A cup is filled with
100 milliliters of water. Every second, 2
milliliters of water are poured out of the
cup. Which function shows the amount
of water in the cup after t seconds?

The ratio of boys to girls (3:4) and girls to adults (5:7) leads to a combined ratio of children to adults at the holiday camp of 5:4 after aligning the ratios on the common term for girls and simplifying.

To determine the ratio of children to adults at the holiday camp, we can use the given ratios:

First, express both ratios with a common term for girls to combine them accurately:

Since the ratio of girls to adults is 5:7, we can align this with the boys to girls ratio by multiplying the boys to girls ratio by 5 (the common term for girls). This gives us:

So, we have 15 boys and 20 girls for every 28 adults. The total number of children (boys and girls) is 15 + 20 = 35.

Therefore, the ratio of children to adults at the camp is 35:28, which simplifies to 5:4 after dividing both terms by 7.

Answer:

he hit the slopes  

Step-by-step explanation:

;)

Answer:

B. 52 beats/min

Step-by-step explanation:

while resting her heart beats : 36×2 = 72 beats/min

while running her heart beats : 1 860÷15 = 124 beats/min

difference = 124-72 = 52 beats/min

:)

Answer:

B. 52 beats/min

Step-by-step explanation:

To find the answer you have to find the bpm of each time that Chandra recorded her heart rate. So when she recorded her heart rate when running, you simply divide 1850 by 15, and you should get 123.333 (repeating) I am assuming by the answers that we are rounding, so we are going to round that answer up. Next to find her heart rate while resting, you take her heart rate in 30 seconds, which is 36, and multiply it by 2, because it was her heart rate in half of the time that we are measuring it in. So when you multiply 36 by 2 you should get 72. The next step is to subtract 124 from 72. You answer is 52.

Part 1: The speed of the boat traveling downstream is [tex](18+w)[/tex] miles per hr.

The speed of the boat traveling upstream is [tex](18-w)[/tex] miles per hr.

Part 2: The speed of the current is 4 miles per hour.

Explanation:

Part (1): The motorboat travels 18 miles per hour in still.

Let w represents the speed of the current.

When the boat travels downstream, the speed of the current will get added to the speed of the boat.

Thus, the expression can be written as [tex](18+w)[/tex] miles per hr

Hence, the speed of the boat traveling downstream is [tex](18+w)[/tex] miles per hr.

When the boat travels upstream, the speed of the current will get subtracted to the speed of the boat.

Thus, the expression can be written as [tex](18-w)[/tex] miles per hr.

Hence, the speed of the boat traveling upstream is [tex](18-w)[/tex] miles per hr.

Part (2): The boat travels 49 miles upstream in the same time it takes to travel 77 miles downstream.

The distance formula is given by [tex]distance $=$ speed $\times$ time[/tex]

Substituting, we have,

[tex]49=(18-w)t\\49=18t-wt[/tex]  ---------------(1)

[tex]77=(18+w)t\\77=18t+wt[/tex]  ---------------(2)

Solving using elimination method,

[tex]49=18 t-w t\\77=18 t+w t\\-------\\126=36t[/tex]

Dividing both sides by 36, we have,

[tex]t=3.5[/tex]

Substituting [tex]t=3.5[/tex] in [tex]$49=18 t-w t$[/tex], we get,

[tex]49=18(3.5)-w (3.5)\\[/tex]

[tex]49=63-3.5w\\[/tex]

[tex]-14=-3.5w\\[/tex]

[tex]4=w[/tex]

Thus, the speed of the current is [tex]w=4[/tex] miles per hour.

Final answer:

The expression for the speed of the motorboat downstream is (18 + w) miles per hour. The expression for the speed of the motorboat upstream is (18 - w) miles per hour. To solve for the speed of the current, a system of equations can be set up and solved using the Elimination Method.

Explanation:

1. When the motorboat is traveling downstream (with the current), the speed of the motorboat will be the sum of its speed in still water and the speed of the river current. So the expression for the speed of the motorboat downstream is: (18 + w) miles per hour.

When the motorboat is traveling upstream (against the current), the speed of the motorboat will be the difference between its speed in still water and the speed of the river current. So the expression for the speed of the motorboat upstream is: (18 - w) miles per hour.

2. To find the speed of the current, we can set up a system of equations. Let t represent the time taken for both the upstream and downstream trips. The distance traveled upstream is 49 miles and the distance traveled downstream is 77 miles. Using the formula Distance = Speed x Time, we can write the following equations:

(18 + w) * t = 77

(18 - w) * t = 49

We can solve this system of equations using the Elimination Method. First, multiply the first equation by (18 - w), and multiply the second equation by (18 + w) to eliminate the variable w:

[(18 + w) * t] * (18 - w) = [(18 - w) * t] * (18 + w)

Simplify both sides of the equation:

(18 + w)(18 - w)t = (18 - w)(18 + w)t

Expand:

(18² - w²)t = (18² - w²)t

Cancel out the like terms:

324 - w² = 324 - w²

This equation is true for any value of w. Therefore, there are infinitely many possible values for the speed of the current w. The specific value of w would depend on the given values of t and the distance.

Answer:

B

Step-by-step explanation:

Because, according to the graph, they are making the most sells.

Answer: 30 ft

Step-by-step explanation: bc 1/2 inch = 3 feet combined length = 2 + 5= 5 inches therefore (5.0/0.5)(3)= 10(3)=30

Answer:

[tex]x = 6[/tex] and [tex]y = 236[/tex]

Step-by-step explanation:

[tex]y = 296 - 10x[/tex]

[tex]y = 200 + 6x[/tex]

By equating both equations, we get:

[tex]296 - 10x = 200+6x[/tex]

[tex]16x = 96[/tex]  [Separate variables and constants]

[tex]x = 6[/tex]

By substituting [tex]x = 6[/tex] to the above equation, we get:

[tex]y = 296 - 10(6)[/tex]

[tex]y = 296 - 60[/tex]

[tex]y = 236[/tex]

Hence, [tex]x = 6[/tex] and [tex]y = 236[/tex]

Answer: intersecting

Step-by-step explanation:

they cross each other

Answer:

How could i answer without her pay rate ?

Step-by-step explanation:

Answer:

  120 mph

Step-by-step explanation:

To find miles per hour, divide miles by hours. ("Per" essentially means "divided by".)

  (24 miles)/(0.2 hour) = 24/0.2 miles/hour = 120 miles/hour

Answer:

Step-by-step explanation:

All equations where x=2 is a solution : a(x-2) = 0......a ≠ 0

Answer:

1   7/20   mixed= 27/20

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

All of them except 8/100 because it results 0.08 or 8%.

The rest:

2/5 = 0.4 = 40%

8/20 = 0.4 = 40%

4/10 = 0.4 = 40%

16/40 = 0.4 = 40%

Measure of the smaller angle is 75°

Step-by-step explanation:

Let angles be 5x and 7x.

⇒ 5x + 7x = 180

⇒ 12x = 180

⇒ x = 15

⇒5x = 5 [tex]\times[/tex] 15 = 75°

To find the measure of the smaller supplementary angle, when the ratio of the two angles is 5:7, you need to set up an equation with 5x and 7x as the angle measures. Solve this equation to find the value of 'x', and then use 'x' to calculate the measure of the smaller angle, which amounts to 75 degrees.

In this mathematics problem, we know that two angles are supplementary if their measures add up to 180 degrees. If the ratio of the two supplementary angles is 5:7, we can set up an equation to solve for the unknowns.

Let 5x represent the measure of the smaller angle and 7x represent the measure of the larger angle. We know that the sum of these two angles should be 180 degrees, thus:

5x + 7x = 180

Combining like terms, we get:

12x = 180

Now, we can solve for 'x' by dividing both sides of the equation by 12:

x = 180 / 12, which equals 15

Now that we know the value of 'x', we can plug it back in to find the measures of the two angles. The smaller angle, which is 5x, is then:

5x = 5 * 15, which equals 75 degrees

So the measure of the smaller angle is 75 degrees.

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Answer: x^2-3x+15

Step-by-step explanation:

Combine the like terms.

x^2 -3x+15

Answer:

x2 – 3x + 15 is the correct answer.

Step-by-step explanation:

Answer:

4 hours is what they use

Step-by-step explanation:

If they use 1/6 of their time each day

A day = 24 hours

1/6 times of that day will be

1/6*24= 4 hours

Answer:

Option A. one rectangle and two triangles

Option E. one triangle and one trapezoid

Step-by-step explanation:

step 1

we know that

The area of the polygon can be decomposed into one rectangle and two triangles

see the attached figure N 1

therefore

Te area of the composite figure is equal to the area of one rectangle plus the area of two triangles

so

[tex]A=(8)(4)+2[\frac{1}{2}((8)(4)]=32+32=64\ yd^2[/tex]

step 2

we know that

The area of the polygon can be decomposed into one triangle and one trapezoid

see the attached figure N 2

therefore

Te area of the composite figure is equal to the area of one triangle plus the area of one trapezoid

so

[tex]A=\frac{1}{2}(8)(4)+\frac{1}{2}((4+8)(8)=16+48=64\ yd^2[/tex]

Question:

How fast should the ant walk to go around the rectangle in 4 minutes if the sides are 12 inches and 16 inches

Answer:

The ant should walk 14 inches per minute

Solution:

Given that,

Dimensions of rectangle are 12 inches and 16 inches

Find the perimeter of rectangle

Perimeter = 2(length + width)

Perimeter = 2(12 + 16)

Perimeter = 2(28) = 56

Thus perimeter of rectangle is 56 inches

Time taken = 4 minutes

We have to find the speed at which ant covers 56 inches in 4 minutes

The speed is given by formula:

[tex]speed = \frac{distance}{time}[/tex]

[tex]speed = \frac{56}{4} = 14[/tex]

Thus the ant should walk 14 inches per minute

Step-by-step explanation:

Jose need at least 94 more points in order to get an A on this semester

Answer:

Step-by-step explanation:

Diagonal = [tex]\sqrt{2^{2} +3^{2}+6^{2} } =\sqrt{49} =7[/tex]

Answer:

- 40, - 50, - 60

Step-by-step explanation:

Note the common difference d between consecutive terms of the sequence.

- 20 - (- 10) = - 20 + 10 = - 10

- 30 - (- 20) = - 30 + 20 = - 10

Thus the difference d = - 10

To obtain a term in the sequence subtract 10 from the previous term

- 30 - 10 = - 40

- 40 - 10 = - 50

- 50 - 10 = - 60

The next 3 terms are - 40, - 50, - 60

Let's begin with point A:

[tex]A(7,-4)[/tex]

So we need to find the coordinates of points D in order for ABCD to be a rectangle. So:

D can be found by reflecting A across the x axis:

So you just need to multiply the y-coordinate by -1, then:

[tex]D(x,y)=D(7,-1(-4))=D(7,4)[/tex]

The length of AD can be found as the change in y from A to D:

[tex]\overline{AD}=4-(-4) \\ \\ \overline{AD}=8units[/tex]

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Answer:

x = 9

Step-by-step explanation:

x+3=2x-6

3=2x-x-6

9=x

The value of the x for the figure ABCD is 9.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Given the quadrilateral ABCD and opposite sides are parallel,

AD ║ BC and AB ║ CD

since the opposite sides of the quadrilateral are parallel so the quadrilateral is a parallelogram,

so AB = CD

AB = x + 3 and CD = 2x - 6

x + 3 = 2x - 6

2x - x = 3 + 6

x = 9

Hence the value of x is 9.

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Answer:

[tex]Amount\ of\ sales=\$ 6000[/tex]

Step-by-step explanation:

[tex]Let\ total\ sales=x\\\\Commission=3\%\ of\ total\ sale\\\\Commission=3\%\ of\ x\\\\It\ is\ given\ that\ salesperson\ gets\ \$ 180\ as\ commission.\\\\3\%\ of\ x=180\\\\\frac{3}{100}x=180\\\\x=\frac{180\times 100}{3}\\\\x=60\times 100\\\\x=6000\$\\\\Amount\ of\ sales=\$ 6000[/tex]

Answer:

Mr. Smiths class has 12 students and Mrs. Brown's class has 10 students.

Step-by-step explanation:

if 1/3 of the class is absent and that amount is four you would multiply 4 by 3 and get 12. If 2/5 of the class are missing and there 4 students first you would divide 4 by 2 and get 2, then you would take the 2 and multiply it by 5 and get 10.

Option c: (-6,1) is a solution for Line 2 only

Option d: (3,-1) is a solution to the system

Explanation:

Option a: (0,3) is a solution for Line 1 only

Line 1 is [tex]6 x-7 y=25[/tex]

Let us substitute the coordinate (0,3) in Line 1, we get,

[tex]\begin{array}{r}{6(0)-7(3)=25} \\{-21=25}\end{array}[/tex]

Since, both sides of the equation are not equal, the coordinate (0,3) cannot be a solution to Line 1.

Thus, Option a is not the correct answer.

Option b: (0,0) is a solution for Line 2 only.

Line 2 is [tex]2 x+9 y=-3[/tex]

Let us substitute the coordinate (0,0) in Line 2, we get,

[tex]\begin{array}{r}{2(0)+9(0)=-3} \\{0=-3}\end{array}[/tex]

Since, both sides of the equation are not equal, the coordinate (0,0) cannot be a solution to Line 2.

Thus, Option b is not the correct answer.

Option c: (-6,1) is a solution for line 2 only.

Line 2 is [tex]2 x+9 y=-3[/tex]

Let us substitute the coordinate (-6,1), in Line 2, we get,

[tex]\begin{array}{r}{2(-6)+9(1)=-3} \\{-12+9=-3} \\{-3=-3}\end{array}[/tex]

Since, both sides of the equation are equal, the coordinate (-6,1) is a solution for line 2 only.

Thus, Option c is the correct answer.

Option d: (3,-1) is a solution to the system

Let us substitute the coordinate (3,-1) in line 1 and line 2, we get,

In line 1, we have,

[tex]\begin{array}{r}{6(3)-7(-1)=25} \\{18+7=25} \\{25=25}\end{array}[/tex]

Substituting (3,-1) in line 2, we have,

[tex]\begin{array}{r}{2(3)+9(-1)=-3} \\{6-9=-3} \\{-3=-3}\end{array}[/tex]

Since, from line 1 and line 2, both sides of the equation are equal, the coordinate (3,-1) is a solution to the system.

Thus, Option d is the correct answer.

Option e: (3,1) is a solution to the system

Let us substitute the coordinate (3,1) in line 1 and line 2, we get,

In line 1, we have,

[tex]\begin{array}{r}{6(3)-7(1)=25} \\{18-7=25} \\{11=25}\end{array}[/tex]

Substituting (3,1) in line 2, we have,

[tex]\begin{array}{r}{2(3)+9(1)=-3} \\{6+9=-3} \\{15=-3}\end{array}[/tex]

Since, from line 1 and line 2, both sides of the equation are not equal, the coordinate (3,1) is a solution to the system.

Thus, Option e is not the correct answer.

Answer:

Option C: (-6,1) is a solution for Line 2 only

Option D: (3,-1) is a solution to the system

Step-by-step explanation:

Step-by-step explanation:

[tex]5 \times 5= 25[/tex]

Answer:

The solution is x = 1 and y = 1.25.

Step-by-step explanation:

The solution to the graphs  [tex]f(x) = -\frac{3}{4} x + 2[/tex]   and [tex]g(x) = \frac{1}{4} x + 1[/tex]  

Solving for x we get

[tex]-\frac{3}{4} x + 2 = \frac{1}{4} x + 1[/tex]    [tex]\Rightarrow[/tex]   x = 1        Therefore y =   1/4   + 1  = 1.25

1 and 0

I took the test and got it right