Two angles are supplementary if the sum of their measures is 180∘. If the measure of one angle is 4 x degrees, represent the measure of its supplement as an expression of x

The domain of the function will be less than or equal to 4 is x ≤ 4

The domain of a function are real values for which the function exists

For the question given, the time taken will serve as the domain of the function while the height after a particular time will be the range.

The domain depends on the time it takes to reach the maximum height. SInce the football reaches its maximum height of 30 feet in 4 seconds, hence the domain of the function will be less than or equal to 4 is x ≤ 4

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Answer:

see below

Step-by-step explanation:

center of circle = (2,-1)

r = 6 -2 = 4

We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.

so the equation will be:

( x - 2 )^2 + ( y +1 )^2 =16

Answer:

60 km

Step-by-step explanation:

the line is constant around 3

Answer: (f)

Step-by-step explanation:

Given

Line that passes through \((-\frac{1}{2},3)\) and \((0,0)\)

Using two point form, equation of a line is given by

\(\Rightarrow \dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}\)

Insert the values

\(\Rightarrow \dfrac{y-0}{x-0}=\dfrac{3-0}{-\frac{1}{2}-0}\\\\\Rightarrow \dfrac{y}{x}=-6\\\\\Rightarrow y=-6x\)

Thus, option (f) is correct

Answer:

$2971.9

Step-by-step explanation:

2000*(1+2%)^20 = 2971.895

Given statement solution is :- The correct answer is: The frequency is 3 more than expected.

To determine the expected frequency of landing on an even number when rolling a fair six-sided number cube, we need to calculate the probability of landing on an even number and multiply it by the total number of rolls.

The number cube has six possible outcomes: 1, 2, 3, 4, 5, and 6. Of these, three are even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2 or 0.5.

The expected frequency can be found by multiplying the probability by the total number of rolls:

Expected frequency = Probability of landing on an even number × Total number of rolls

Expected frequency = 0.5 × 30 = 15

Now, we can compare the expected frequency (15) to the actual frequency (18) given in the problem statement.

The actual frequency is 18, and it is 3 more than the expected frequency (18 - 15 = 3).

Therefore, the correct answer is: The frequency is 3 more than expected.

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To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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The researcher can anticipate that 2.28 per cent of the children in their study will consume less sugar than 40 grammes every day.

According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.

To find the percentage of children in the study who had a decrease in their sugar intake to below 40 grams per day, we need to determine the proportion of children whose sugar intake is below 40g.

We can use the standard normal distribution and the z-score formula to find this proportion:

z = (40 - 50) / 5 = -2

Using a standard normal distribution table, we can find that the proportion of children with a sugar intake below 40g is approximately 0.0228 or 2.28%.

Therefore, the researcher can expect that approximately 2.28% of children in their study will have a sugar intake below 40 grams per day with the new behavioural method.

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Answer:

I added the answer as a screenshot, using math solvers is helpful for math problems, I haven't learned this yet but I found the answer. Also, I only need one more person to mark me brainliest to move onto the next level which is expert.

Hope I helped :)

Answer:

Step-by-step explanation:

4(x^2 = 6x + 9)

4(x + 3)(x + 3)

The graphed function is: y = (x + 2)(x − 1)(x − 3).

Option (a) is correct.

From the graph given in the question, it can be seen that the graph has 3 critical points, namely, x= -2, x = 1 and x = 3.

From all the five options given, the first option, that is, y = (x + 2)(x − 1)(x − 3), has the critical points x= -2, x = 1 and x = 3.

The critical points for a function are obtained by substituting the function to be equal to zero.

So, (x + 2)(x − 1)(x − 3) = 0

That is, x= -2, x = 1 and x = 3.

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Answer:

b) -6

Step-by-step explanation:

\(2\sqrt{10+n} = 4\)

Divide both sides by 2

\(\sqrt{10+n} = 2\)

Square both sides of the equation

\(10+n=4\)

Isolate the variable

\(n = 4 - 10\)

\(4 -10 = - 6\)

\(n = - 6\)

Answer:

r^2 + 6rs  - 4rd - 2d^2 + 3s^2

Step-by-step explanation:

3(r+s)^2 - 2(r+d)^2

PEMDAS

parenthesis, exponents, multiplication, division, addition, subtraction

in that order

3( r^2 + 2rs + s^2 ) - 2(r^2+ 2rd + d^2)

3r^2 + 6rs + 3s^2 - 2r^2 - 4rd - 2d^2

r^2 + 6rs  - 4rd - 2d^2 + 3s^2

The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV is the future value of the annuity,

P is the yearly payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.

Let's substitute these values into the formula and calculate the total value of the annuity:

FV = 693 * ((1 + 0.053)^16 - 1) / 0.053

FV = 693 * (1.053^16 - 1) / 0.053

Using a calculator, we can evaluate the expression inside the parentheses:

1.053^16 ≈ 1.9738

Substituting this value back into the formula:

FV = 693 * (1.9738 - 1) / 0.053

FV = 693 * 0.9738 / 0.053

FV ≈ 12739.62

Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

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Answer: We can use Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male. Bayes' theorem states:

P(A|B) = P(B|A) * P(A) / P(B)

where A and B are events, P(A|B) is the conditional probability of event A given that event B has occurred, P(B|A) is the conditional probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this case, we want to find P(grad degree | male), which is the probability that an applicant has a graduate degree given that they are male. Using Bayes' theorem, we have:

P(grad degree | male) = P(male | grad degree) * P(grad degree) / P(male)

We are given that 134 applicants are male, and 40 of those males have a graduate degree. Therefore:

P(male | grad degree) = 40 / total number of applicants with a graduate degree

We are not given the total number of applicants with a graduate degree, but we can find it using the fact that 40 applicants are male and have a graduate degree, and that there are 134 male applicants in total. Therefore:

total number of applicants with a graduate degree = 40 / (40/134) = 118.33 (rounded to the nearest whole number)

Next, we need to find the prior probability of having a graduate degree, P(grad degree). We can use the total number of applicants and the number of applicants with a graduate degree to calculate this probability:

P(grad degree) = number of applicants with a graduate degree / total number of applicants = 118 / 300 = 0.3933 (rounded to four decimal places)

Finally, we need to find the prior probability of being male, P(male). This probability can be calculated similarly:

P(male) = number of male applicants / total number of applicants = 134 / 300 = 0.4467 (rounded to four decimal places)

Now, we can substitute these values into Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male:

P(grad degree | male) = (40 / 118) * 0.3933 / 0.4467 = 0.332 (rounded to three decimal places)

Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they are male, is approximately 0.332 or 33.2%.

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

Answer: the first one is 7/9 and the second one is option 2

Step-by-step explanation:

4+7 = 11

< or> = open dot

Answer: he wrote for an five hours and forty-five minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

multiply lengthx weith

The options are not clear enough, so i have attached it.

Answer:

A: The independent variable (x) is the amount of time Rosetta shoots photos. The dependent variable (y) is the amount, in dollars, Rosetta earns for a wedding.

Rosetta charges a one-time fee of $100 (this is when x = 0), so the y-intercept is 100. Rosetta earns $50 for each hour she works, so the slope is 50

Step-by-step explanation:

We are given the equation of total amount of money Rosetta earns per wedding as;

y = 50x + 100

Where x is number of hours.

Now, the independent variable will be x because it doesn't depend on any other variable whereas the dependent variable will be y because it depends on how many hours which is x.

Now, the y-intercept occurs when x = 0.

Thus;

y = 50(0) + 100

y = 100

Thus,she charges a one time fee of $100, so the y-intercept = $100 at x = 0.

From slope intercept equation which is;

y = mx + c and comparing with y = 50x + 100, where m is the slope, we can see that m = 50.

Thus, since she earns $50 per hour, the slope is 50.

The correct option is Option A.

A logarithmic function is the inverse of an exponential function.

A logarithmic function is the inverse of an exponential function.

Now we have the function;

f(x) = log(x) and the translated function f(x) = log (x-h) + k.

Similarly;

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Missing parts;

Use the graphing calculator to graph the parent function.

f(x) = log(x)

Add the translated function.

f(x) = log (x-h) + k

Plug in different values of h and k to answer the following questions.

What happens when h is positive?

What happens when h is negative?

What happens when k is positive?

What happens when k is negative?

Answer:

When h is positive: horizontal shift to the right

When h is negative: horizontal shift to the left

When k is positive: vertical shift up

When k is negative: vertical shift down

Step-by-step explanation:

got it right on Edge

Answer:

Hi

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Thanks

Step-by-step explanation:

10 + x / 3 = 12

Cross multiply

10 + x = 12× 3

10 + x = 36

Collect like terms

x= 36 - 10

x = 26

It is to be noted that the boat traveled a distance of 8.39 miles South, and 12.44 miles west. This is solved using trigonometric ratios principles.

Using the trigonometric ratio involving the right triangle, we can answer how far the boat moved northward and westward, or the vertical and horizontal components of the displacement vector.

Solving for the horizontal component Vₓ, we'll be using the ratio of the sine function with regard to angle 34°

Thus,

Sin 34° = Vₓ/ 15

Vₓ = 15 * (Sin 34°)

= 15 * 0.55919290

Vₓ  = 8.39 miles.

Solving for the vertical component of, V\(_{y}\) we'll be using the ratio of Cosine Function with respect to the angle 34°

Cos 34° = V\(_{y}\) / 15

V\(_{y}\) = 15 * Cos 34°

V\(_{y}\)= 15 * 0.82903757255

V\(_{y}\) = 12.44 miles.

Thus, the boat traveled a distance of 8.39 miles South, and 12.44 miles west.

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Answer:

(1,-1)

Step-by-step explanation

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places.

Therefore, the image of (-1,1) is (1,-1)

Answer:

  A, C, D

Step-by-step explanation:

You want the angles in the list that have π/3 as the reference angle.

The reference angle is the smallest angle between the angle's terminal side and the x-axis. The cosine and sine of the reference angle have the same magnitude of the cosine and sine of the angle in question.

The attached table shows that 7π/3, 2π/3, and 19π/3 have the same reference angle: π/3.