Use a tape diagram to model the following problem. Solve using a simplifying strategy or an algorithm, and write your answer as a statement. 3. The Smith's hot tub has a capacity of 1,458 liters. Mrs. Smith put 487 liters 750 milliliters of water in the tub. How much water needs to be added to fill the hot tub completely?

Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

Answer:

x = 15

Step-by-step explanation:

3x - y = 30

Let y = 15

3x - 15 = 30

Add 15 to each side

3x-15+15 = 30+15

3x= 45

Divide each side by 3

3x/3=45/3

x = 15

Answer

Step-by-step explanation:

\(3x - y = 30 \\ 3x = 30 + y \\ x = \frac{30 + y}{3} \\ \\ \)

\(y = 15\)

\(x = \frac{30 + y}{3} \\ x = \frac{30 + 15}{3} \\ x = \frac{45}{3} \\ x = 15\)

hope this helps

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The estimated probability of a success is 3/5 or 0.6

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

Integers = 5

Success = 3

The probability of success is then calculated as

Probability = Success/Integrs

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

probability = 3/5 = 0.6

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21x29=609

    21

x   29

_______

  189

+ 420

______

  609

Answer:

609

Step-by-step explanation:

21 * 29 = 609

Answer:

B. The type II error in this context is when the agency concludes that the program does not increase the recycling rate, when in fact it does increase the rate. This consequence of this error is that the agency will not implement a program that could have increased the water bottle recycling rate.

Answer:

I hope this helps!

Step-by-step explanation:

Please mark brainiest

The number of tiles that would be required to cover a floor that is 288 square feet is 512.

According to the question,

We have the following information:

Area of the tile = 9*9 square inches

Area of the tile = 81 square inches

Area of the floor = 288 square feet

So, we will convert the area of the floor from square feet to square inches.

We know that 1 feet = 12 inches.

So, we have the following expression:

Area of the floor = (288*12*12) square inches

Area of the floor = 41,472 square inches

Number of tiles required to cover the floor = area of the floor/area of the tile

Number of tiles required to cover the floor = 41,472/81

Number of tiles required to cover the floor = 512

Hence, the number of tiles that would be required to cover a floor that is 288 square feet is 512.

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Answer:

The answer is 30.

Step-by-step explanation:

Don't worry about the x and y it just make your head confuse, that's what my teacher said just add up the number.

Answer:

Y=30

X=40

Step-by-step explanation:

for Y is because 46-16=30

for X is because 180÷3=60

80+60=140

180-140=40

9514 1404 393

Answer:

  a) (-7, -2)

  b) 15 square units

Step-by-step explanation:

The slope at x is given by the derivative:

  y' = 3x^2 -10x +3

The slope of the normal is the negative reciprocal of this.

at a(4, -3) the slope of the normal is ...

  ma = -1/y' = -1/((3(4) -10)(4) +3) = -1/11

Then the point-slope equation of the line is ...

  y +3 = -1/11(x -4)

__

at b(1, 0) the slope of the normal is ...

  mb = -1/y' = -1/((3(1) -10)(1) +3) = -1/-4 = 1/4

Then the point-slope equation of the line is ...

  y = 1/4(x -1)

Solving these two equations will give the coordinates of point C.

  (1/4(x -1) +3) = -1/11(x -4)

  11(x -1) +132 = -4(x -4)

  15x = -105

  x = -7

  y = 1/4(-7 -1) = -2

The coordinates of point C are (-7, -2).

__

There are a few ways to find the area of a triangle that is specified by its vertex coordinates. I like the method that involves finding the determinants of pairs of coordinates around the figure. The area is half the absolute value of their sum. This can be made a little easier by listing the coordinates, repeating the first pair:

  a(4, -3)

  b(1, 0)

  c(-7, -2)

  a(4, -3)

Working down the list, the area will be ...

  A = 1/2|(4(0) -1(-3)) +(1(-2) -(-7)(0)) +((-7)(-3) -4(-2))| = 1/2|(0 +3) +(-2 +0) +(21 +8)|

  A = 1/2|30| = 15 . . . . square units

_____

The attached graph finds the intersection of the normals quite easily. The attached spreadsheet does the area calculation from the triangle coordinates. These tools are very handy for problems like this.

Answer:

Step-by-step explanation:

\(Curve:\ y=x^3-5x^2+3x+1\\\\y'(x)=3x^2-10x+3\\A=(4,-3)\\B=(1,0)\\y'(4)=3*4^2-10*4+3=11\\slope\ of\ the\ normal\ in \ A: -\frac{1}{11} \\Equation\ normal\ in \ A:\\y+3= -\frac{1}{11}*(x-4)\ or\ -x-11*y=29\ (1)\\\\y'(1)=3*1^2-10*1+3=-4\\slope\ of\ the\ normal\ in \ B: \frac{1}{4} \\Equation\ normal\ in \ B:\\y-0=\frac{1}{4} (x-1)\ or\ -x+4y=-1\ (2)\\\\Coordinates\ of\ C:\\(1)-(2) ==> y=-2\\(2) ==> x=-7\\\\C=(-7,-2)\\\)

Area of the  triangle ABC:

\(S=\dfrac{|CB|*|CA|*sin(\widehat{ACB})}{2}\\A=(4,-3),B=(1,0),C=(-7,-2)\\AB^2=(4-1)^2+(-3-0)^2=9+9=18\\AC^2=122\\BC^2=68\\\\Using\ Al'Kashi\ theorem:\\AB^2=CB^2+CA^2-2|CB||CA|*cos(\widehat{ACB})\\\\cos(\widehat{ACB})=\dfrac{68+122-18}{2\sqrt{68*122} } =\dfrac{86}{\sqrt{68*122} } \\\\sin^2(\widehat{ACB})=1-cos^2(\widehat{ACB})=1-\dfrac{86^2}{68*122} \\\\S=\dfrac{\sqrt{68} *\sqrt{122}*\sqrt{\dfrac{900}{68*122} }}{2}=15\\\)

Answer:

I think it is 4:3

Step-by-step explanation:

From $960,000 take away $720,000 and you get $240,000 and that $960,000 divide by $240,000 and you get 4 and you do the same with $720,000 and you get 3

The requried ratio of candidate A's campaign spending to candidate B's campaign spending is 4 : 3.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

here,
During a mayoral election, candidate A spent $960,000 on her campaign, and candidate B spent $720,000 on her campaign.

The ratio of candidate A's campaign spending to candidate B's campaign spending,

= 960000 / 720000

= 96 / 72
= 4 / 3

Thus, the requried ratio of candidate A's campaign spending to candidate B's campaign spending is 4 : 3.

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The equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

We know that the method to find the axis of the symmetry of the parabola is given by:

x = - b / 2 a

We have the general equation of the parabola as:

y = a x² + b x + c

We have the equation of the parabola as:

y = - 4 x² + 24 x - 35

Comparing from this equation, we get that:

a = - 4

b = 24

c = - 35

Now, substituting the values, we get that:

x = - 24 / 2 (- 4)

x = - 24 / - 8

x = 24 / 8

x = 3

Therefore, the equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

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Answer:

  2.  Tenths place

Step-by-step explanation:

When you're concerned with the precision of a sum, the final value must be rounded to the precision of the least-precise contributor.

The numbers contributing to this sum are ...

  7.273, with least significant digit in the thousandth's place.

  -12.4, with least significant digit in the tenths place.

The smaller the place value of the least significant digit of a number, the greater the precision it has. The least-precise number will have the largest place value of its least-significant digit.

  tenths > thousandths, so -12.4 has less precision

First of all, we compute the sum as though every contributor were exact. This is especially important when there are more than two contributors. With only two contributors, you get the same result if you round the more precise number first.

  7.273 -12.4 = -5.127 . . . . . preferred method of finding the sum

  7.3 -12.4 = -5.1 . . . . . . . . . . alternate approach for 2 contributors

Finally, we round that sum to the nearest tenth, reflecting the precision of -12.4:

  sum = -5.1

__

Additional comment

As a general rule, this fixation on precision applies to quantities that are measured, estimated, or rounded.

For example, it doesn't make much sense to report a financial value to the penny if one of the contributors has already been rounded to the nearest hundred-thousand dollars. The amount could already be in error by up to $50,000, so precision to the penny is meaningless.

When working many kinds of problems, it can be useful to report answers to the same precision used for the problem values. In some cases, you are told exactly what precision to use for an answer (nearest integer, tenth, or hundredth). Where you are not told, it usually doesn't make much sense to use 6 significant digits for an answer to a problem with values given as one significant digit. However, it can be sensible to report the answer to 2 or 3 significant digits.

__

Here (in this problem), we're concerned with a sum. When you are computing a product or ratio, the rules are different. In those cases, the (least) number of significant digits in the contributors will determine the number of significant digits in the answer. Where mixed arithmetic (products and sums) is involved, the rounding of the final answer will depend on the final operation:

  a(b+c) . . . the final operation is multiplication

  ab +ac . . . the final operation is addition

As with all computation, the intermediate results should be carried to full calculator precision (unless directed otherwise). Only the final answer should be rounded to the necessary precision.

About 14,586 will the population be in 4 years.

About 9,872 was the population 4 years ago.

Assuming an exponential function

\(f(x) = 12,000(1 + 0. 05)^x\)

(Where x is the number of years and f(x) is the population of fish in a lake.)

Put x = 4 in the function to determine the population in 4 years:

\(If, x=4,\\f(4) = 12,000(1 + 0. 05)^4\\f(4) = 12,000(1 . 05)^4\\f(4) = 12,000(1.21550625)\\f(4) = 14586.075\\f(4) = 14586approx\)

Add x = -4 to the function to determine the population four years ago:

\(If, x=-4,\\f(-4) = 12,000(1 + 0. 05)^{-4}\\f(-4) = 12,000(1. 05)^{-4}\\f(-4) = 12,000(0.8227024748)\\f(4) = 9872.429698\\f(-4) = 9872approx\)

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Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

Your question is missing some parts

and the degree seems off is it 90⁰

Answer:

The spread of the data in Set B is greater than the spread of the data in Set A.

Step-by-step explanation:

Just took the test :3

Answer:

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

it wouldn't change if it was to be rotated

Answer: 22

Step-by-step explanation:

Take the equation

4x-18+3y

Now plug in the values given

4(7)-18+3(4)

28-18+12

10+12

22

Answer:

y=-3/4x+1/4

Step-by-step explanation:

This is the concept of equations of graphs; We are required to calculate for the equation if the line that is perpendicular to the line 4x-3y=-8 and passes through point (3,-2).

Here we proceed as follows;

4x-3y=-8 can be written in he form y=mx+c as follows;

-3y=-4x-8

thus;

y=4/3x+8/3

The slope of the line perpendicular to this is -3/4. Thus using point (3,-2) the equation will be as follows;

-3/4=(y--2)/(x-3)

-3/4(x-3)=y+2

y+2=-3/4(x-3)

y+2=-3/4x+9/4

thus;

y=-3/4x+1/4

the answer is:

y=-3/4x+1/4

Answer:

11 1/6 miles

Step-by-step explanation:

10 min = 1/6hr

67 * 1/6 = 11 1/6 miles

Answer:

Fire ant, 1000 mm

Step-by-step explanation:

If you do the equations for both insects you'll see the fire ant is 4000mm long while the tree hopper is 3000mm long. The difference in length is 1000mm.

The perimeter of the plane figure which is a quadrilateral with four straight sides is equal to 16 inches.

To know the perimeter of a plane figure, we add up all the length of its sides or boundaries together. That is the sum total of the length of a plane figure is called its perimeter.

The plene figure has for sides who two of it is 5 inches each and the other two is 3 inches each.

thus we calculate for the perimeter as follows:

perimeter of the plane figure = 5 in + 5 in + 3 in + 3 in

perimeter of the plane figure = 16 inches

Therefore, the perimeter of the plane figure which is a quadrilateral with four straight sides is equal to 16 inches.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A graphing calculator does this nicely.

The biscuits should be placed 2.54 centimeters apart on the baking tray.

The unitary method is a way for solving a problem by the first value of a single unit and than finding the value by multiplying the single unit. Unitary method is a technique by which we can find the value of a single value from the value of more than one devices and the value of more than one unit from the value of a single unit. We can this method use for most of the calculations in math.

We are given that;

Elana must roll the dough into 7 inch rounds.

a) To convert this measurement to centimeters, we can use the conversion factor 1 inch = 2.54 centimeters. Therefore, 7 inches is equal to:

7 inches x 2.54 centimeters/inch = 17.78 centimeters

So, Elana must roll the dough into 17.78 centimeter rounds.

b) To rewrite all the ingredients using grams or milliliters, we need to know the density of each ingredient. Assuming that the density of each ingredient is the same as that of all-purpose flour (which is approximately 125 grams per cup), we can convert the measurements as follows:

1 cup flour = 125 grams flour

1/2 cup sugar = 100 grams sugar

2 teaspoons baking powder = 10 grams baking powder

1 teaspoon salt = 5 grams salt

1/2 cup cream = 120 milliliters cream (assuming a density of 1 gram per milliliter)

So, the rewritten ingredients are:

125 grams flour

100 grams sugar

10 grams baking powder

5 grams salt

120 milliliters cream

c) The recipe states that the oven should be preheated to 350 °F. To convert this temperature to Celsius, we can use the formula:

Celsius = (Fahrenheit - 32) x 5/9

So, the temperature in Celsius is:

Celsius = (350 - 32) x 5/9 = 176.67 °C

Therefore, Elana should heat the oven to 176.67 °C.

d) The recipe states that the biscuits should be placed on the baking tray 1 inch apart. To convert this measurement to centimeters, we can use the conversion factor 1 inch = 2.54 centimeters. Therefore, the biscuits should be placed on the baking tray:

1 inch x 2.54 centimeters/inch = 2.54 centimeters

Therefore, by unitary method answer will be 2.54 centimeters.

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Answer:

13

Step-by-step explanation:

Given

\(\sqrt{25+144}\)

= \(\sqrt{169}\)

= 13

Answer: Racing $.50

Pinball $.75

Air Hockey $1.50