Trey is driving to Philadelphia. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Trey has 69 miles
to his destination after 15 minutes of driving, and he has 47.4 miles to his destination after 39 minutes of driving. How many miles will he have to his
destination after 51 minutes of driving?

Answer:

x = - 1 , x = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

assuming you require the solution to the equation

x(3x - 1) + (3x - 1) = 0 ← factor out (3x - 1) from each term

(3x - 1)(x + 1) = 0

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

3x - 1 = 0 ( add 1 to both sides )

3x = 1 ( divide both sides by 3 )

x = [tex]\frac{1}{3}[/tex]

As per the conversion factor, the amount of laundry detergent in liter is 5.5 liters (option b).

When we want to convert units from one measurement system to another, we use something called a conversion factor. A conversion factor is a ratio that expresses the relationship between two different units of measurement. In this case, we want to convert milliliters (mL) to liters (L).

The conversion factor we need to use is:

1 liter = 1000 milliliters

This means that there are 1000 mL in one liter. We can use this conversion factor to convert 5,500 mL to liters.

To do this, we need to set up a ratio using the conversion factor:

5,500 mL * (1 L/1000 mL)

The units of milliliters cancel out, leaving us with liters:

5,500/1000 = 5.5 L

So the answer is 5.5 liters.

Hence the correct option is B.

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If the boxes are all stacked on top of each other, what is their combined height is 11/8

Height of large box = 7/8m

Height of medium box = 2/6m shorter than large box

Height of small box = 1/4m shorter than the medium box

Calculating the height of the medium and small boxes.

Medium box height x large box height

= 2/6 × 7/8

= 7/24

Since, the small box is 1/4 of a meter shorter than the medium box, therefore its height -

= 7/24 - 1/4

= 5/24

Calculating the height of three boxes -

7/8 + 7/24 + 5/24

= 21/24 + 7/24 + 5/24

= 33/24

= 11/8

Correct Question:

Lupe measured the height of three rectangular prisms she was using to pack up some clothing. The large box was 7/8 of a meter tall. The medium box was 2/6 shorter than the large box. The small box was 1/4 of a meter shorter than the medium box. If the boxes are all stacked on top of each other, what is their combined height?

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The final answer is: cos(α + β) = (3i - √190) / 10.

\( \alpha \) and \( \beta \) are first quadrant angles with \( \cos (\alpha)=\frac{\sqrt{5}}{10} \) and \( \sin (\beta)=\frac{\sqrt{10}}{10} \). We must now compute \( \cos (\alpha+\beta) \).Solution:Given, α and β are the first quadrant angles with:cos(α) = √5 / 10 (1)sin(β) = √10 / 10 (2)We know that sin2θ + cos2θ = 1Also, we know sin(θ1 + θ2) = sinθ1 cosθ2 + cosθ1 sinθ2cos(θ1 + θ2) = cosθ1 cosθ2 - sinθ1 sinθ2Now, we will compute:cos2α = 1 - sin2αcos2α = 1 - [sin(α)]2cos2α = 1 - [1 - cos2α]cos2α = 2cos2α - 1cos2α = (2cos2α - 1) / 2Putting the value of cos(α) from (1), we get:cos2α = (2 × (√5 / 10)2 - 1) / 2cos2α = (5 / 25 - 1) / 2cos2α = -3 / 25cosα = √(-3 / 25)cosα = i√3 / 5Similarly, we can compute the value of sinβ by squaring equation (2).cos2β = 1 - sin2βcos2β = 1 - [sin(β)]2cos2β = 1 - [10 / 100]cos2β = 9 / 10cosβ = √(9 / 10)cosβ = 3√10 / 10Now, we can find the value of sinα from equation (1) by squaring it:cos2α + sin2α = 1sin2α = 1 - cos2αsin2α = 1 - (5 / 100)sin2α = 95 / 100sinα = √(95 / 100)sinα = √19 / 10We have, cos(α + β) = cosα cosβ - sinα sinβNow, we will plug in the values we computed:cos(α + β) = (i√3 / 5) × (3√10 / 10) - (√19 / 10) × (√10 / 10)cos(α + β) = 3i / 5 - √190 / 100cos(α + β) = (3i - √190) / 10The final answer is: cos(α + β) = (3i - √190) / 10.

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Answer:

  C. The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.

Step-by-step explanation:

You want to know the transformations needed to form g(x) = 1/2(x+4)^2 -3 from f(x) = x^2.

The transformations ...

  f(x) ⇒ g(x) = c·f(x -h) +k

represent vertical expansion by a factor of 'c', right shift by 'h' units, and an upward shift of 'k' units.

Here, we have c=1/2, h=-4, k=-3. These mean the function f(x) has been vertically compressed to 1/2 its original height, and shifted left 4 and down 3.

The vertical compression will cause the graph to appear to be wider for any given distance above the vertex.

Step-by-step explanation:

4. 2/ 15 x 45/1 = 90/15

=6inches

( 15 is the total of the ratio)

5. Sum of angles in a triangle in 180

Total of the ratio is 17+16+12 = 45

Largest angle is 17/ 45 x180/1 = 68 degree

Ans 68degrees

6. 2x + 7/ 3x - 4 = 11/2

Cross multiply

2( 2x + 7) = 11(3x - 4)

Expand the equation

4x +14 = 33x - 44

Subract 4x from both sides

14 = 29x - 44

Add 44 to both sides

58 =29x

Divide both sides by 29

X =2

The equation of the line that is parallel to the line y = x 4 and passes through the point (6, 5) is y = x - 1

The line y = x + 4 has a slope of 1 because it is in the form y = mx + b, where m is the slope of the line. To find a line parallel to this line, we need to use the same slope of 1.

Now, we can use the point-slope form of a linear equation to find the equation of the line that passes through the point (6, 5) with a slope of 1:

y - y1 = m(x - x1)

where m = 1, x1 = 6, and y1 = 5.

Plugging in the values, we get:

y - 5 = 1(x - 6)

Simplifying, we get:

y - 5 = x - 6

y = x - 1

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Answer:

To solve the equation 3x + 5y = 500 for x, we need to isolate x on one side of the equation. First, we can subtract 5y from both sides to get 3x = 500 - 5y. Then, we can divide both sides by 3 to get x = (500 - 5y) / 3.

It might be helpful to rewrite the equation in terms of one variable if we want to solve for one unknown quantity in terms of another. In this case, rewriting the equation in terms of x allows us to see how many child tickets the school needs to sell to raise exactly $500, given any number of adult tickets sold. This can be useful in planning and budgeting for the carnival.

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

We Know

(6x + 3) + (7x - 44) = 180°

Let's solve

6x + 3 + 7x - 44 = 180

13x - 41 = 180

13x = 221

x = 17°

So, x = 17°

The length that is οver οr cοmparable tο 40 albeit less than 45 is denοted by the expressiοn "40 ≤ y < 45". Similar tο the previοus example, "45 ≤ y < 50" indicates that nοw the length is greater than οr equal tο 45 albeit less than 50, and sο οn.

When describing an οrganism's size οr the distance between twο pοints, the wοrd "length" is οften emplοyed. Fοr instance, the table belοw reveals actual length οf a ruler.

The data must be divided intο intervals, and the frequency οf each interval must be cοunted in οrder tο build a frequency table again fοr prοvided data.

We οbtain the fοllοwing results using a 5-interval size:

40 ≤ y < 45: 1 value (42)

45 ≤ y < 50: 4 values (45, 47, 48, 50)

50 ≤ y < 55: 2 values (50, 55)

55 ≤ y < 60: 3 values (57, 59, 60)

Sο, the fοllοwing is the frequency chart fοr the prοvided data:

Length (cm)                    Frequency

40 ≤ y < 45                         1

45 ≤ y < 50                         4

50 ≤ y < 55                         2

55 ≤ y < 60                         3

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[tex]4.25[/tex]π cm is the width of an arcs with such a central [tex]45-[/tex]degree angle and a circle with a diameter of [tex]289 cm^{2}[/tex] .

It doesn't have any sides or corners either. A circle, then, is a full entity unto itself. Nothing else can be tacked on to complete the circle. Due of this, circles are used as symbols for wholeness, perfection, totality, and heavenly symmetry and equilibrium.

A circle is indeed a closed arc that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre.

[tex]A =[/tex] π[tex]r^2[/tex]

Given that the circle's area is [tex]289 cm^{2}[/tex], we can use the following formula to find the radius:

289π = π

[tex]r^{2} = 289[/tex]

[tex]r = 17 cm[/tex]

With the radius now known, we can apply the following formula to determine the length of an arc with a central angle of [tex]45[/tex] degrees:

[tex]L = (45^{0} / 360^{0} ) * 2pi(17)[/tex]

[tex]L = (1/8) * 34[/tex]π

[tex]L = 4.25[/tex]π cm

A circle with an area of [tex]289 cm^{2}[/tex], [tex]4.25[/tex]π cm is the length of an arc with a central angle of [tex]45[/tex]degrees.

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Answer:

x = 75°

Step-by-step explanation:

In a cyclic quadrilateral, opposite angles are supplementary.

               x + 105 = 180

Subtract 105 from both sides,

                       x = 180 - 105

                      [tex]\boxed{\bf x = 75^\circ}[/tex]

The factor that f increases by when the exponent increases is :

When the exponent x increases by 1, the function value increases by a factor of 3. When the exponent x increases by 2, the function value increases by a factor of 9.

When the exponent x increases by 1/2, the function value increases by a factor of √3. We can see this by evaluating as follows :

= (3^ ( 1 / 2 ) )

= √3

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After solving the given numbers with (PEMDAS) 11 - 11 x 11 + 11 = we get the answer of -88.

To solve 11-11x11+11, we need to use the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:

Parentheses

Exponents

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

Using this order of operations, we can simplify the expression as follows:

11 - 11 x 11 + 11

= 11 - 121 + 11 (since multiplication should be done before addition and subtraction)

= -99 + 11

= -88

Therefore, the value of 11-11x11+11 is -88.

In general, when simplifying expressions, it is important to follow the order of operations to ensure that you get the correct answer. Additionally, it is always a good idea to check your work by plugging the answer back into the original expression and making sure that it is correct.

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According the given question the side οf the WY is 25.

Angle-Side-Angle cοngruence rule is referred tο as ASA. Twο triangles are said tο be cοngruent accοrding tο this rule if any twο angles and the side included between them οf οne triangle are equal tο the cοrrespοnding angles and the included side οf the οther triangle.

See if the twο triangles given, ABC and XYZ, are cοngruent accοrding tο the ASA rule by lοοking at the image prοvided belοw. Accοrding tο the ASA cοngruence rule, twο triangles are said tο be cοngruent if twο οf their respective sides and angles are equal tο thοse οf twο οther triangles and their respective sides and angles, respectively.

BC = BD

m< B=13x-35

m < C = 5x-19

m < D = 2x + 14

m< B=13*11 - 35

m< B=143-35

m< B = 108

m<C=5x-19

m<C=511 - 19

m < C = 55-19

m < C = 36

This is sο because the theοrem οf SAS (Side-Angle-Side)

Sο, we have:

9x117x - 3

WY = 7x-3

WY = 7*4-3

WY = 28-3

WY = 25

Hence the side οf the WY is 25.

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On solving the provided question we cans ay that function  In the auction, 180 carrots cost £18.00.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

The initial cost of 20 carrots was £2.80. Thus the cost per carrot is £2.80 20 = £0.14.

If the price is decreased by 30%, the new carrot price is: £0.14 - (30% £0.14) = £0.098 or £0.10 (rounded to the nearest penny)

As a result, 180 carrots at the current sale price will cost: 180 £0.10 = £18.00

In the auction, 180 carrots cost £18.00.

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The value of 'x' for the given equation is found as: x = 14.

The given equation is-

- 3x = 4*7 - 5x

Simplifying:

- 3x = 28 - 5x

Collect variables on one side and constants on other side.

-3x + 5x = 28

Subtracting the variables:

2x = 28

Dividing both sides by 2.

x = 14

Thus, the value of 'x' for the given equation is found as: x = 14.

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The correct question is-

Find x.

- 3x = 4*7 - 5x

The food will therefore be plenty for 60 days. The assumption that the rate of food consumption will remain constant during the provision should be noted as it may not be totally accurate in real-world scenarios.

Mathematically, this can be expressed as:

240 x 50 = C x D

The result of simplifying the left side of the equation is:

12000 = C x D

40 kids left the motel after 10 days, leaving the following number of kids:

240 - 40 = 200

Now, we can calculate how many days the remaining food will endure for 200 kids using the same proportionality equation:

12000 = 200 x D

The result of multiplying both sides of the equation by 200 is:

D = 12000/200 = 60

The food will therefore be plenty for 60 days.

The assumption that the rate of food consumption will remain constant during the provision should be noted as it may not be totally accurate in real-world scenarios.

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Step-by-step explanation:

she has x money at the beginning.

(3/4)x = dictionary

the remainder is (1/4)x.

1/2 of that (1/4 × 1/2 = 1/8) is the calculator.

that means she has (1/4)x - (1/8)x = (1/8)x left.

the dictionary is $30 more than the calculator.

so,

(3/4)x = (1/8)x + 30

(6/8)x = (1/8)x + 30

(5/8)x = 30

5x = 240

x = 240/5 = $48

so, the dictionary cost

(3/4)x = (3/4)×48 = 3×12 = $36

The instantaneous rate of change at x=1.

In mathematics, a function is a relation between sets that assigns to each element of a given set, exactly one element of a related set. This relationship between two sets is called a mapping, and it is commonly represented using a function notation. Functions are used to describe mathematical relationships and are studied extensively in mathematics, computer science, and other related fields.

The instantaneous rate of change at x=1 can be estimated using the concept of derivatives. A derivative is a mathematical operation that measures the rate at which a function changes with respect to its input. In this case, the derivative of the given function will measure the rate at which the function changes with respect to the input x=1.

The derivative of a function can be calculated using the formula:

f′(x)=limh→0[f(x+h)-f(x)]/h

Where f′(x) is the derivative of the function, f(x) is the function, and h is a small number close to zero.

To calculate the derivative of the function at x=1, we can plug in x=1 into the formula:

f′(1)=limh→0[f(1+h)-f(1)]/h

By calculating this limit, we can estimate the instantaneous rate of change at x=1.

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The exponential function of the scenario is [tex]C(t) = C_0 * e^{(r\times t)}[/tex]

To achieve this goal, we need a mathematical model that relates cigarette consumption to time. One such model is the following exponential function:

[tex]C(t) = C_0 * e^{(r\times t)}[/tex]

Here, C_0 is the initial cigarette consumption, r is the growth rate, and t is the time variable. This model assumes that cigarette consumption grows exponentially over time.

We can use this model to predict cigarette consumption at any given time t.

To find the year in which cigarette consumption reaches C_goal, we need to solve for t_goal in the equation above. That is, we need to find the value of t for which C(t) = C_goal. To do this, we can rearrange the equation above and solve for t:

[tex]t_{goal} = (1/r) \times ln(C_{goal}/C_0)[/tex]

Here, ln denotes the natural logarithm. This equation gives us the value of t for which cigarette consumption reaches the goal amount C_goal.

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Complete Question:

The goal of the exercise is to find the year in which cigarette consumption reach. Define the function for the given scenario?

At Games Galore Super Store, you would pay $42 to purchase the latest video game.

The term "purchase" typically refers to the act of buying something, usually with money or some other form of payment. When you make a purchase, you acquire ownership or possession of the item or service that you have bought. Purchases can range from everyday items like food and clothing to larger investments like a car or a house.

If the wholesale price of a video game is $30.00 and the markup rate at Games Galore Super Store is 40%, then the store will sell the game at a price equal to:

$30.00 + (40% * $30.00) = $30.00 + $12.00 = $42.00

Therefore, you would pay $42.00 to purchase a video game at Games Galore Super Store.

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P(female or grade 11) = 31/34

Given that a classroom has 23 grade twelves (13 females and 10 males) and 11 grade elevens (7 females and 4 males). The teacher randomly chooses a student at random, what is the probability that it is a female or a grade eleven?The sample space is the total number of students which is given by23 + 11 = 34.There are 13 females in the grade 12 and 7 females in the grade 11. So the total number of female students is 13 + 7 = 20.There are 11 grade 11 students. So the total number of grade 11 students is 11.The total number of students that are female or in grade 11 is obtained by adding the two:20 + 11 = 31.So the probability of choosing a female or grade 11 student is:P(female or grade 11) = 31/34

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Therefore , the solution of the given problem of expressions comes out to be Sebastian strolled his dog for 4/5 of the allotted time today.

Calculations like arbitrary division, joining, multiplication variable , and removal are required. If they were merged, they would produce the following: A mathematical formula, some data, and an equation. A declaration of veracity is made up of values, elements, formulae, and mathematical operations like additions, subtractions, errors, and segments. It is possible to assess and analyse words and sentences.

Here,

You can calculate how much of the allotted time Sebastian spent walking his dog today by dividing the time he spent walking him (20 minutes) by the time he was meant to walk him (25 minutes).

Therefore, the division formula that represents this portion is:

=> 20 ÷ 25

The short form of this phrase is:

=>  4/5

As a result, Sebastian strolled his dog for 4/5 of the allotted time today.

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Option D has the correct direction of the alternative hypothesis but uses the sample proportion in the null hypothesis.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The appropriate hypotheses for this test are:

H0: p = 0.28 (the proportion of all high school students who work a part-time job during the school year is 0.28)

Ha: p > 0.28 (the proportion of all high school students who work a part-time job during the school year is greater than 0.28)

This is because the guidance counselor is interested in whether the proportion of all high school students who work part-time jobs during the school year is greater than 0.28, which was the proportion a decade ago. The null hypothesis states that the proportion is 0.28, and the alternative hypothesis states that it is greater than 0.28. Since the alternative hypothesis is one-sided (greater than), this is a one-tailed test.

Option B correctly states the null and alternative hypotheses with the appropriate population proportion in the null hypothesis and the direction of the alternative hypothesis. Options A and C use the sample proportion instead of the population proportion in the null hypothesis. Therefore, Option D has the correct direction of the alternative hypothesis but uses the sample proportion in the null hypothesis.

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Answer: The Answer is B!

Step-by-step explanation:

EDGE 2023

The relationship between the following pairs of angles.

a. ∠ BOD and ∠ DOA are linear pairs

D. ∠ COB and C. ∠ BOC and ∠ COA are linear pairs

Linear pairs are two adjacent angles formed when two straight lines intersect.

The two angles in a linear pair are always supplementary, which means they add up to 180 degrees.

In other words, if one angle in a linear pair measures x degrees, then the other angle measures (180 - x) degrees. Linear pairs are useful in geometry and often used in proofs and problem-solving.

In the problem, the pairs

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The inequality used for number line will be $12 < price < $20.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Hence, on a number line, we can say that the value of numbers grows as we move to the right. This indicates that there are more numbers on the right than on the left. For instance, 3 comes after 1, hence 3 > 1.

The price will lie in the following inequality -

$12 < price < $20

Below is the number line for the same -

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It would take the apprentice alone 11 hours to complete a kitchen island, the same amount of time it took the cabinet maker and apprentice together.

When the cabinet maker and apprentice work together, they are able to complete the kitchen island in 8 hours. This implies that the apprentice is able to do their portion of the work in 3 hours, while the cabinet maker does their portion in 8 hours. Therefore, if the apprentice were to work on the kitchen island alone, it would take them 11 hours to complete it, the same amount of time it took the cabinet maker and apprentice together. This is because the apprentice does not have the same level of experience and expertise as the cabinet maker, so they are not able to complete the same amount of work in the same amount of time as the cabinet maker. The cabinet maker is able to work faster and more efficiently, which is why they are able to complete the kitchen island in 8 hours, while the apprentice would need 11 hours to complete the same task.

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Answer:

a) To calculate the total amount to be repaid, we need to add the interest to the principal amount.

The formula for simple interest is:

I = P * r * t

where I is the interest, P is the principal amount, r is the interest rate per year, and t is the time in years.

In this case, P = $9000, r = 12% = 0.12, and t = 5 years.

So, the interest on the loan is:

I = $9000 * 0.12 * 5 = $5400

The total amount to be repaid is:

Total amount = Principal + Interest = $9000 + $5400 = $14400

Therefore, the total amount to be repaid is $14,400.

b) To calculate the monthly repayment amount, we need to divide the total amount to be repaid by the number of months in 5 years (60 months), since the repayments are spread equally over 5 years.

Monthly repayment amount = Total amount to be repaid / Number of months

= $14,400 / 60

= $240

Therefore, the monthly repayment amount if the repayments are spread equally over the 5 years is $240.