What is the domain of the function y = log(x +
3)?
(-0,00) (-0,00)
(-00,-3)
(0,00)
(-3,00)
DONE

The 45th term in the sequence 5, 8, 11, 14, 17, 20, 23, 26 can be found using the formula nth term = a + (n-1)d, where a is the first term, d is a common difference, and n is the number of the term we want to find. The 45th term is 137.

To find the 45th term in the sequence 5, 8, 11, 14, 17, 20, 23, 26, we need to first find the common difference between the terms. In this case, the common difference is 3 because each term is 3 more than the previous one.
To find the 45th term, we can use the formula for the nth term of an arithmetic sequence:
nth term = a + (n-1)d
where a is the first term, d is the common difference, and n is the number of the term we want to find.
Plugging in the values we know, we get:
45th term = 5 + (45-1)3
45th term = 5 + 44(3)
45th term = 5 + 132
45th term = 137
Therefore, the 45th term in the sequence is 137.

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Answer:

$12.50

Step-by-step explanation:

$100 divided by 8 hours = $12.50

Using the normal distribution, it is found that about 81.8% of Internet users spend between 78 minutes and 174 minutes on social networking platforms each day.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, the mean and the standard deviation are given, respectively, by:

\(\mu = 142, \sigma = 32\).

Th proportion of Internet users spend between 78 minutes and 174 minutes on social networking platforms each day is the p-value of Z when X = 174 subtracted by the p-value of Z when X = 78, hence:

X = 174:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{174 - 142}{32}\)

Z = 1

Z = 1 has a p-value of 0.841.

X = 78:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{78 - 142}{32}\)

Z = -2

Z = -2 has a p-value of 0.023.

0.841 - 0.023 = 0.818 = 81.8%.

81.8% of Internet users spend between 78 minutes and 174 minutes on social networking platforms each day.

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Answer:

The answer is "$80".

Step-by-step explanation:

Please see the attached file for the whole question.

Yolanda's total pay y changes for each 'English is fun' sold x, i.e.

\(\frac{\delta y}{\delta x} = \frac{dy}{dx} \\\\y = 1900+80 x\)

separating the above equation:

\(\frac{dy}{dx}= 80\)

Therefore,

\(\frac{dy}{dx} = \$80\)

For each 'English is enjoyable' sold x, the change in Yolanda total compensation y is \(\$80\).

Answer: If you are asking for the reflection, it will be (-2,3)

Step-by-step explanation:

Hope I helped!

Answer: 30t + 30m ≤ 330

Step-by-step explanation:

The maximum amount of pounds the truck can carry is 330 pounds so whatever will be carried has to either be equal to or less than 330 pounds.

= ≤ 330

t represents the number of bags of top soil and m represents the number of bags of mulch.

Each bag of top soil is 30 pounds and each bag of mulch is 30 pounds as well.

= 30t + 30m

Put together;

30t + 30m ≤ 330

The amount of monthly increase will be 8$

What is Quadratic Equation?

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The quadratic equation has the following general form: ax² + bx + c = 0. x is an unknown variable, whereas a, b, and c are numerical coefficients.

Solution:

Given Equation is x² - 16x + 64 = 0

Using the formula method we will first find the discriminant

D = b² - 4ac

D = 256 - 256 = 0

x = -b +- √D / 2a

x = 16/2 = 8

x = 8

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Answer:

Step-by-step explanation:

Mode is the one that occurs the most.

Stem is first number repeated for leaf

so your list of numbers is

10,12,12,22,23,24,30

The one that occurs the most is 12.  So your mode is 12.

If there are multiple numbers that are "most" then there is no mode.

$100

Step-by-step explanation:

hopes it helps :)))

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

OK so i have already answered it but B was incorrect i think but i did it differently and i got -20000000.

The answers in standard form are

(a) 3.45 × 10² .

(b) 6.48 × 10⁻³ .

The exponent of a number indicates how long it will take to multiply that number in its entirety. A number's power or exponent, in other words, tells how many times it must be multiplied by itself.

Any integer, fraction, or decimal can serve as the basis in this situation. Additionally, the exponent can have any value, whether positive or negative.

Given :

(a) (2.3 × 10⁴) × (1.5×10⁻²)

    =\($ 2.3\times1.5\times10^{(4-2)\)

    = 3.45 × 10² .

(b) 3.6 × 10⁻⁵× 1.8 × 10²

\(= 3.6\times1.8\times10^{(-5+2)\)

= 6.48 × 10⁻³

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Estimated change = 11.98 - Objective function value with a right-hand side of 9

To determine how much the objective function is expected to change when the right-hand side of the constraint is increased from 8 to 9, we need to calculate the shadow price or dual value associated with that constraint.

In the given problem:

Objective function: Minimize 3X^2 - 22X + 2XY + Y^2 - 16Y + 60

Constraint: X + 5Y ≤ 8

To find the shadow price or dual value, we can solve the problem using linear programming techniques. However, without access to the specific methodology or algorithm used to solve the problem, I am unable to provide an exact solution or calculate the shadow price accurately.

However, if we assume that the linear programming problem has been solved, and the optimal solution for the original problem with a right-hand side of 8 is X = 3.08 and Y = 0.98, with an optimal objective function value of 11.98, we can estimate the change in the objective function value.

The estimated change in the objective function value can be calculated by subtracting the optimal objective function value with the new right-hand side (9) from the original optimal objective function value (11.98).

Estimated change = 11.98 - Objective function value with a right-hand side of 9

Please note that without access to the specific methodology used to solve the problem or the actual shadow price/dual value, this calculation is an estimation based on the provided information.

To obtain the actual change and re-solve the problem with a new right-hand side of 9, I would need the specific linear programming methodology used to solve the problem or more details on the specific algorithm employed.

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The estimation no of the students who owns a reptile for pet is 141.

Given data :

Total students = 2820

2 out of 40 students own reptile

No of students own reptile = ?

2 out of 40 students own reptile

so in total students =  2840 / 40 = 70.5

Lets take 70 times = 70 x 2 = 140

and take 0.5 as 1 student = 140 + 1

= 141 students own reptile

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Using a t-distribution table or calculator with 74 degrees of freedom (sample size minus 1), we find that the p-value for this test is approximately 0.026. Since the p-value is less than the significance level of 0.05

The home inspector's conclusion that radon abatement is not necessary based on the sample mean being less than 4.0 is wrong because the sample mean may not accurately reflect the true population mean. The sample mean is subject to sampling variability, and it is possible that the true population mean is actually greater than 4.0, even if the sample mean is less than 4.0. Additionally, even if the true population mean is less than 4.0, it is still possible that some areas of the home have higher concentrations of radon, which may require abatement.

The appropriate null and alternative hypotheses for determining whether radon abatement is appropriate are:

Null hypothesis: The mean radon concentration in the home is less than or equal to 4.0 pCi/L.

Alternative hypothesis: The mean radon concentration in the home is greater than 4.0 pCi/L.

To compute the p-value, we can use a one-sample t-test with a significance level of 0.05. The test statistic is calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

where the hypothesized mean is 4.0, the sample mean is 3.72, the sample standard deviation is 1.93, and the sample size is 75. Plugging in these values, we get:

t = (3.72 - 4.0) / (1.93 / sqrt(75)) = -1.99

Using a t-distribution table or calculator with 74 degrees of freedom (sample size minus 1), we find that the p-value for this test is approximately 0.026. Since the p-value is less than the significance level of 0.05.

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Answer:

C

Step-by-step explanation:

They all have and addition and subtraction pattern in each cube, thank me later - PrObLeM OcCuReD

Answer:

B

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) = \(\frac{1}{a^{m} }\)

Given

y = 12 × \(3^{x}\) ← substitute x = - 2 into the expression

y = 12 × \(3^{-2}\) = 12 × \(\frac{1}{3^{2} }\) = 12 × \(\frac{1}{9}\) = \(\frac{12}{9}\) = \(\frac{4}{3}\) → B

Answer:

B

Step-by-step explanation:

y= 12 *3 ^x , substitute x with -2

y=12 *3^-2 , use the rule  a^ - b =  1 /a^b

y= 12 / 3^2 , 3^2 =3*3 = 9

y= 12/9, divide both numbers by 3,  12÷3/ 9÷3

y= 4/3

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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The work done by the force vector F over the curve in the direction of increasing t can be calculated using the line integral. In this case, we are given F = xyi + yj - yzk and the parameterized curve r(t) = ti + t²j + tk, where t ranges from 0 to 1.

To find the work, we need to evaluate the dot product of F and the derivative of r with respect to t, and then integrate this dot product over the given interval.

The derivative of r with respect to t is dr/dt = i + 2tj + k. Taking the dot product of F and dr/dt gives (xy)(1) + y(2t) - y(1) = xy + 2ty - y.

To calculate the work, we integrate this dot product over the interval [0,1] with respect to t. The integral becomes ∫[0,1] (xy + 2ty - y) dt.

Evaluating this integral gives the work done by F over the curve in the direction of increasing t.

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The number of combination 6-letter words using five vowels in alphabetical order,

5*4*3*2*1*21=2520

Permutation and combination are methods for representing a collection of objects by selecting them from a set and forming subsets. It specifies the various ways to arrange a specific set of data. Permutations are when we select data or objects from a specific group, whereas combinations are the order in which they are represented.

The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.

We have five vowels: a, i, e,0, and u.

make the 6-letter word using five vowels in alphabetical order,

5*4*3*2*1*21=2520

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Step-by-step explanation:

By Sine Rule,

x/sin42° = 37/sin110°.

Hence x = 37sin42°/sin110° = 26.35 in. (A)

The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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Answer:

\( \huge \color{purple}{answer}\)

To draw a circle whose radius is given, we require a ruler and compasses. Given that the radius is 5 cm, the steps to be followed are:

Step 1: Place the pointer of the compass at the initial point of the ruler (0 cm) and extend the other end of the pencil measuring 5 cm from the initial point (i.e. 5 cm)

Step 2: Mark a point O on a piece of paper. This point is supposed to be the center of the circle that you are about to construct.

Step 3: Place the pointer of the compass at point 0.

Step 4: Turn the compass slowly through 360 degrees to draw a circle.

Make sure that you hold the point of the compass stiffly on the paper. You are also required to move the compass through the 360 degrees in one go for accuracy and neatness.

A circle is a locus of all points in 2 dimensional space which are equidistant from some fixed point. The constructed circle with radius 5 units is constructed below.

We need two tools. first is ruler, and second is compass.

This is the needed circle.

One such circle (radius of 5 units) is constructed is attached below.

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We know that 1 gallon = 3.785 L,Therefore, 24.1364 L = 24.1364/3.785 gallons= 6.3781 gallons (rounded to four decimal places)Therefore, the car will use approximately 6.3781 gallons of gas on this trip.

The car travels for 3.0 hours at a velocity of 55 miles per hour. The gas mileage of the car is 11 km/L. We have to find how many gallons of gas will be used on this trip. We can solve this problem by using the following steps:Step 1: Convert the velocity from miles per hour to km/hourWe know that 1 mile

= 1.609 km Therefore, 55 miles per hour

= 55 × 1.609 km per hour

= 88.5 km per hour Step 2: Calculate the distance traveled by the car We know that distance = velocity × time Therefore, distance traveled by the car

= 88.5 km/hour × 3.0 hours

= 265.5 km

Step 3: Convert the distance from kilometers to miles We know that 1 mile

= 1.609 km Therefore, 265.5 km

= 265.5/1.609 miles

= 165.1287 miles (rounded to four decimal places)Step 4: Calculate the fuel consumption in liters We know that fuel consumption

= distance traveled/gas mileage Therefore, fuel consumption

= 265.5 km/11 km/L

= 24.1364 L (rounded to four decimal places)Step 5: Convert the fuel consumption from liters to gallons.We know that 1 gallon

= 3.785 L,Therefore, 24.1364 L

= 24.1364/3.785 gallon

s= 6.3781 gallons (rounded to four decimal places)Therefore, the car will use approximately 6.3781 gallons of gas on this trip.

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Answer:

a=36, b=18, c=39

Step-by-step explanation:

a + b + c = 93

You are told side a is is twice as long as b so a=2b.  Plug that into your equation.

2b + b + c = 93

simplified gives you 3b + c = 93

Now you know c is 3 feet longer than a.  You already know a is equal to 2b.  So c is equal to 2b + 3.  Plug that into your equation.

3b + (2b + 3) = 93

Simplified it is now 5b + 3 = 93.

Subtract 3 from both sides of the equal sign to get

5b = 90

Divide both sides by 5.

b = 18

Now you know side a is twice as long as b so side a must be 36.

a = 36

You also know side c is 3 feet longer than side a so side c must be 39

c = 39

Test your answers by adding all 3.  18 + 36 + 39 = 93

Answer:

There are 18 weeks in the semester

Step-by-step explanation:

We can model using a linear equation in the form y = mx + b, where

Let's start by figuring out what values we can plug in for y = mx + b and which variable we must solve for:

180 = -15x + 450

-270 = -15x

x = 18

Thus, there are 18 weeks in the semester

Answer:

A.

Step-by-step explanation:

When it says (x + 7), that means the graph will be shifting to the right (so parallel to the x-axis.

Answer:

7/8 or 0.875

hope that helped <3

Answer:

Step-by-step explanation:

We only have the sides of the triangles. Therefore, we can decide if the triangles are similar only by SSS.

If triangles are similar, then corresponding sides make proportion.

We have (let's set the sides in ascending order):

triangle 1: 30, 42 and 51

triangle 2: 10, 14 and 17.

Check:

30 : 10 =3

42 : 14 = 3

51 : 17 = 3

correct

Answer:

SSS

Step-by-step explanation:

\( \frac{51}{17} = 3 \\ \frac{30}{10} = 3 \\ \frac{42}{14} = 3 \\ hope \: this \: helps. \: good \: luck\)