Which problem solving strategy would be best to solve this problem?Austin, Texas is two hours ahead of San Diego, California. If the time in Austin is 1:00 P.M., what time is it in San Diego?A.guess, check and reviseB.use a formulaC.work backwardsD.write an equation

Answer;

Explanation;

Generally, we have the vertex form of a parabola as;

Where, we have the vertex as (-h,k)

So, we proceed now to complete the square

We start by re-arranging and equating to zero as follows;

We divide the coefficient of x by 2, square it and add to both sides of the equation;

From the above, we have h as 5 and k as -10

The vertex which is (-h,k) would be (-5,-10)

Answer:

18

Step-by-step explanation:

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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Explanation:

Use the difference of squares rule

a^2 - b^2 = (a+b)(a-b)

(5d)^2 - 8^2 = (5d+8)(5d-8)

25d^2 - 64 = (5d+8)(5d-8)

Andy would pay $23.94 more in finance charges compared to Brett, given their respective APRs, average daily balances, and monthly percentage rates.

To calculate the monthly percentage rate (MPR) from the given annual percentage rate (APR), we divide the APR by 12.

For Brett:

APR = 12.6%

MPR = 12.6% / 12 = 1.05%

For Andy:

APR = 16.2%

MPR = 16.2% / 12 = 1.35%

Next, we can calculate the finance charge for each individual using the formula: finance charge = average daily balance * MPR.

For Brett:

Finance charge = $7,980 * 1.05% = $83.79

For Andy:

Finance charge = $7,980 * 1.35% = $107.73

To find the difference in the finance charges between Andy and Brett, we subtract Brett's finance charge from Andy's finance charge:

Difference = $107.73 - $83.79 = $23.94

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Answer:

D

Step-by-step explanation:

Edge 2020

The time taken by the barnacle to get back to its starting point is A = 2π seconds

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be represented as r

Now , the value of r = 1 m

And , the boat is traveling at a rate of 1 m/s

where the total path of the barnacle = circumference of the circle

So , the time taken by the barnacle to get back to its starting point A = circumference of the circle / speed of the boat

On simplifying , we get

The circumference of the circle = 2πr = 2π meters

The time taken by the barnacle to get back to its starting point A = ( 2π / 1 )

The time taken by the barnacle to get back to its starting point A = 2π seconds

Therefore , the value of A is 2π seconds

Hence , the time taken for the circular path is 2π seconds

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The complete question is attached below :

The boat is traveling at a rate of 1 meter per second. How long does it take the barnacle to get back to its starting point?

Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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Answer:

To find 29% of 150, we can first express 29% as a decimal by dividing 29 by 100. 29% is the same as 0.29.

Then, we multiply 0.29 by 150 to find the answer:

0.29 * 150 = 43.5

So, 29% of 150 is equal to 43.5.

Here's the work:

29% * 150 = 0.29 * 150 = 43.5

\(\huge\text{Hey there!}\)

\(\mathsf{29\%\ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \times 150}\)

\(\mathsf{= \dfrac{29}{100} \times \dfrac{150}{1}}\)

\(\mathsf{= \dfrac{29(150)}{100(1)}}\)

\(\mathsf{= \dfrac{4,350}{100}}\)

\(\mathsf{= \dfrac{4,350 \div 50}{100 \div 50}}\)

\(\mathsf{= \dfrac{87}{2}}\)

\(\mathsf{= 43 \dfrac{1}{2}}\)

\(\mathsf{= 43.5}\)

\(\huge\text{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{87}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43 \dfrac{1}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43.5}}\huge\checkmark\)

\(\large\text{Either of those should work because they are all equivalent to each}\\\large\text{other}\uparrow\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

Answer:

Step-by-step explanation:

Let x be a random variable representing the number of guesses made for the sat questions.

Since the probability of getting the correct answer to a question is fixed for any number of trials and the outcome is either getting it correctly or not, then it is a binomial distribution. The probability of success, p = 0.2

Probability of failure, q = 1 - p = 1 - 0.2 = 0.8

the probability that the number x of correct answers is fewer than 4 is expressed as

P(x < 4)

From the binomial distribution calculator,

P(x < 4) = 0.97

The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².

From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.

It should be noted that 15% of the material will be:

= 15% × 115.4

= 17.31 ft²

It should be noted that 20% of the material will be:

= 20% × 115.4

= 23.08 ft²

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Answer:

A

Step-by-step explanation:

I just took the test

:>

Answer:

I hope this helps

Step-by-step explanation:

Answer:

\(\displaystyle{f(x)=3^x-5}\)

Step-by-step explanation:

Being translated up-down means that the value exists outside of x. Therefore, we can cancel B and C choice since those are horizontal (left-right) translation.

Our only choice is A and D. However, D is being translated up since it's +5. Thus, the only correct answer that a function is being translated down is:

\(\displaystyle{f(x)=3^x-5}\)

or A choice.

Answer:

Step-by-step explanation:

608,000

you go to thousands look next number left and round up or down and the rest after the thousands becomes zeros

Answer:

A)  Mr. Simpson's class; it has a larger median value 14.5 pencils.

Step-by-step explanation:

A box plot is a visual display of the five-number summary:

From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:

Mr Johnson's class:

Mr Simpson's class:

In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.

The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.

The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).

As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.

In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.

Scenario #2 answered using scenario #1 is :

1. Blocking on the factor of drivers is involved for the layout for this experiment.

2. The statistical model for this experiment is: Yijk = µ + Ti + Bj + Dk + εijk

3. Two columns of the ANOVA table for this experiment is attached as figure.

4. The number of experimental units and the number of observational units is 16.

1. The layout for this experiment involves blocking on the factor of drivers. The four buses will be randomly assigned to the four drivers, and each driver will drive each of the four tire pressures on a different day. Each day, 4 gallons of gas will be used to fuel the four buses.

2. The statistical model for this experiment is:

Yijk = µ + Ti + Bj + Dk + εijk

where Yijk is the observed fuel consumption for the ith tire pressure, jth day, and kth driver, µ is the overall mean fuel consumption, Ti is the effect of the ith tire pressure (i = A, B, C, D), Bj is the effect of the jth day (j = 1, 2, 3, 4), Dk is the effect of the kth driver (k = 1, 2, 3, 4), and εijk is the random error term.

3. Two columns of the ANOVA table for this experiment are:

Source of Variation Degrees of Freedom

Tire Pressure (T)          3

Day (D)                          3

Driver (B)               3

Error                   36

4. The number of experimental units is 16 (4 tire pressures x 4 days), and the number of observational units is also 16, since there is one observation (fuel consumption) for each combination of tire pressure, day, and driver.

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The equation that can be used to find the number of pieces of candy Joey has is j = (315 - 18) / 3 .

Number of candies Sal has = 3(number of candies that Joey has) + 18

315 = 3(j) + 18

Where j represents the number of candies that Joey has.

Given this equation, 315 = 3(j) + 18 , we are to make j the subject of the formula. To do this, take the following steps.

Combine similar terms :

(315 - 18) = 3j

Divide both sides by j

j = (315 - 18) / 3

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Answer:

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is \((x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30\).

Step-by-step explanation:

There are two kew parameters for a sphere: Center (\(h\), \(k\), \(s\)) and Radius (\(r\)). The radius is the midpoint of the line segment between endpoints. That is:

\(C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2} \right)\)

\(C(x,y,z) = (1,-2,4)\)

The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:

\(r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}\)

\(r = 10\sqrt{3}\)

The general formula of a sphere centered at (h, k, s) and with a radius r is:

\((x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}\)

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is \((x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30\).

By answering the presented question, we may conclude that Therefore, 1  expressions cm on the map corresponds to a real distance of 3.2 km. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Scale 1:

320000 means that 1 unit on the map represents his 320000 units in the real world.

To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.

1 kilometer = 100000 cm

So,

1 unit on the map = 320000 units in the real world

1 cm on the map = (1/100000) km in the real world

Multiplying both sides by 1 cm gives:

1 cm on the map = (1/100000) km * 320000

A simplification of this expression:

1 cm on the map = 3.2 km

Therefore, 1 cm on the map corresponds to a real distance of 3.2 km. 

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Answer:

\(\frac{cos^{2} \theta + sin\theta}{cos\theta}\)

Step-by-step explanation:

Solving :

The solution of your question is here :)

Answer:

14 divided by 9 = 1.5

The result of 14/9 is a non-terminating, repeating decimal.

Answer:

1.56 [?]

this question's wording was slightly confusing but I think this is what you meant

Step-by-step explanation:

by dividing the two numbers, (you can use long division or a calculator) while they are not in a fraction state (don't rewrite it as \(\frac{14}{9}\), actually divide

14 by 9) you will end up with a number:

1.55555556

(repeating decimal)

So, you can either write this as 1.5 with a little dash over the 5

Or, you can round the decimal to 1.56 .

(method: by actual division)

The polynomial -6x⁵ - 1/8 - x³ in standard form is -6x⁵ - x³ - 1/8

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

-6x⁵ - 1/8 - x³

To rewrite polynomial in standard form, we order the powers in decreasing order

Using the above as a guide, we have the following:

-6x⁵ - x³ - 1/8

Hence, the polynomial in standard form is -6x⁵ - x³ - 1/8

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Step-by-step explanation:

Let a be the price of 1 adult ticket.

Let c be the price of 1 child ticket.

given,

\(6a + 2c = 124\)

as equation 1,

and

\(3a + 5c = 100\)

as equation 2.

Now we will solve for a and c using elimination method of simultaneous equations.

Now we multiply equation 2 by 2 to eliminate a and solve for c.

\(3a \times 2 + 5c \times 2 = 100 \times 2 \\ 6a + 10c = 200\)

This new equation will be equation 3.

Now we will use equation 1 - equation 3 to eliminate a and solve for c.

\((6a - 6a) + (2c - 10c) = 124 - 200 \\ 0 + ( - 8c) = - 76 \\ - 8c = - 76 \\ c = - 76 \div - 8 \\ = 9.5\)

Now substitute c into equation 2.

\(3a + 5(9.5) = 100 \\ 3a + 47.5 = 100 \\ 3a = 100 - 47.5 \\ 3a = 52.5 \\ a = 52.5 \div 3 \\ = 17.5\)

Therefore one adult ticket will cost $17.50 and one child ticket will cost $9.50.

Step-by-step explanation:

Volume of a cylinder = pi r^2 h      diameter =1.5 ft so r = .75 ft

                                  pi * .75^2 * 25 = 44.18 ft^3

Find price (based on $ 12.09 /ft^3)

44.18 ft^3  *  $  12.09 /ft^3  = $ 534.12

Answer:

Choice D. 17:850

Answer:

D

Step-by-step explanation:

17/7=2.42857142857

multiply 350 by that big number=850 So D

the answer is

option A

Step-by-step explanation:

(2√3)/3