Find the area of the trapezoid.

( The answer is not 12 )

The exponential function in the form y=a(bˣ) that passes through the points (0,1500) and (1,2250) is y = 1500(1.5ˣ).

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

We are given two points (0,1500) and (1,2250) through which the exponential function passes.

We can substitute these points into the formula y = a(bˣ) to get two equations:

When x=0, y=1500:

1500 = a(b⁰) = a

When x=1, y=2250:

2250 = a(b¹) = ab

We can solve for b by dividing the second equation by the first:

2250/1500 = ab/a

1.5 = b

Now we can substitute b=1.5 and a=1500 into the exponential function equation to get:

y = 1500(1.5ˣ)

Therefore, the exponential function in the form y=a(bˣ) that passes through the points (0,1500) and (1,2250) is y = 1500(1.5ˣ).

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Answer:

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.Adding Casper's 18 marbles, they had a total of 17/6 + 18 = 50/3 marbles.

Answer:If Aaron had ⅙ of the marbles, then Bob had (1/6 + 1/6) + 6 = 2/6 + 6 = 8/3 of the marbles.Together, Aaron and Bob had 1/6 + 8/3 = 17/6 of the marbles.Adding Casper's 18 marbles, they had a total of 17/6 + 18 = 50/3 marbles.Converting to a mixed number, they had 16 2/3 marbles altogether.

The equation Y = x/100 * 11.9 represents the value of the fee on the value of the coins (x) if we use the container machine.

A mathematical assertion that proves the equality of two mathematical expressions is what an equation in algebra means.

For instance, the expressions 3x + 5 and 14 make up the equation 3x + 5 = 14, with the 'equal' sign separating them.

So, we know that the machine charges:

11.9%

Then, the equation that will tell the total charge would be:

Let Y represents the total charge and x be the value of coins.

Then, the equation would be:

Y = x/100 * 11.9

Therefore, the equation Y = x/100 * 11.9 represents the value of the fee on the value of the coins (x) if we use the container machine.

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Correct question:

Many grocery stores have machines that will give you cash for your change but charge a fee. Coinstar machines charge an average fee of 11.9% of your coins' value. Write an equation that models the total fee you pay (y) based on the value of your coins (x) if you use a Coinstar machine.

Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).

As the sample size increases, the t distribution becomes narrower and closer to a normal distribution.

The t statistic for the larger sample size is larger than the t statistic for the smaller sample size, indicating stronger evidence against the null hypothesis.

To calculate the estimated standard error for the larger sample size of n=89:

sM = √(sample variance / sample size)

sM = √(39.7 / 89)

sM= 0.6527

To calculate the t statistic for the larger sample size:

t = (sample mean - population mean) / sM = (16.9 - 16) / 0.6527

t = 1.375

The probability of getting the t statistic or something more extreme for the sample size of n=35 can be found by using the t distribution with degrees of freedom (df) = 34 (n-1). Using the Distributions tool and the given t statistic of 0.85, we find that the probability is approximately 0.2.

The probability of getting the t statistic or something more extreme for the sample size of n=89 can be found by using the t distribution with df=88. Using the Distributions tool and the calculated t statistic of 1.375, we find that the probability is approximately 0.085.

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The events are Not Mutually Exclusive (Inclusive)

The concept of mutually exclusive events is based on the idea that two events cannot occur at the same time. In other words, the occurrence of one event means that the other event cannot happen.

In the case of the jersey example, the events "picking a purple jersey" and "picking a jersey with a number greater than five" are not mutually exclusive because it is possible to pick a jersey that satisfies both conditions (i.e., a purple jersey with a number greater than five).

On the other hand, if the events were mutually exclusive, it would mean that it is impossible for them to happen at the same time. For example, if we modified the scenario to have only yellow jerseys numbered one to five and purple jerseys numbered six to ten, then the events "picking a purple jersey" and "picking a jersey with a number greater than five" would be mutually exclusive, as no jersey can satisfy both conditions.

Therefore, in the original scenario where the bag contains six yellow jerseys numbered one to six and four purple jerseys numbered one to four, the events are not mutually exclusive (inclusive).

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In the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

A sample space is a set of potential results from a random experiment.

The letter "S" is used to denote the sample space.

Events are the subset of possible experiment results.

Depending on the experiment, a sample area could contain a variety of results.

There are just two possible results when we toss a coin: either head or tail.

So, S = H, T, where H is the head and T is the tail, will be the sample space.

As a result, we are aware that there will be a total of 2n outcomes available if there are 'n' coins.

So, the coin has 2 outcomes which are H and T.

And the spinner has 8 outcomes which are 1 - 8.

Then, the sample space would be as follows:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

So, the sample space has a total of 16 elements.

Therefore, in the given situation the sample space has 16 elements and the sample space is:

1H   2H    3H    4H    5H    6H    7H    8H

1T    2T    3T     4T    5T     6T     7T    8T

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Answer:

2.5

Step-by-step explanation:

I took the test :)

The volume of the solid figure compromising of two rectangular prism is derived to be 152 cubic feet.

The volume of a cuboid also known as a rectangular prism can be calculated using the formula:

V = l x w x h

where:

V is the volume of the cuboid

l is the length of the cuboid

w is the width of the cuboid

h is the height of the cuboid

We shall evaluate for the volume of two rectangular prism observed and thus derive the volume of the solid figure by the sum of our results as follows:

Volume of larger cuboid = 5 ft x 4 ft x 4 ft = 80 ft³

Volume of smaller cuboid = 6 ft x 4 ft x ft = 72 ft³

Volume of solid figure = 80 ft³ + 72 ft³ = 152 ft³

Therefore, the volume of the solid figure compromising of two rectangular prism is derived to be 152 cubic feet.

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Answer:

Step-by-step explanation:

Here we have a quadratic polynomial which has a general form:

[tex]ax^2+bx+c[/tex] ;

A quadratic polynomial can be factored into product of two linear polynomials as: [tex](x-a_1)(x-a_2)=x^2-(a_1+a_2)x+a_1\times a_2[/tex] .

In our case [tex]a=1, b=-18, c=-175[/tex].

Which implies that [tex]a_1+a_2=18\ and \ a_1\times a_2=-175[/tex]. Now 25 times -7 is equal to -175 and sum of 25 and -7 is 18 which can perfectly fit our description so we can say that [tex]a_1=-7 \ a_2=25[/tex]. Hence we can factorize our equation as:

[tex](x+7)(x-25)=x^2-18x-175[/tex]

The amount of the Pilipino pesos that we are going to obtain here is 59220.

Direct proportionality is a mathematical relationship between two variables, where an increase in one variable is accompanied by a corresponding increase in the other variable, and a decrease in one variable is accompanied by a corresponding decrease in the other variable. In other words, if two variables are directly proportional, they change in the same direction at the same rate.

Let the Philippines pesos be P and the US dollars be D

P α D

P = kD

k = P/D

k = 44391.90/1050

k = 42.3

Then;

P = 42.3 * 1400

P = 59220

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The vertex of the graph of the given equation y = x² - x - 2 is calculated as: (1/2, -9/4).

To find the vertex of a parabolic function in the form of y = ax² + bx + c, we use the formula x = -b/2a to find the x-coordinate of the vertex.

In this case, the given equation is y = x² - x - 2, so a = 1, b = -1, and c = -2.

Using the formula, we have:

x = -b/2a = -(-1)/(2*1) = 1/2

To find the y-coordinate of the vertex, we substitute this value of x back into the original equation:

y = (1/2)² - (1/2) - 2 = -9/4

Therefore, the vertex of the equation, y = x² - x - 2, is: (1/2, -9/4).

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A) 252 [tex]ft^2[/tex] of carpet will Jairo need for his  trapezoid office.

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here the given trapezoid , Base a = 10ft , Base b= 18ft and Height h = 18ft.

Now using area of trapezoid formula then,

=> Area A = [tex]\frac{a+b}{2}\times h[/tex] square unit.

=> A = [tex]\frac{10+18}{2}\times 18[/tex]

=> A = [tex]\frac{28}{2}\times 18[/tex]

=> A = [tex]14\times18[/tex]

=> A = 252 [tex]ft^2[/tex]

Hence A) 252 [tex]ft^2[/tex] of carpet will Jairo need for his office.

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Answer:

The value for theta is 16.7 degrees and that of alpha is 73.3 degrees.

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions

The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio.

To find alpha, we can take the inverse tangent of both sides of the equation:

tan α = 10/3

tan⁻¹(tan α) = tan⁻¹(10/3)

α = tan⁻¹(10/3)

Using a calculator, we get:

α ≈ 73.3 degrees (rounded to one decimal place)

Therefore, the value of alpha is approximately 73.3 degrees.

To find theta, we can take the inverse tangent of both sides of the equation:

tan θ = 3/10

tan⁻¹(tan θ) = tan⁻¹(3/10)

θ = tan⁻¹(3/10)

Using a calculator, we get:

θ ≈ 16.7 degrees (rounded to one decimal place)

Therefore, the value of theta is approximately 16.7 degrees.\

Step-by-step explanation:

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be the vehicle's speed befοre tο using the brakes was rοughly 352.7256 mph.

The speed (cοmmοnly referred tο as v) οf an οbject is the magnitude οf the change οf its pοsitiοn οver time οr the magnitude οf the change οf its pοsitiοn per unit οf time; it is thus a scalar quantity.

The average speed οf an οbject in an interval οf time is the distance travelled by the οbject divided by the duratiοn οf the interval the instantaneοus speed is the limit οf the average speed as the duratiοn οf the time interval apprοaches zerο. Speed is nοt the same as velοcity.

Here,

The 216-fοοt length οf the car's skid marks is all that is presented tο us. The speed οf the car befοre the brakes were applied can be calculated using the fοrmula s = 24d(1/2), where s is the speed οf the car in miles per hοur (mph) and d is the length οf the skid marks in feet.

When we replace the specified value οf d, we οbtain:

=> s = 24√(216)

=> s = 24(14.6969)

=> s = 352.7256

Thus, the vehicle's speed befοre tο using the brakes was rοughly 352.7256 mph.

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The following functions, for instance, satisfy the given domain and range: (2, 0), (-5, 1), (7, 8), (6, 0), (-7, 8)

Since there are five points in the domain and three points in the range, there is no single function that has the necessary domain and range because there are more points in the domain than in the range.

A function is a collection of ordered pairs where each input belongs to the domain and each output belongs to the range. As a result, a function with the given domain and range must have five ordered pairs, each of which has a number from the domain and a number from the range as the second element.

The following functions, for instance, satisfy the given domain and range: (2, 0), (-5, 1), (7, 8), (6, 0), (-7, 8)

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After 14 years, Bryn will owe £2,109.47, when Bryn takes out a loan of £800 and that debt interest increases by 28% every year.

Determine the annual interest rate: 28%

Convert the interest rate from a percentage to a decimal: 28% ÷ 100 = 0.28

Calculate the total interest owed over 14 years: £800 * 0.28 = £224

Calculate the new loan amount after the first year: £800 + £224 = £1024

Repeat steps 3 and 4 for each subsequent year, using the updated loan amount from the previous year instead of the original loan amount:

The amount owed by Bryn after 14 years can be calculated by multiplying the original loan amount by (1 + the annual interest rate) raised to the power of the number of years:

£800 * (1 + 0.28)¹⁴

= £800 * 1.28¹⁴

= £800 * 2.636849

= £2,109.47

So, Bryn will owe £2,109.47 after 14 years; when Bryn takes out a loan of £800 and that debt interest increases by 28% every year.

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The probability of taking salmon packet  is 5/12.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here Total number of packets = 18

Then the cat eat all tune . Number of tune packets = 6.

Then remaining packet= 18-6 = 12

Now number of salmon packet = 5.

Then probability that it will be salmon is,

=> P = Number of salmon packet/ Total number of remaining packet.

=> P = 5/12.

Hence the probability of taking salmon packet in fraction is 5/12.

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7 is the mode of this dataset since, as we can see, it appears twice.

The most common occurrence of a number, or the one that does so most frequently.

Example: The mode of the digits 4, 2, 4, 3, and 2 is the number 2, which appears three times, more than any other number.

The mode computation is a rather straightforward procedure.

Calculate the frequency with which each number appears in the group after arranging the numbers in the set in any order—from lowest to highest or highest to lowest.

The most frequent mode is the one that appears.

So, we have the dataset:

3, 6, 8, 7, 2, 4, 5, 10, 7, 14

A number of terms repeated:

3 = 1

6 = 1

8 = 1

7 = 2

2 = 1

4 = 1

5 = 1

10 = 1

14 = 1

Since we can see that 7 is repeated twice then, 7 is the mode of this dataset.

Therefore, 7 is the mode of this dataset since, as we can see, it appears twice.

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Correct question:

The gym offers multiple exercise classes per day. The number of people in an exercise class this week is represented in the list.

3, 6, 8, 7, 2, 4, 5, 10, 7, 14

What is the value of the mode for this data set?

A. 14

B. 8

C. 7

D. 3

Applying the triangle proportionality theorem, the measure of side FD in the image is calculated as: FD = 13.6.

The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Use the triangle proportionality theorem to find AB:

AB/BC = AE/ED

Substitute:

AB/12 = 6/9

AB = (12 * 6) / 9

AB = 8

Find CD using the Pythagorean theorem:

CD = √(AC² - AD²)

Substitute:

CD = √(20² - 15²)

CD = 13.2

Since ΔACD ~ ΔDFC, therefore their sides are proportional:

AC/FD= CD/FC

Substitute:

20/FD= 13.2/9

FD= (20 * 9) / 13.2

FD = 13.6

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Answer:

X+5

Step-by-step explanation:

you carry 5 to be corresponding to x

and angles on a straight line add

Answer:

x = 7.5

Step-by-step explanation:

Because the two quadrilaterals formed by the two parallel lines are similar, [tex]\frac{4}{6} =\frac{5}{x}[/tex]

Using cross multiplication, [tex]x = \frac{6*5}{4}[/tex]

Thus, x = [tex]\frac{15}{2}[/tex] = 7.5.

Lorna uses 2.4 cups of flour in each of the 3 different baking recipes.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

If Lorna uses 7.2 cups of flour in 3 different baking recipes, and uses an equal amount of flour in each recipe, we can find the amount of flour she uses in each recipe by dividing the total amount of flour by the number of recipes:

Flour per recipe = Total flour / Number of recipes

Flour per recipe = 7.2 cups / 3 recipes

Flour per recipe = 2.4 cups per recipe

Therefore, Lorna uses 2.4 cups of flour in each of the 3 different baking recipes.

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The inequality that represents c, the number of candles she needs to sell to pay for a visit to Knotts costing $100 when each candle is sold for $5, is expressed as: c ≥ 20.

The inequality c * 5 ≥ 100 is derived from the fact that each candle is sold for $5, so the total amount of money she earns from selling c candles is given by 5c. This amount must be greater than or equal to the cost of the visit, which is $100.

By multiplying both sides of the inequality by 1/5, we get c ≥ 20, which means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

Therefore, the answer is: c ≥ 20.

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Answer:

answer is (C).

Step-by-step explanation:

Substituting y = -x + 2 from the second inequality into the first inequality, we get:

z^2x + 1 < (-x + 2)z^2

Rearranging, we get:

z^2(x + 1) < (-x + 2)z^2 - 1

Dividing both sides by z^2, and noting that z^2 > 0, we get:

x + 1 < (-x + 2) - 1/z^2

Simplifying, we get:

2x < -1/z^2

x < -1/(2z^2)

Therefore, for any value of z, the solution set of the system is the set of all ordered pairs (x, y) where x < -1/(2z^2) and y < -x + 2.

Checking each of the answer choices:

   (-6, 3.5): Not in the solution set, since -6 is not less than -1/(2z^2) for any value of z.

   (-6, -3): Not in the solution set, since -6 is not less than -1/(2z^2) for any value of z.

   (-4, 3): In the solution set, since -4 is less than -1/(2z^2) for any value of z, and 3 is less than -(-4) + 2 = 6.

   (-4, 4): Not in the solution set, since -4 is not less than -1/(2z^2) for any value of z.

Therefore, the ordered pair included in the solution set is (-4, 3), and the answer is (C).

Answer:

Step-by-step explanation:

Given a total expense of $175 for 4 tickets and an included parking fee of $25, you want an equation for the cost of a ticket, and the solution to that equation.

The total cost is the sum of the items that contribute to that total. Here, the 175 total cost is the sum of 25 and the price of 4 tickets. If we let 't' represent the price of a ticket, we can describe this relation by ...

   175 = 25 + 4t . . . . . . equation for the cost of a ticket

This is a 2-step linear equation. The two steps to the solution are ...

  Step 1: isolate the variable term by subtracting the constant

     175 -25 = 25 -25 +4t

     150 = 4t

  Step 2: find the value of the variable by dividing by its coefficient

     150/4 = 4t/4

     37.50 = t

This tells us the cost of a ticket is $37.50.

__

Additional comment

"Write an equation that can be used ..." covers a lot of territory. It is simplest to interpret it to mean "describe the given relationships using one or more equations." You are expected to know how costs are added based on your life experience: the total you pay is the sum of the costs of the individual items.

We could write the equation as ...

  t + t + t + t + 25 = 175

Some cashiers will add every item separately like this. Others will enter the price once and tell how many times that price is part of the total:

  4t +25 = 175

Multiplication was invented for the purpose of simplifying repeated addition.

It is not differential at interval [-2,0].

What is the mean value theorem?

The mean value Theorem basically asserts that there is at least one place where the tangent to the arc is parallel to the secant through its ends for any given planar arc between two endpoints. One of the most significant findings from the serious analysis is this one.

Here, we have

Given: f(x) = [tex]\left \{ {{x^2-x, -2\leq x\leq -1} \atop {2x^2-3x-3, -1 < x\leq 0}} \right.[/tex]

We have to find that the function satisfies the hypotheses of the Mean Value Theorem on the given interval.

We need to check the continuity at -1.

LHL: [tex]\lim_{n \to \ -1} x^2-x[/tex]

= (-1)² -(-1)

= 1 + 1 = 2

RHL:  [tex]\lim_{n \to \ -1} x^2-x[/tex]

= 2(-1)² - 3(-1) -3

= 2 + 3 - 3

= 2

f(-1) = 2

f(x) is continuous at x = -1

Now,

f'(x) = [tex]\left \{ {{2x-1, -2\leq x\leq -1} \atop {4x - 3, -1 < x\leq 0}} \right.[/tex]

LHL: [tex]\lim_{n \to \ -1} 2x - 1[/tex]

= 2(-1) - 1

= -3

RHL: [tex]\lim_{n \to \ -1} 4x - 3[/tex]

= 4(-1) - 3

= -7

∴ LHL ≠ RHL

It is not differential at interval [-2,0]

Hence, it is not differential at interval [-2,0].

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Answer:

Step-by-step explanation:

(x-5)^2 +5=49

(x-5)(x-5)+5=49

x^2-10x+25+5=49

x^2-10x-19 -  quadratic formula

2[tex]\sqrt{11}[/tex]+5 and -2[tex]\sqrt{11}[/tex]+5

Step-by-step explanation:

(x-5)² + 5 =49

(x-5)(x-5) + 5 = 49

(x² - 5x -5x + 25) + 5 = 49

x² - 10x + 25 + 5 = 49

x² - 10x + 30 =49

x² - 10x = 19

x² - 10x - 19 = 0( USING QÜÃDRATÏC FØRMÛLÂ)

2√11 +5 / -2√11 + 5

~~KIM~~