Hilda can run one mile in 7.5 minutes.
Write and solve an equation to
determine how far she can run in 67.5 minutes
minutes.

The linear equation of the line is y = 12x + 33.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = ax + k

Slope = a = 12

Passing through (-3, -3) = (x, y)

-3 = 12 x -3 + k

-3 = -36 + k

k = -3 + 36

k = 33

Now,

The equation of the line is y = 12x + 33

Thus,

y = 12x + 33 is the equation of the line.

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you didnt put a number line tho :/

Answer:

25

Step-by-step explanation:

that one spongebob meme

haha

:(

theres no number line

Answer:

198

Step-by-step explanation:

2(9)(11)

Since you know that r = 9 and t = 11, you can substitute the variables to numbers. Then you just multiply to get 198. Hope this helps :)

Answer:

198

Step-by-step explanation:

Since r=9, replace r with 9 then since t=11 replace t with 11. And multiply all of them together.

To find the ordered triple of digits $(a,b,c)$ in the base 2 representation of the number $n$, we can analyze the given representation \[10110101010101abc110\]

Since $n$ is a multiple of 7, we need to examine the last three digits of the binary representation to determine if they form a multiple of 7 in base 10. In base 10, the value of each digit is determined by its position, with the rightmost digit being in the ones place, the next digit to the left in the twos place, the next digit in the fours place, and so on, doubling with each position.


To determine if this expression is a multiple of 7, we can check if it is divisible by 7 without a remainder. If it is, then the ordered triple of digits $(a,b,c)$ is the solution. Now, let's analyze the expression $c + 2b + 4a$: Looking at the expression, we can see that $c$ has a coefficient of 1, $b$ has a coefficient of 2, and $a$ has a coefficient of 4. To find the possible values of $(a,b,c)$, we need to find the combinations of $(a,b,c)$ that make the expression divisible by 7. Since $c$ has a coefficient of 1, it can only be either 0 or 7, as these are the only values that are divisible by 7.


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Answer:

If an event is affected by previous events then it is a dependent event, while if an event is not affected by the previous event then it is an independent event.

Since we have replaced the card that we first drew from the deck, it wont affect the event of pulling a card second time.

So, we can say that it is an example of independent event.

Answer:

\(x=11\)

Step-by-step explanation:

So we have the equation:

\(\frac{-2-2x}{3} =-8\)

First, multiply both sides by 3. This cancels out the denominator:

\(3(\frac{-2-2x}{3} )=3(-8)\)

The left side cancels. Multiply the right:

\((-2-2x)=-24\)

Add 2 to both sides. The 2s on the left cancel:

\((-2-2x)+2=(-24)+2\\-2x=-22\)

Divide both sides by -2. The -2 on the left cancel.

\((-2x)/-2=(-22)/-2\\x=11\)

Therefore, the answer is 11.

Answer:

x = 11

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:

*(-2-2*x)/(3)-(-8)=0

Simplify:

*-2 - 2x  / 3

Pull out like factors:

*-2 - 2x  =   -2 • (x + 1)

Now It should look like this:

-2 • (x + 1) / 3 - (-8)  = 0

Rewrite the whole as a equivalent fraction using 3 as the denominator:

*-8 = -8 / 1 = -8 • 3 / 3

Add the two equivalent fractions which now have a common denominator

-Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

*-2 • (x+1) - (-8 • 3) / 3 = 22 - 2x / 3

Pull out like factors:

*22 - 2x  =   -2 • (x - 11)

Now you should have this:

*-2 • (x - 11)  / 3  = 0

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

-Now, to get rid of the denominator, multiply both sides of the equation by the denominator.

*-2•(x-11)  / 3 • 3 = 0 • 3

-Now, on the left hand side, the  3  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

Now you should have this:

*-2  •  (x-11)  = 0

Now Solve:

x-11 = 0  

-Add  11  to both sides of the equation:

x = 11

The correct inequality that describes the problem is 4x ≥ 40. Thus, the correct answer is A.

The answer is A because Ms. Wells is ordering 4 large cheese pizzas, and she expects to spend at least $40 on the pizzas. The inequality 4x ≥ 40 represents the total cost of the pizzas, which is 4 times the cost of each pizza (4x) and should be greater than or equal to $40. This inequality tells us that the total cost of the pizzas is at least $40, which is what Ms. Wells expects.

Option B, 4x > 40x, is incorrect because it doesn't make sense mathematically. The right side of the inequality is 40x, which is not related to the problem, and it also doesn't make sense that each pizza will cost 40 dollars.

Option C, 4x ≤ 40, is incorrect because it represents the total cost of the pizzas as less than or equal to $40, which doesn't match with Ms. Wells' expectation that she expects to spend at least $40 on the pizzas.

This question should be provided with answer choices, which are:

The correct answer is A.

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The exponential smoothing forecast for period 5, assuming an alpha (α) value of 0.4, is determined by applying the exponential smoothing formula.

The exponential smoothing formula is given by:

Forecast for period t = α * Actual value for period t + (1 - α) * Forecast for period t-1

In this case, we need the forecast for period 5, so we will use the formula to calculate it based on the available data.

To calculate the exponential smoothing forecast for period 5, we use the given alpha (α) value of 0.4 and the available data for previous periods. The formula considers the actual value for period t and the forecast for the previous period (t-1).

Since we are calculating the forecast for period 5, we need the actual value for period 5 and the forecast for period 4. However, these values are not provided in the given information. Without the actual value for period 5 or the forecast for period 4, it is not possible to provide a specific numerical answer for the exponential smoothing forecast for period 5.

The exponential smoothing technique is commonly used for forecasting, where the alpha (α) value determines the weight given to the most recent observations. A higher alpha value places more weight on recent data, while a lower alpha value gives more weight to historical data. By adjusting the alpha value, the forecast can be adjusted to respond more quickly or more slowly to changes in the data.

To calculate the exponential smoothing forecast for period 5, it is essential to have the necessary data points. With the provided alpha (α) value of 0.4, the formula can be applied once the required data is available.

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Answer:

It is C

Step-by-step explanation: The explanation says that he subtracted 10 by 20 and divided by 5 so the real answer is 18 but the answer in your page is C

Your Welcome :)

Answer:

∠DBC

Step-by-step explanation:

Since ∠ABD shares the same vertex and side with ∠DBC, then they are adjacent angles.

Both sides of the equation are not equal, therefore, Massa was wrong.

For an equation to be correct, the values on both sides of the equation must be equal and balance.

Given the expression, 540 ÷ 6 = 9, 540 divided by 6 is 90. 90 is not equal to 9.

Thus, the value on the both sides are not balanced, therefore, Massa is incorrect.

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Answer:

The equation is 3/10 × s = 162

Alexandra's salary before taxes for the pay period was $540

Step-by-step explanation:

Let

Alexander's salary before taxes

=s

3/10 if Alexander's take home pay is $162 after taxes

3/10 of s = $162

The equation is

3/10 × s = 162

Divide both sides by 3/10

s = 162 ÷ 3/10

= 162 × 10/3

= 1620 / 3

= $540

Alexandra's salary before taxes for the pay period was $540

The value of x that will satisfy the equation is x=-1.

We have given that,

\(\left|x-1\right|=\left|x+3\right|\)

We have to solve the above inequality

Inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.

Find the positive and negative intervals

\(x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1\)

Solve the inequality for each interval

\(x < -3,\:\:-3\le \:x < 1,\:\:x\ge \:1\)

\(\mathrm{No\:Solution}\quad \mathrm{or}\quad \:x=-1\)

Therefore we get,

\(x=-1\)

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Which of the following is an accurate definition for the power of a statistical test is C. The power of a statistical test refers to the probability of rejecting a false null hypothesis. This means that the test is able to correctly identify when there is a significant difference between two groups or conditions.

statistical tests are used to determine whether the results of an experiment are likely due to chance or whether there is a real effect. The null hypothesis states that there is no significant difference, while the alternative hypothesis states that there is. The power of a statistical test refers to the ability of the test to correctly reject the null hypothesis when it is false, and thus support the alternative hypothesis.

, the power of a statistical test is the probability of correctly rejecting a false null hypothesis, which indicates that there is a significant difference between two groups or conditions.

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The selling price of the game is (d) $111.80

The given parameters are:

Discount = 30%

Selling price = $86.00

Since the item is sold less, then the original price would be more.

So, we have:

Price = Selling price * (1 + Discount)

This gives

Price = $86.00 * (1 + 30%)

Evaluate

Price = $111.80

Hence, the selling price is (d) $111.80

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Answer:

1.  Y = -1/4x + 1

3. Y = 2/5x + 1

5. Y = 4/5x + 5

7. Y = -x + 5

9. Y = -5/2x - 16

Step-by-step explanation:

Find the slope using the formula

Use the slope and one of the points to find the y-intercept

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

Answer:

vertical angles

Step-by-step explanation:

They don't share a common side, so they are not adjacent!

Hope that helps!

Answer:

58 weeks

Step-by-step explanation:

Water tank A = 522 - 4x

Water tank B = 696 - 7x

Where,

x = number of weeks

Equate both equations

522 - 4x = 696 - 7x

Collect like terms

522 - 696 = -7x + 4x

-174 = -3x

Divide both sides by - 3

x = -174/-3

x = 58 weeks

The amount of water in the two tanks will be the same in 58

weeks

Answer:

9.30 × 10⁰ bro that was so easy

The correct option is D. Behavioral economics studies the influence of cognitive biases and irrational decision-making on consumer behavior.

Behavioral economics combines insights from psychology and economics to understand how individuals make choices that deviate from the assumptions of classical economics. It recognizes that human behavior is often influenced by emotions, cognitive biases, and heuristics.

leading to deviations from rational decision-making. Behavioral economists study these behavioral patterns to develop more realistic models and theories that better capture the complexities of decision-making in real-world situations.

By incorporating psychological factors into economic analysis, behavioral economics provides a broader understanding of human behavior and its implications for economic outcomes.

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Remove the brackets.

Take the like terms closer.

Now do the addition and subtraction

Let us split the middle term

Now take x as common from the first two terms and -1 from the next two terms.

Answer:

(x - 1)(7x + 12)

Hope you could understand.

If you have any query, feel free to ask.

Solve (6x² + 5x - 3) + (x² - 9)

(x-1) (7x+12)

please look at the attached picture :)

Answer:

the input is the number or gallons aka b

the output is the balance in the account aka c

and the two points described are (5,442) and (13,226) aka c

Step-by-step explanation:

i did it on edge and got it right :)

Answer:

here the answer

Step-by-step explanation:

Therefore, the second Taylor polynomial for the function \(f(x) = e^x * cos(x)\) about x₀ = 0 is p₂(x) = 1 + x.

To find the second Taylor polynomial for the function \(f(x) = e^x * cos(x)\) about x₀ = 0, we need to find the values of the function and its  derivatives at x₀ and then construct the polynomial.

Let's start by finding the first and second derivatives of f(x):

\(f'(x) = (e^x * cos(x))' \\= e^x * cos(x) - e^x * sin(x) \\= e^x * (cos(x) - sin(x)) \\f''(x) = (e^x * (cos(x) - sin(x)))' \\= e^x * (cos(x) - sin(x)) - e^x * (sin(x) + cos(x)) \\= e^x * (cos(x) - sin(x) - sin(x) - cos(x)) \\= -2e^x * sin(x) \\\)

Now, let's evaluate the function and its derivatives at x₀ = 0:

\(f(0) = e^0 * cos(0) \\= 1 * 1 \\= 1 \\f'(0) = e^0 * (cos(0) - sin(0)) \\= 1 * (1 - 0) \\= 1\\f''(0) = -2e^0 * sin(0) \\= -2 * 0 \\= 0\\\)

Now, we can construct the second Taylor polynomial using the values we obtained:

p₂(x) = f(x₀) + f'(x₀) * (x - x₀) + (f''(x₀) / 2!) * (x - x₀)²

p₂(x) = 1 + 1 * x + (0 / 2!) * x²

p₂(x) = 1 + x

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The second Taylor polynomial P2(x) for the function f(x) = e^x * cos(x) about x0 = 0 is P2(x) = 1 + x.

To find the second Taylor polynomial, denoted as P2(x), for the function f(x) = e^x * cos(x) about x0 = 0, we need to calculate the function's derivatives at x = 0 up to the second derivative.

First, let's find the derivatives:

f(x) = e^x * cos(x)

f'(x) = e^x * cos(x) - e^x * sin(x)

f''(x) = 2e^x * sin(x)

Now, we can evaluate the derivatives at x = 0:

f(0) = e^0 * cos(0) = 1 * 1 = 1

f'(0) = e^0 * cos(0) - e^0 * sin(0) = 1 * 1 - 1 * 0 = 1

f''(0) = 2e^0 * sin(0) = 2 * 0 = 0

Using the derivatives at x = 0, we can construct the second Taylor polynomial, which has the general form:

P2(x) = f(0) + f'(0) * x + (f''(0) / 2!) * x^2

Plugging in the values, we get:

P2(x) = 1 + 1 * x + (0 / 2!) * x^2

= 1 + x

Therefore, the second Taylor polynomial P2(x) for the function f(x) = e^x * cos(x) about x0 = 0 is P2(x) = 1 + x.

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The ratio of false positives to true positives is 8 over 54.

According to the Question

Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.

We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.

We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.

As a result, the ratio becomes 8% / 54%, or 8/54.

It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.

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If a theater charges $8 for an adult ticket and $6 for a children's ticket on a certain day. The amount of children tickets that were sold than adult tickets is 175 tickets.

Let A represent  the number of adults' tickets sold

Let C represent the number of children's tickets sold.

We know that A + C = 225 and  8A + 6C = 1850 now let combine the two equations to solve for one of the variables.

A + C = 225, A = 225 – C

Plug the value into the second equation and solve for C:

8(225– C) + 6C = 1850

1800 – 8C + 6C = 1850

1800 – 2C = 1850

1800 – 1850 = 2C

50 = 2C

Divide both side by 2C

C=50/2

C=25 children tickets sold

Adult tickets sold=225-25

Adult tickets sold=200 tickets

Hence,

Number of children ticket sold than adult tickets= 200-25

Number of children ticket sold than adult tickets= 175 tickets

Therefore the amount of children tickets that were sold than adult tickets is 175 tickets.

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Answer:

9.8

Step-by-step explanation:

To prove the angles congruent by SAS, you need to know that two sides of one triangle are congruent to two sides of another triangle, and the included angle between the congruent sides is congruent.

To prove that angles are congruent by SAS (Side-Angle-Side), you must know the following:

1. Side: You need to know that two sides of one triangle are congruent to two sides of another triangle.
2. Angle: You need to know that the included angle between the two congruent sides is congruent.

For example, let's say we have two triangles, Triangle ABC and Triangle DEF. To prove that angle A is congruent to angle D using SAS, you must know the following:

1. Side: You need to know that side AB is congruent to side DE and side AC is congruent to side DF.
2. Angle: You need to know that angle B is congruent to angle E.

By knowing that side AB is congruent to side DE, side AC is congruent to side DF, and angle B is congruent to angle E, you can conclude that angle A is congruent to angle D.

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