Anyone know the answer to this?

The domain and range of the given function are [−3,∞) and [0,∞) respectively.

The given function is f(x)=2√(x+3).

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.

Domain: [−3,∞),{x|x≥−3}

Range: [0,∞),{y|y≥0}

Therefore, the domain and range of the given function are [−3,∞) and [0,∞) respectively.

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Answer:

60

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

a^2+25^2 = 65^2

a^2 +625 = 4225

a^2 = 4225-625

a^2=3600

Taking the square root of each side

sqrt(a^2) = sqrt(3600)

a = 60

Answer:

Step-by-step explanation:

Hypotenuse: 65

Leg: 25

Let Hypotenuse be c, and leg be a

\(a^{2}\) + \(b^{2} = c^{2}\)

\(a^{2} + 25^{2} = 65^{2}\)

\(a^{2} + 625 = 4225\\\)

\(a^{2}\) = 4225 - 625

\(a^{2}\) = 3600

3600 is the exponential value of a, meaning we need to apply the opposite of squaring to get the value of b. Which is square rooting.

a = \(\sqrt{3600\\}\)

a = 60

Therefore a is equal to 60 feet

A complex number Z be 4 + j6.22. The logarithmic formula:

loge(Z) ≈ ln(7.39) + j * 1.005

To calculate the natural logarithm of a complex number, we can use the logarithmic properties of complex numbers. The logarithm of a complex number Z is defined as:

loge(Z) = ln(|Z|) + j * arg(Z)

where |Z| is the magnitude (or absolute value) of Z, and arg(Z) is the argument (or angle) of Z.

Given Z = 4 + j6.22, we can calculate the magnitude and argument as follows:

|Z| = √(Re(Z)² + Im(Z)²)

    = √(4² + 6.22²)

    = √(16 + 38.6484)

    = √(54.6484)

    ≈ 7.39

arg(Z) = arctan(Im(Z) / Re(Z))

      = arctan(6.22 / 4)

      ≈ 1.005

Now we can substitute these values into the logarithmic formula:

loge(Z) ≈ ln(7.39) + j * 1.005

Using a scientific calculator or a calculator that supports natural logarithm (ln), you can find the approximate value of ln(7.39), and the result will be:

loge(Z) ≈ 1.999 + j * 1.005

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The y-intercept for the regression equation is 3, given that b = 4, Mx = 12, and My = 51. So, the correct option is C).

The formula for the y-intercept of the regression equation is

a = My - b(Mx)

where My is the mean of the dependent variable (y), b is the slope, and Mx is the mean of the independent variable (x).

Given that b = 4, Mx = 12, and My = 51, we can substitute these values in the formula to find the y-intercept

a = 51 - 4(12)

a = 51 - 48

a = 3

Therefore, the y-intercept (a) for the regression equation is 3.

The correct Answer is C) 3.

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--The given question is incomplete, the complete question is given

" A set of X and Y scores has b = 4, Mx = 12, and My = 51. What is the y-intercept (a) for the regression equation? O 9.75 17.36 3.00 8.25 "--

An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.

The solution is 21.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;

7n + 16 = 163

7n = 163 - 16

7n = 147

n = 147/7

n = 21.

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Answer:

The probability of a success can be calculated by dividing the number of successes by the total number of trials.

In this case, the number of successes is the sum of the occurrences of the numbers 0, 1, and 2. These numbers occur with equal probability, so the total number of occurrences of these numbers is:

3 * (1/6) = 1/2

This means that the probability of a success is:

P(success) = # of successes / total # of trials = (1/2) / 1 = 1/2

Therefore, the estimated probability of a success is 0.5 or 50%.

To estimate the probability of a success in this scenario, we need to determine the proportion of the randomly generated numbers that represent a success. Since the numbers 0, 1, and 2 represent a success, out of the possible six numbers (0, 1, 2, 3, 4, and 5), there are three that correspond to a success. Therefore, the estimated probability of a success is 3/6 or 0.5.

It is important to note that this is only an estimated probability, as it is based on a simulation and not a true experiment with a large sample size. The actual probability of a success may differ slightly from this estimate.
In order to obtain a more accurate estimate, we would need to perform multiple simulations and calculate the proportion of successes across all of the trials. This would give us a better idea of the true probability of a success in this scenario.
Additionally, it is important to consider the context of the event being simulated and whether or not this estimated probability is sufficient for the desired outcome. If a success rate of 50% is not acceptable, alternative methods may need to be explored to increase the likelihood of success.

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To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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Answer:

substract.

Step-by-step explanation:

eg. 5 before 17 = 17-5

so 5 before 17= 12

same for others

Answer: The walking path around it.

Step-by-step explanation:

Remember the Pythagorean's theorem, for a triangle rectangle with catheti A and B, and with hypotenuse H, we have:

A^2 + B^2 = H^2

or

H = √(A^2 + B^2)

Here, A + B is the total distance for the path, while the hypotenuse is the distance for the bridge

Here we can see that:

A = 1170 ft

B = 520 ft

Then:

H = √( (520 ft)^2 + (1170 ft)^2) = 1280.4 ft

Now, let's compute the costs.

For the bridge, we know that each foot costs $11, then for 1280.4 ft the cost is:

Cost of the bridge = (1280.4)*$11 = $14,084.4

And for the walking path, the cost is $6 per foot, then the total cost of the path is:

Cost of the path = (520 ft + 1170 ft)*$6 = $10,140

We know that the bridge is preferred if it is within the range of $1500 for the path's cost.

This range is:

($10,140 - $1,500, $10,140 + $1,500) = ($8,640, $11,640)

Here we can see that the cost of the bridge does not belong to this range, (is higher) so the option we should recommend is the walking path around.

Toby cycles 12 miles each day.

To find out how far Toby cycles each day, we need to add up the distance he covers during his morning and afternoon trips. Here are the steps we need to follow:

Step 1: Determine Toby's cycling distance from his house to his schoolDistance from Toby's house to his school = 4 miles west. Toby bicycles this distance every day. Therefore, his one-way cycling distance from home to school is 4 miles.

Step 2: Determine Toby's cycling distance from his school to Erica's house.Distance from Toby's school to Erica's house = 3 miles south. Toby cycles this distance every day after school. Therefore, his one-way cycling distance from school to Erica's house is 3 miles.

Step 3: Determine Toby's cycling distance from Erica's house to his house.Distance from Erica's house to Toby's house = we don't know. But we know that Toby takes a bike path that goes straight from Erica's house to his own house. Therefore, we can assume that the distance from Erica's house to Toby's house is the hypotenuse of a right-angled triangle with legs of 3 miles (south) and 4 miles (west).

We can use the Pythagorean Theorem to find the hypotenuse: c2 = a2 + b2c2 = 32 + 42c2 = 9 + 16c2 = 25c = √25c = 5 milesTherefore, Toby cycles 5 miles every day on his bike path from Erica's house to his own house.Step 4: Add up Toby's one-way cycling distances to find out how far he cycles each day.Toby's one-way cycling distance from home to school = 4 milesToby's one-way cycling distance from school to Erica's house = 3 milesToby's one-way cycling distance from Erica's house to his house = 5 milesTotal cycling distance = 4 + 3 + 5Total cycling distance = 12 miles.

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The base of the packaging will be,x =3.35 mm. The volume right triangular prism is 54 mm³

Join the edges of three rectangles. Now, from both ends, seal their triangle mouths. A triangular prism is a name for the form.

The volume of the packaging(right triangular prism)  = 54 mm³

Height of the cheese(H)= 2 mm-2x

Length(L)=3+2x

The volume of a right triangular prism is v = 1/2bhl

\(\rm V = \frac{1}{2} \times b \times h \times \\\\ 108 = 6+4x-6x-4x^2 \\\\ x=3.35\)

Hence, the base of the packaging will be,x =3.35 mm.

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Answer:

Hope this helps with your question :)

B

Step-by-step explanation:

This is because in the slope-intercept form,

y = mx + b, the m = slope, and the b = y-intercept. So the final answer would be

y = 1/2x - 5

Answer:

you press/click the small crown icon below the user's answer

Step-by-step explanation:

answer is D) 7x < 10

Answer:

22.5

Step-by-step explanation:

4 days=15

2days=7.5

6=22.5

The statement is true because if the cross product of two vectors ~u and ~v in three-dimensional space is equal to the zero vector ~0, then it implies that either ~u or ~v is equal to the zero vector ~0.

The cross product ~u × ~v produces a vector that is perpendicular (orthogonal) to both ~u and ~v. If the resulting cross product is the zero vector ~0, it means that ~u and ~v are either parallel or collinear.

If ~u and ~v are parallel or collinear, it implies that they are scalar multiples of each other. In this case, one of the vectors can be expressed as a scaled version of the other. Consequently, either ~u or ~v can be the zero vector ~0.

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John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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There are 144 combinations of 1 entree, 2 vegetables, and 1 dessert that can be selected from 4 entrees, 6 vegetables, and 6 desserts.

To determine the number of combinations, we multiply the number of options for each category.

For the entree, we have 4 options to choose from.

For the vegetables, we need to select 2 out of 6, which can be done in 6 choose 2 ways.

This is calculated as 6! / (2!(6-2)!), which simplifies to

6! / (2!4!)

Similarly, for the dessert, we have 6 options to choose from.

To calculate 6 choose 2, we can use the formula for combinations:

n choose r = n! / (r!(n-r)!).

Plugging in the values, we have

6! / (2!4!) = (6 × 5 × 4 × 3 × 2 × 1) / [(2 × 1) × (4 × 3 × 2 × 1)] = 15.

Therefore, we have 4 options for the entree, 15 options for the vegetables, and 6 options for the dessert.

Multiplying these numbers together, we get 4 × 15 × 6 = 144.

Therefore, there are 144 possible combinations of 1 entree, 2 vegetables, and 1 dessert, given the options of 4 entrees, 6 vegetables, and 6 desserts.

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Answer:

C. Translation 5 units left and 2 units down

Step-by-step explanation:

Let's take a look at A', which is (0, 0). This is the result of A, which is (5, 2) being transformed somehow. Notice that the x-coordinate moved 5 units to the left (from 5 to 0, which means we subtract 5 from 5). And, notice that the y-coordinate moved 2 units down (from 2 to 0, so we subtract 2 from 2).

Look to see if this works for the other two points:

B(6, 1): if we subtract 5 from the x-coordinate 6, we get 6 - 5 = 1, which matches the x-coordinate of the image B'. If we subtract 2 from the y-coordinate of B, which is 1, we get 1 - 2 = -1, which also matches the y-coordinate of B'. So, this works.

C(4, 5): if we subtract 5 from the x-coordinate 4, we get 4 - 5 = -1, which matches the x-coordinate of the image C'. If we subtract 2 from the y-coordinate of C, which is 5, we get 5 - 2 = 3, which also matches the y-coordinate of C'. So, this again works.

Therefore, we know that the transformation is a translation 5 units left and 2 units down, or C.

A picture will be shown below of a graph with the points in the table.

We only need to use (5, 2) and (0, 0) to solve this problem.

We take both points and see what it took for the old point to get to where the new point is (Shown in picture below).

Therefore, the answer is [ C. Translation 5 units left and 2 units down ]

Best of Luck!

The 98% "confidence-interval" for which the difference in mean volumes of 10-week recycling for all households with 60 , 75-gallon bins is (-66.886, 0.886).

In order to construct the confidence-interval for the difference in the mean-volumes of 10-week recycling for all households with the 60- and 75-gallon bins, we can use the two-sample t-test with unequal variances.

Let μ₁ and μ₂ be the true mean volumes of recycling for all households with the 60- and 75-gallon bins, respectively.

We want to estimate the difference in the means, μ₁ - μ₂, with a 98% confidence interval.

First, we calculate sample means and standard-deviations;

x'₁ = 382 gallons, s₁ = 52.5 gallons (for 60-gallon bins)

x'₂ = 415 gallons, s₂ = 43.8 gallons (for 75-gallon bins)

Next, we calculate "standard-error" of difference in the means;

SE(μ₁ - μ₂) = √(s₁²/n₁ + s₂²/n²₂);

where n₁ = 25 and n₂ = 22 are the sample sizes.

Substituting the values,

We get,

SE(μ₁ - μ₂) = √((52.5)²/25 + (43.8)²/22) = 14.05 gallons,

The "critical-value" for a 98% confidence interval with (n₁-1) + (n₂-1) = 45 degrees of freedom is : t = 2.412,

The confidence interval can be written as : (x'₁ - x'₂) ± t × SE(μ₁ - μ₂),

Substituting the values,

We get,

= (382 - 415) ± 2.412 × 14.05,

= -33 ± 33.886,

= (-33-33.886, -33+33.886) = (-66.886, 0.886).

Therefore, the required 98% confidence-interval is (-66.886, 0.886).

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The probability that x is greater than 102 is approximately 0.2119.

We need to standardize the random variable x before finding the required probability.

The standardized random variable Z is given by:

Z = (x - μ) / σ

Here, x = 102, μ = 90, and σ = 15.

So,

Z = (102 - 90) / 15 = 0.8

Now, we need to find P(Z > 0.8). We can use a standard normal distribution table or calculator to find this probability.

Using a standard normal distribution table, we find that the probability of Z being greater than 0.8 is approximately 0.2119.

Therefore,

P(x > 102) = P(Z > 0.8) ≈ 0.2119

So, the probability that x is greater than 102 is approximately 0.2119.

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The number of ordered quadruplets of non-negative integers that satisfy the given condition is:
|A| - |B| = 161,700 - 16,215 = 145,485

To solve this problem, we need to use the Principle of Inclusion-Exclusion (PIE). Let A be the set of all quadruplets (a1,a2,a3,a4) of non-negative integers that satisfy the equation a1+a2+a3+a4=100, and let B be the set of all quadruplets where all four integers are odd. Then the number of quadruplets that satisfy the given condition is given by:
|A| - |B|
To find |A|, we can use stars and bars. If we consider 100 stars and 3 bars, we can partition the stars into 4 groups, corresponding to the four integers. There will be 99 gaps between the stars and bars, and we need to choose 3 of them to place the bars. This gives us:
|A| = (99 choose 3) = 161,700
To find |B|, we can use a similar approach. If all four integers are odd, then they must be of the form 2k+1, where k is a non-negative integer. Substituting this into the equation a1+a2+a3+a4=100, we get:
2k1 + 1 + 2k2 + 1 + 2k3 + 1 + 2k4 + 1 = 100
Simplifying this equation, we get:
k1 + k2 + k3 + k4 = 48
This is now an equation in non-negative integers, which we can solve using stars and bars. We need to partition 48 stars into 4 groups, and there will be 3 bars separating them. This gives us:
|B| = (47 choose 3) = 16,215.

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To estimate the number of sandwiches the deli manager should anticipate selling when 178 customers visit the deli, we can analyze the given data and approximate it using a linear function.

By observing the table, we notice that the number of sandwiches sold varies with the number of customers. This indicates a relationship between the two variables.

To estimate the number of sandwiches, we can fit a line to the data points and use the linear function to make predictions. Using a statistical software or a spreadsheet, we can perform linear regression analysis to find the equation of the best-fit line. However, since we are limited to text-based interaction, I will provide a general approach.

Let's assume the number of customers is the independent variable (x) and the number of sandwiches is the dependent variable (y). Using the given data points, we can calculate the equation of the line.

After calculating the linear equation, we can substitute the value of 178 for the number of customers (x) into the equation to estimate the number of sandwiches (y).

Please provide the data points for the number of sandwiches sold corresponding to each number of customers so that I can perform the linear regression analysis and provide a more accurate estimate for you.

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Answer:

When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is multiplied by -1.

So, the coordinates of X' are (9, -5) since the x-coordinate remains the same and the y-coordinate is multiplied by -1.

Similarly, the coordinates of Y' are (-3, -6) and the coordinates of Z' are (-8, -4).

Therefore, X′ is (9,−5), Y′ is (−3,−6), and Z′ is (−8,−4).

A common everyday counting unit that is used to mean 12 of an object is a Dozen

Dozen is derived from the Old French word "douzaine" which means twelve each. In most situations, a dozen is used to refer to a group of twelve items. The term dozen is also used in informal situations to refer to a very large number of objects. For example, one might say "I have dozens of friends!" to mean that they have a lot of friends.

Dozen is a useful term when counting items. It allows for large numbers to be easily broken down into manageable groups. For example, if you have 120 pencils, you could easily count them by saying that you have 10 dozen pencils. It can also be useful when talking about fractions. For example, instead of saying "one and a half of an item," one could say "one and a half dozen of an item."

Dozen is a common everyday counting unit that is used to mean 12 of an object. It is a useful term when counting items and when talking about fractions, and can be used in both formal and informal settings.

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The correct answer is c. − 16x^3 / ((x^2 + 16)^(3/2)) + C. To evaluate the integral, we substitute x = 4tan(t) as explained earlier.

The integral simplifies to:

∫ x^4 / ((x^2 + 16)^(3/2)) dx = ∫ (16tan^4(t)) / (16sec^3(t)) sec^2(t) dt

= ∫ tan^4(t) / sec(t) dt.

Using the trigonometric identity tan^2(t) = sec^2(t) - 1, we have:

∫ tan^4(t) / sec(t) dt = ∫ (sec^2(t) - 1)^2 / sec(t) dt

= ∫ (sec^4(t) - 2sec^2(t) + 1) / sec(t) dt

= ∫ sec^3(t) - sec(t) dt.

Integrating each term separately, we obtain:

∫ sec^3(t) dt = (1/2)sec(t)tan(t) + (1/2)ln|sec(t) + tan(t)| + C.

Finally, substituting back x = 4tan(t), we get:

∫ x^4 / ((x^2 + 16)^(3/2)) dx = (1/2)sec(t)tan(t) + C.

Using the relationship sec(t) = sqrt(x^2 + 16) / 4 and tan(t) = x / 4, we can rewrite the answer as c. − 16x^3 / ((x^2 + 16)^(3/2)) + C.

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Answer:

The record high temperature of 118°F is 63°F higher than the mean temperature of 55°F. The record low temperature of -40°F is 95°F lower than the mean temperature of 55°F. The record high temperature of 118°F is closer to the mean temperature than the record low temperature of -40°F by 32°F.