3t.

The value of the colour printer is 117000 $ and machine has no value after 7 years.

As it is given that the machine has no value after 7 years. That mean rate is decreasing every year. So, the decreasing rate is, 117000/7 = 16714.3.

Let us assume v is the value of the machine and t is the time. Then, the linear equation for the given problem is, v = 117000 - 16714.3t

Thus, the required linear equation is v = 117000 - 16714.3t.

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Answer:

The maximum total cost for tickets is $320 + $160 = $480.

Step-by-step explanation:

The maximum number of people that can go on the field trip is 100, so the maximum number of students is 100 - (100/5) = 80 students.

The maximum number of adult chaperones is 1 adult chaperone for every 4 students, so the maximum number of chaperones is 80/4 = 20 chaperones.

The total cost for student tickets is $4 x 80 = $320.

The total cost for adult chaperone tickets is $8 x 20 = $160.

The maximum total cost for tickets is $320 + $160 = $480.

Answer:

the maximum amount for the equation is 320+160=480

6.93 × 10⁷ dogs were household pets in the U. S. In 2012.

To find the total number of dogs as household pets in the U.S. in 2012, we need to multiply the number of households by the average number of dogs per household.

Number of households = 4.33 × 10⁷

The average number of dogs per household = 1.6

Total number of dogs = (4.33 x 10⁷) × (1.6) = 6.93 × 10⁷

Therefore, approximately 6.93 × 10⁷ dogs were household pets in the U.S. in 2012.

Hence, the correct answer is D.

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y= -2.6717 + 0.0043(660) + 0.0045(630) = 3.00 is the GPA Score for Bobby Eagle.

A statistical method known as multiple linear regression (MLR), usually referred to as multiple regression, employs a number of explanatory variables to forecast the result of a response variable. One explanatory variable is used just once in multiple regression, an extension of linear (OLS) regression. Financial and econometric inference both make heavy use of MLR.

Score on critical reading = 660

Score on mathematics  = 630

Intercept = -2.6717

Reading(x1) = 0.0043

Mathematics(x2) = 0.0045

Hence, y = -2.6717 + 0.0043(660) + 0.0045(630) is the GPA score for Bobby.

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The solution set to the inequality as represented in another way is {x | x ∈ ≤ 4.5}. The second option is correct from the photo.

The set builder form is the representation of components of a set by a statement or an expression. The represented element(s) will be written using a variable, accompanied by a vertical line or colon, then the general attribute of the same represented element. This approach avoids listing the elements as seen in the roster method or the listing method.

From the given sets in roster form:

{-5,-4, -3, -2, -1, 0, 1, 2, 3, 4.5}

The same set above can be denoted by x, where x represents all the elements in the set and can be written as:

= {x | x ∈ ≤ 4.5}

This is read as x is an element of x such that x represent all the values from negative infinity to 4.5.

Therefore, we can conclude that the second option is correct from the photo.

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When it's a quarter full, the shipping container holds a volume of 350 cubic feet.

Bassically, we want to find one quarter (1/4) of the volume of the rectangular prims.

The dimensions are 20ft by 8ft by (8ft + 9in)

Let's rewrite that last part only using feet.

Remember that 12 in = 1ft

Then:

9 in = (9/12)ft = 0.75 ft

Then we can rewrite the dimensions as:

20ft by 8ft by 8.75 ft

The volume is the product between these numbers, and we want one fourt of the volume, so we need to find:

V = (1/4)*(20ft)*(8 ft)*(8 .75 ft) = 350ft³

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The solution set to the system of linear equations as an ordered pair is (3, -3).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines cross each other (intersect), which is represented as an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.

Note: Each interval on this graph represents 1 unit.

By critically observing the graph of the lines representing the system of linear equations, we can reasonably infer and logically deduce that the correct solution set lies in Quadrant IV and it is denoted by the point of intersection of both the x-coordinate and y-coordinate, which is given by the ordered pair (3, -3).

In conclusion, the ordered pair (3, -3) represents the solution set to the system of linear equations represented by the graph.

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Answer:

I think 9/10 but I am not sure

The simplification of the given expression after addition would be = 163.241.

Addition is the combination of two or more given values and it's one of the major arithmetic operations in mathematics.

The given expression is a s follows;

127.98+35.261 = 163.241

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Spanish 45 and french 42.5. When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common.

When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common. After that, input how many items are still there in each pair of sets' overlapping zone.

The quantity of each set's leftover pieces should be entered. Lastly, locate any missing numbers using any known totals.

Using a Venn diagram to determine probabilities: The Venn diagram's subset's components should be identified. Figure out the subset's frequency. Work out the larger set's overall frequency.  

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Answer:

y = x + 7  

Step-by-step explanation:

     [tex]\boxed{(y-y_1)=m(x -x_1)}[/tex]

m = 1

(1 , 8)  ; x₁ = 1  & y₁= 8;

    y - 8 = 1*(x - 1)

    y - 8 = x - 1

          y = x - 1 + 8

          y = x + 7