how do i check 160 = 7x + 6
i found the answer (x = 22) i just need help with the check part!

Answer:

To be a function a graph must pass the vertical line test and the only one that does this is the bottom right one.

Answer:

Bottom Right

Step-by-step explanation:

A function has only one y value for every x value. The upper left graph has many y values for the x value of 1, the bottom left graph has two y values for each x value and so does the upper right graph. the Bottom right graph is the only option with one y value for every x value.

The perimeter  of the triangle ABC is 8 + 6√2 + 2√10 while the area of the triangle ABC is 4√(5)√(3).

To find the perimeter and area of triangle ABC, we can use the distance formula to calculate the lengths of the sides.

The distance formula is given by:

Distance = \(\sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the lengths of the sides first:

Side AB:

x1 = -2, y1 = 2 (coordinates of A)

x2 = 6, y2 = 2 (coordinates of B)

Distance_AB = √((6 - (-2))² + (2 - 2)²)

           = √(8² + 0²)

           = √(64)

           = 8

Side BC:

x1 = 6, y1 = 2 (coordinates of B)

x2 = 0, y2 = 8 (coordinates of C)

Distance_BC = √((0 - 6)² + (8 - 2)²)

           = √((-6)² + 6²)

           = √(36 + 36)

           = √(72)

           = 6√2

Side CA:

x1 = 0, y1 = 8 (coordinates of C)

x2 = -2, y2 = 2 (coordinates of A)

Distance_CA = √((-2 - 0)² + (2 - 8)²)

           = √((-2)² + (-6)²)

           = √(4 + 36)

           = √(40)

           = 2√10

Now that we have the lengths of the sides, we can calculate the perimeter:

Perimeter = AB + BC + CA

         = 8 + 6√2 + 2√10

To calculate the area, we can use the formula for the area of a triangle given its side lengths, which is Heron's formula:

Area = \(\sqrt{s(s - AB)(s - BC)(s - CA)}\)

where s is the semiperimeter of the triangle, given by:

s = (AB + BC + CA) / 2

Substituting the values:

s = (8 + 6√2 + 2√10) / 2

Now we can calculate the area:

Area = √(s(s - AB)(s - BC)(s - CA))

= √(((8 + 6√2 + 2√10) / 2) * (((8 + 6√2 + 2√10) / 2) - 8) * (((8 + 6√2 + 2√10) / 2) - 6√2) * (((8 + 6√2 + 2√10) / 2) - 2√10))

To simplify the expression, we can perform the calculations step by step:

Area = √((8 + 6√2 + 2√10) / 2 * (-8) * (6√2) * (2√10))

= √((8 + 6√2 + 2√10) * (-8) * 6√2 * 2√10)

= √((-8)(6)(2)(8)(2)(√2)(√10)(√2)(√10))

= √((-8)(6)(2)(8)(2)(2)(10))

= √(-2⁵ * 3 * 5)

= 4√(5)√(3)

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Answer:

I think the answer would be F(7) ,because :

Step-by-step explanation:

2 < 4 -> |8-2| + 6 = 12

7 ⩾ 4 -> 15

15>12 .

Using simple unitary method and expanding the provided mixed fractions, The answer is 1/3 glass of water in one hour.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

4/5 of 10-ounce glass is 8 ounce of water.

\(2\frac{2}{5} \\=\frac {12}{5}\\=2.4\)

8 ounce of water in 2.4 hours.

8/2.4 ounce of water in 1 hour.

3.33 ounce of water in an hour.

1 glass consist of 10 ounce of water.

1/10 glass consist of 1 ounce of water.

3.33/10 glass consist of 3.33 ounce of water.

1/3 is the final answer.

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================================================

Work Shown:

One way to express exponential form is to use

y = a*b^x

where 'a' is the initial value and 'b' is linked to the growth rate.

Since we're told 34 bees are there initially, we know a = 34.

Then after 4 days, we have 48 bees. So we can say,

y = a*b^x

y = 34*b^x

48 = 34*b^4

48/34 = b^4

24/17 = b^4

b^4 = 24/17

b = (24/17)^(1/4)

b = 1.090035

Which is approximate.

The function updates to

y = a*b^x

y = 34*(1.090035)^x

------------------------

As a way to check to see if we have the right function, plug in x = 0 and we find:

y = 34*(1.090035)^x

y = 34*(1.090035)^0

y = 34*(1)

y = 34

So there are 34 bees on day 0, ie the starting day.

Plug in x = 4

y = 34*(1.090035)^x

y = 34*(1.090035)^4

y = 34*1.4117629

y = 47.9999386

Due to rounding error we don't land on 48 exactly, but we can round to this value.

We see that after 4 days, there are 48 bees.

So we confirmed the correct exponential function.

------------------------

At this point we can find out how many bees there are expected to be after 20 days.

Plug in x = 20 to get

y = 34*(1.090035)^x

y = 34*(1.090035)^20

y = 190.672374978452

Round to the nearest whole number to get 191.

There are expected to be roughly 191 bees on day 20.

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

96% confidence interval for the population mean life of light bulbs produced by the electrical firm to be between 747.63 and 812.37 hours. This can be answered by the concept of standard deviation.

To calculate the confidence interval, we first need to determine the standard error of the mean, which can be calculated using the formula:

Standard Error of Mean = (Standard Deviation of Population) / sqrt(Sample Size)

In this case, the standard deviation of the population is given as 40 hours, and the sample size is 30. Thus, the standard error of the mean can be calculated as:

Standard Error of Mean = 40 / sqrt(30) = 7.32

Next, we need to find the critical value of t for a 96% confidence level with 29 degrees of freedom (n-1). Using a t-distribution table or calculator, we find this to be 2.048.

Using these values, we can calculate the confidence interval using the formula:

Confidence Interval = Sample Mean +/- (Critical Value * Standard Error of Mean)

Substituting the given values, we get:

Confidence Interval = 780 +/- (2.048 * 7.32) = 780 +/- 15.02

Therefore, the 96% confidence interval for the population mean life of light bulbs produced by the electrical firm is between 747.63 and 812.37 hours. This means we can be 96% confident that the true mean life of all light bulbs produced by the firm falls within this interval.

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Answer:

3

Step-by-step explanation:

3, 6, and 9 are all divisible by 3. And it's the lowest whole number you can divide them all by.

Step-by-step explanation:

as in the attachment, i have named the lines by letters for easiness

Answer:

Therefore, the standard deviation of the GMC vehicles, when randomly selecting 300 vehicles, is approximately 6.18.

To calculate the standard deviation of the GMC vehicles, we need to know the probability of selecting a GMC vehicle and the probability of not selecting a GMC vehicle.

Given:

Global market share of GMC (General Motors Corporation) = 15%

Global market share of Toyota = 10%

Total number of vehicles selected = 300

Let's calculate the probabilities first:

Probability of selecting a GMC vehicle (p) = 15%

= 0.15

Probability of not selecting a GMC vehicle (1 - p) = 1 - 0.15

= 0.85

The standard deviation of a binomial distribution can be calculated using the following formula:

Standard deviation (σ) = √[n * p * (1 - p)]

Substituting the values:

Standard deviation (σ) = √[300 * 0.15 * 0.85]

= √[38.25]

≈ 6.18

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The proportion of STEM students who participate in at least one AP course is 0.19.

It can be deduced that the proportion of STEM students who participate in at least one AP course will be:

= 38/200

= 0.19

The proportion of regular students in the sample who participate in at least one AP course will be:

= 70/200

= 0.35

Also, participating in two or more AP courses is independent of student status. This is because the p value is more than the 0.05.

A method that could have been used to select a simple random sample of 200 students from the high school is by writing all the registration numbers of the students in a container an randomly picking.

There is bias in the sampling because the convenience sampling is used. This doesn't give everyone an equal chance.

In conclusion, status is not related to level of participation in AP courses.

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So the amount of water needed to fill the aquarium is approximately 1.87 gallons. This is our final answer, rounded to the nearest tenth.

To calculate the amount of water needed to fill the aquarium, we first need to find the volume of the tank. To do this, we can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height
Plugging in the measurements given in the problem, we get:
Volume = 2 feet x 0.5 feet x 1.5 feet
Volume = 0.75 cubic feet
Next, we need to convert cubic feet to gallons. There are 7.48 gallons in one cubic foot, so we can multiply the volume by 7.48 to get the amount of water in gallons:
0.75 cubic feet x 7.48 gallons/cubic foot = 5.61 gallons
However, we need to subtract the amount of space taken up by the gravel and the water that won't be filled to the top of the tank. The layer of gravel takes up 3 inches at the bottom of the tank, which is 0.25 feet. To find the volume of the gravel, we can use the same formula:
Volume = length x width x height
Volume = 2 feet x 0.5 feet x 0.25 feet
Volume = 0.25 cubic feet
We also need to subtract the volume of water that won't be filled to the top. The tank will be filled to a height of 1.25 feet (1.5 feet - 0.25 feet for the gravel), but we need to leave a 3-inch gap at the top. This gap is 0.25 feet, so we can find the volume of the unfilled space:
Volume = length x width x height
Volume = 2 feet x 0.5 feet x 0.25 feet
Volume = 0.25 cubic feet
Now we can subtract the volume of the gravel and unfilled space from the total volume of the tank:
Total volume - volume of gravel - volume of unfilled space = volume of water
0.75 cubic feet - 0.25 cubic feet - 0.25 cubic feet = 0.25 cubic feet
Finally, we can convert this to gallons:
0.25 cubic feet x 7.48 gallons/cubic foot = 1.87 gallons

So the amount of water needed to fill the aquarium is approximately 1.87 gallons. This is our final answer, rounded to the nearest tenth.

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The graph of the relation is shown in the diagram attached below.

domain: {-1, -1/2, 3/2, 2}

range: {-1, 0, 1/2, 3/2}

A relation has the domain values (x-values) and the range values (y-values). The domain values are plotted on a graph's x-axis (horizontal axis), while the corresponding range values are plotted on a graph's y-axis (vertical axis).

Thus, given the relation, (-1, 1/2), (-1/2, -1), (3/2, 0), (2, 3/2), the set of x-values of the relation are: -1, -1/2, 3/2, and 2. Therefore, the domain of the relation is: {-1, -1/2, 3/2, 2}.

The set of y-values of the relation are: 1/2, -1, 0, and 3/2. Therefore, the range of the relation is: {-1, 0, 1/2, 3/2}.

In conclusion,

domain: {-1, -1/2, 3/2, 2}

range: {-1, 0, 1/2, 3/2}

Thus, the graph of the relation is shown in the diagram attached below.

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Answer:

A. (see pic)

Step-by-step explanation:

The domain would be the x-values. The range would be the y-values.

Answer:

x = -11, y = -2

Step-by-step explanation:

There's two equations. Let's say the first number is x, and the second number is y. Then, there is 4y-3 = x, and 2y-x = 7. We plug in 4y-3 for x into the second equation, and we get 2y - (4y-3) = 7. Solving more gets us -2y + 3 = 7. thus, -2y = 4, meaning y = -2. We plug back into the second equation, getting -4 - x = 7. This 11 = -x, or x = -11.

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The quadratic equation written in the vertex form is:

y = 2*(x - 3)^2 - 1

We know that for a leading coefficient a, and a vertex (h, k), we can write the quadratic equation as:

f(x) = a*(x - h)^2 + k

Here we know that the leading coefficient is 2, and the vertex of our quadratic equation is (3, -1)

Then the values that we have are:

a = 2

h = 3

k = -1

Then we can write the quadratic equation in the vertex form as:

y = 2*(x - 3)^2 - 1

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The system of inequalities is

x + y ≥ 14

5x + 2.5y ≤ 60

Given, that Yaritza and her children went into a restaurant that sells hamburgers for $5 each and tacos for $2.50 each.

Yaritza has $60 to spend and must buy at least 14 hamburgers and tacos altogether.

As, x represents the number of hamburgers purchased and y represents the number of tacos purchased

Now, according to the question

x + y ≥ 14

as, she must buy at least 14 hamburgers and tacos altogether.

Now, 5x + 2.5y ≤ 60

as, she has $60 to spend.

So, we have two inequalities

x + y ≥ 14

5x + 2.5y ≤ 60

Hence, the system of inequalities for the given problem is

x + y ≥ 14

5x + 2.5y ≤ 60

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Answer:

\(3x + 15 = 4x + 12 \\ 4x - 3x = 15 - 12 \\ \boxed{x = 3}\)

The weight οf the kayak is 49 pοunds and 8 οunces. Sο the weight οf the kayak is 49 pοunds and 8 οunces.

A unit cοnversiοn expresses the same prοperty as a different unit οf measurement. Fοr instance, time can be expressed in minutes instead οf hοurs, while distance can be cοnverted frοm miles tο kilοmeters, οr feet, οr any οther measure οf length.

Tο cοnvert 792 οunces tο pοunds and οunces, we need tο divide the tοtal number οf οunces by the number οf οunces in a pοund (which is 16).

The quοtient will be the number οf pοunds, and the remainder will be the number οf remaining οunces.

Here are the calculatiοns:

792 οunces ÷ 16 οunces/pοund = 49.5 pοunds

The number befοre the decimal pοint (49) represents the pοunds, and the number after the decimal pοint (0.5) represents the remaining οunces.

Tο cοnvert the remaining οunces tο pοunds, we can multiply the decimal by 16 (the number οf οunces in a pοund).

0.5 * 16 = 8 οunces

Therefοre, the weight οf the kayak is 49 pοunds and 8 οunces.

Sο the weight οf the kayak is 49 pοunds and 8 οunces.

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Answer: 8 inches: 10 hours

Step-by-step explanation:

From the above question, we are informed that during the last snow storm, the snow accumulated at 4/5 inch per hour and that the snow continues at this rate for 10 hours.

The the ratio of the amount of snow in inches to the amount of time in hours first thus:

We have to calculate the amount of snow in inches first. This will be:

= 4/5 × 10

= 8 inches

Therefore, the the ratio of the amount of snow in inches to the amount of time in hours will be 8 inches for 10 hours

The first cylinder, weighing 2.5 pounds and running at a rate of 6 liters per minute, would last approximately 143.3 minutes.

To calculate the duration, we use the formula: Duration = (Weight of cylinder * Conversion factor) / Flow rate. Here, the conversion factor is 866 (which converts pounds to liters). Plugging in the values, we get (2.5 * 866) / 6 = 143.3 minutes.

Similarly, for the second cylinder weighing 3.5 pounds and running at 7 liters per minute, the estimated duration would be approximately 179.2 minutes. For the third cylinder weighing 7.5 pounds and running at 13 liters per minute, the estimated duration would be approximately 144.2 minutes. Finally, for the fourth cylinder weighing 6.5 pounds and running at 12 liters per minute, the estimated duration would be approximately 169.8 minutes.

By applying the formula and considering the weight of the cylinder and the flow rate, we can calculate an approximate duration for each scenario.

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Answer:

A-1/216

Step-by-step explanation:

(1/6)^3 is the same as: 1^3/6^3. Since one to any power is always 1, it woudl just be 1/6^3.  6^3 is 216, so the answer would be 1/216.

Hope this is helpfule! :)

Answer:

1/216

Step-by-step explanation:

(1/6)^3

(1/6) * (1/6) * (1/6)

1/216

Answer:

If they are parallel then angle b is

A. 51°

Step-by-step explanation:

P(54 < X1 + X2 + X3 < 72) is approximately 0.8972.

-The sum of independent normal random variables is also a normal random variable. Therefore, X1 + X2 + X3 is also a normal random variable with mean

E(X1 + X2 + X3) = E(X1) + E(X2) + E(X3) = 10 + 20 + 30 = 60 and variance Var(X1 + X2 + X3) = Var(X1) + Var(X2) + Var(X3) = 12.

So, X1 + X2 + X3 ~ N(60, 12).

-To find P(54 < X1 + X2 + X3 < 72), we standardize the random variable as follows:

\(Z = \frac{(X1 + X2 + X3 - 60)}{\sqrt{12} }\)

-Then, we need to find \(p(\frac{(54-60)}{\sqrt{120} } < Z < \frac{(72-60)}{\sqrt{12} }\).

Simplifying, we get P(-1.73 < Z < 1.73).

Using a standard normal table or calculator, we can find that this probability is approximately 0.8972.

Therefore, P(54 < X1 + X2 + X3 < 72) is approximately 0.8972.

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

Step-by-step explanation:

Set your x and y axis first, then you’re gonna need to permute the order of the equation, through inverse operations

x+2y=6

Get x on the other side of the equation,

x+2y=6
-x      -x

2y=6-x

The rule is to leave y alone, so divide by 2

2y=6-x

/2    /2

y=-1/2x + 3

Now that you know what y equals, plug it the other equation

(Other equation) x+2y=6

2x+ (-1/2x+3)=6

Like terms
1.5x+3=6

Inverse operation

1.5x+3=6
       -3  -3

1.5x=3

Isolate the variable

1.5x=3

/1.5  /1.5

x=2

You're not done yet!

Plug it back in to the original equation to unveil the value of y

y=-1/2x+3

Substitute

y=-1/2(2) +3

y= -1 +3

y=2

What does this mean? The lines intersect both at (2,2)

So now you know one of the lines, but you need to discern the slope of the other one in which we first plugged our values in.

2x+y=6
-2x   -2x

^
|
Inverse operations

y=-2x+6

Now plot it, that's it!

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