you travel 243 miles in 4.5 .find the speed you travel.

M<1 =  52*

M<2 = 38*

Step-by-step explanation:

The angle is a 90 degree angle (we know because of the little square.)

(X+33) + 2x = 90

3x+33=90

3x= 57

X=19

( Then solve the original problems with X -=19)

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

Length: 18 yards Width: 12 yards

Step-by-step explanation:

Perimeter = (L+W) x 2

L = W + 6

60 yd = (W+W+6) x 2

30 yd = 2W + 6

24 yd = 2W

W = 12

L = 12 + 6 = 18

The ethnicity of respondents in a political poll of randomly selected adults is an example of a categorical variable.

A categorical variable is a type of variable that represents data that can be categorized into distinct groups or categories. In this case, the ethnicity of the individual respondents in the political poll represents different categories such as Asian, African American, Hispanic, Caucasian, etc. Each respondent falls into one of these categories based on their ethnicity.

The variable is categorical because it does not have numerical values that can be quantified or measured. Instead, it represents qualitative data that can be described using labels or categories.

Therefore, the ethnicity of the individual respondents in a political poll of randomly selected adults is an example of a categorical variable.

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The critical numbers of the function f(theta) are:

theta = nπ for any integer n

theta = 2nπ + π/3 and 2nπ + 5π/3 for any integer n.

To find the critical numbers of the function \(f(theta) = 2cos(theta) + sin^2(theta)\), we need to find the values of theta where the derivative of the function equals zero or does not exist.

The derivative of f(theta) with respect to theta is:

f'(theta) = -2sin(theta) + 2sin(theta)cos(theta)

Setting f'(theta) equal to zero and factoring out sin(theta), we get:

f'(theta) = 0

sin(theta)(2cos(theta) - 2) = 0

This equation is true when either sin(theta) = 0 or 2cos(theta) - 2 = 0.

When sin(theta) = 0, theta can be any integer multiple of π.

When 2cos(theta) - 2 = 0, we have:

2cos(theta) = 2

cos(theta) = 1

This is true when theta = 2nπ for any integer n.

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The 90% confidence interval is: (2.51, 3.22)

It is a boundary of values which is eventually to comprise a population value with a certain degree of confidence. It is usually shown as a percentage whereby a population means lies within the upper and lower limit of the provided confidence interval.

We have the following information :

The level of significance is calculated as:

\(\alpha =1-c\\\\\alpha =1-0.90\\\\\alpha =0.10\)

The degrees of freedom for the case is:

df = n - 1

df = 15 - 1

df = 14

The 90% confidence interval is calculated as:

=x(bar) ±\(t_\frac{\alpha }{2}\), df \(\frac{s}{\sqrt{n} }\)

= 2.86 ±\(t_\frac{0.10 }{2}\), 14 \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 1.761 × \(\frac{0.78}{\sqrt{15} }\)

= 2.86 ± 0.3547

= (2.51, 3.22)

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Answer:

3

Step-by-step explanation:

4/6 - x/8 = 14/48

make all the denominators 48

32/48 - 6x/48 = 14/48

since all the denominators are the same

32 -6x = 14

-6x = -18

x = 3

Answer:

b

Step-by-step explanation:

Answer: (B

Step-by-step explanation:

Answer:

its 99

Step-by-step explanation:

The values of c for which y = C is a constant solution of y' = y² + 5y - 6 are 1 and -6.

Option d is the correct answer.

To find out the constant solutions of the equation (1), we need to first solve it. Let's solve equation (1) using separation of variables.

Separating variables in equation (1), we get:

dy / dx = y² + 5y - 6Now, multiplying both sides by dx, we get:

dy = (y² + 5y - 6) dxIntegrating both sides, we get:

∫ dy = ∫ (y² + 5y - 6) dxy = (y³ / 3) + (5y² / 2) - 6y + C1... (2)

where C1 is the constant of integration.

We can see that equation (2) is not in the form of y = f(x), which means we can't use it to find the values of c for which y = c is a constant solution of equation (1).

To convert equation (2) into the required form, we need to first simplify it.

Let's do that.Simplifying equation (2), we get:

y (y² + 5y - 12 / 3) + C1y (y² + 5y - 12) / 3 + C1

Now, for y = c to be a constant solution of equation (1), we have:

y (y² + 5y - 12) / 3 + C1 = c

Multiplying both sides by 3, we get:

y (y² + 5y - 12) + 3C1 = 3c

Rearranging, we get:y³ + 5y² - 12y - 3c + 3C1 = 0

Now, if y = c is a constant solution of equation (1), it means that equation (1) should be equal to 0.

So, we have:

y' = 0

On substituting y = c in equation (1), we get:(dy / dx) = c² + 5c - 6= 0

Solving the above equation, we get:

c = 1 and -6

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Answer:

-$32

Step-by-step explanation:

(Withdrawal: - for the balance), (Deposition: + for the balance)

149-49+11+30-24

100+11+30-24

111+30-24

141-24

117

117-149= -$32

Net change: -$32

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Answer: \(26.4\ \text{days}\)

Step-by-step explanation:

Given

Half life of radioactive substance is \(T_{\frac{1}{2}}=20\ \text{days}\)

Initial amount \(A_o=2\ \text{days}\)

Amount left at any time is given by

\(\Rightarrow A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow 2=52^{\dfrac{-t}{20}}\\\\\Rightarrow 0.4=2^{\dfrac{-t}{20}}\\\\\Rightarrow 2^{\dfrac{t}{20}}=2.5\\\\\Rightarrow \dfrac{t}{20}\ln 2=\ln (2.5)\\\\\Rightarrow t=\dfrac{20\ln (2.5)}{\ln 2}\\\\\Rightarrow t=26.4\ \text{days}\)

It takes 26.4 days to reach 2 gm.

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

is it written like this?

if so then the coefficient of y is 1

Answer:

¼

Step-by-step explanation:

A coefficient is the number that comes before a variable, including its sign (plus/minus). Thus, the coefficient of y is the number that comes before the variable y.

\( \frac{y}{4} \) can also be written as \( \frac{1}{4} y\). Since the sign before ¼ is a plus sign, the coefficient of y can simply be written as ¼.

Answer:

The T shirt choice

Step-by-step explanation:

Both values increase at the same rate therefore is proportional.

Answer:

8

Step-by-step explanation:

8/2 equals 4 minus 10 is -6

Answer:

-6= n/2 -10

-12=n-20

-12-n=-20

-n=-20+ 12

-n=-8

n=8

Step-by-step explanation:

1. multiply both sides of the equations by 2

2.Move the N varaiableto the left hand side and change its sign

3. Calculate the sum of -20+12

4. change the signs from negative N to positive N giving you the value of 8

n=8

Solved.

:)

Answer:

f(x)=1

Step-by-step explanation:



Answer:(4 x 103) x (2 x 107) = ( 4 x 2 ) x ( 103 + 7 ) = 8 x 10 10.

Step-by-step explanation:

The obtained expression after subtracting  8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Is given expression is, Subtract 8x¹⁰ from x² - 2x.

In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.

=8x¹⁰-x²+2x

=8(x²)⁵-x²+2x

=x²(8x⁴-1)+2x

Thus, the obtained expression after subtracting  8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.

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Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

By using the perimeter formula for an orthogonally oriented rectangle set on a Cartesian plane, we find that the perimeter of the figure is 68/3 units.

In this question we have a rectangle oriented with respect to the two orthogonal axes of a Cartesian plane. In this case, the vertices of the figure are of the form:

A(x, y) = (a, b), B(x, y) = (c, b), C(x, y) = (a, d), D(x, y) = (c, d)

And the perimeter of this rectangle is equal to this:

p = 2 · |a - c| + 2 · |b - d|

If we know that a = - 5, b = 2, c = 2, d = - 7/3, then the perimeter of the rectangle is:

p = 2 · |- 5 - 2| + 2 · |2 - (- 7/3)|

p = 14 + 26/3

p = 68/3

By using the perimeter formula for an orthogonally oriented rectangle set on a Cartesian plane, we find that the perimeter of the figure is 68/3 units.

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Given :

▪︎This triangle is an isosceles triangle.

▪︎Measure of one of its legs = 6 inches

▪︎Measure of its equivalent leg \( = \tt \frac{x}{9} \) inches

▪︎Measure of its base \( = \tt \frac{5}{2} \) inches

Which means :

\( =\tt 6 = \frac{x}{9} \)

\( =\tt \frac{6}{1} = \frac{x}{9} \)

\( =\tt 6 \times 9 = x \times 1\)

\(\hookrightarrow\color{plum}\tt 54 = x\)

Let us check whether or not we have found out the correct value of x by placing 54 in the place of x :

\( =\tt 6 = \frac{54}{9} \)

\( = \tt6 = 6\)

Since the Left Hand Side of the equation is equivalent to the Right Hand Side of the equation, we can conclude that we have found out the correct value of x.

▪︎Therefore, the value of x = 54

The ordered pair which is the solution of the equation is (2,4). The solution has been obtained by solving the linear equation.

What is a linear equation?

The linear equation has a degree of one as its highest. It is evident that linear equations with exponents greater than one are devoid of variables as a result. A straight line results from this equation on the graph.

We are given an equation as y = 22 - 9x

Also, we are given one element of the ordered pair which is y = 4.

Substituting this value in the equation, we get

⇒y = 22 - 9x

⇒4 = 22 - 9x

⇒9x = 18

⇒x = 2

Hence, the ordered pair is (2,4).

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Question: Fill in the blank so that the ordered pair is a solution of y = 22 – 9x. ( ,4)

Answer:

its b cause -2/3 is the same as 2/3

Step-by-step explanation: the explanation is that ily bae

Answer:

1.4071

Step-by-step explanation:

The relationship between the elapsed time, t in days, since an ocean sunfish is born, and its mass is given by:

\(M_{day}(t)=3.5(1.05)^t\)

This function represents an exponential growth increasing as the number of days increases since (3.5 > 1), it means that at day 0 , the mass of the sunfish is 3.5 milligrams and every day, its mass increases by a factor of 1.05.

Since the mass of the sunfish increases by \(1.05^t\), therefore the mass of the sunfish increases every one week (that is 7 days) by a factor of \(1.05^{7} = 1.4071\)

The formula for the annualized cost of not taking a discount is: Annualized Cost = (1 + r)^t * [(1 - d) / d] * C

Where:

r = the interest rate

t = the number of years

d = the discount rate

C = the cost of the item

This formula calculates the cost of not taking a discount over a given period of time (t) with a certain interest rate (r). It takes into account the original cost of item (C), the discount rate (d), and the time period (t) to determine the total cost of not taking the discount.

For example, if an item costs $100 with a discount rate of 10%, the cost of not taking the discount over 1 year with an interest rate of 5% would be calculated as follows:

Annualized Cost = (1 + 0.05)^1 * [(1 - 0.1) / 0.1] * 100

= 1.05 * (0.9 / 0.1) * 100

= 1.05 * 9 * 100

= 945

So the annualized cost of not taking the discount would be $945

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Magnification if lens #2 were absent: M1 = 1

Properties of the final image: real, enlarged, and upright.

To determine the magnification if lens #2 were absent (i.e., the magnification of lens #1), we need to consider the properties of the lenses in combination.

Given the options for the magnification of lens #1, we can eliminate some options based on the properties of the final image:

real, enlarged and inverted

virtual, enlarged and upright

virtual, reduced and inverted

virtual, enlarged and inverted

real, reduced and upright

real, enlarged and upright

real, reduced and inverted

virtual, reduced and upright

Lens #2, being absent, does not contribute to the overall magnification of the system. Therefore, the magnification of the entire system is determined solely by lens #1.

From the given options, we can see that the only possible choice for the magnification of lens #1 that matches the properties of the final image is:

M1 = 1 (real, enlarged, and upright)

As for the properties of the final image for the present two-lens problem, we can conclude:

real, enlarged, and upright

Therefore, the correct answers are:

Magnification if lens #2 were absent: M1 = 1

Properties of the final image: real, enlarged, and upright.

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The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

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

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Answer:

469.1 yd²

Step-by-step explanation:

The area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \(\frac{210}{360}\)

   = π × 16² × \(\frac{21}{36}\)

   = 256π × \(\frac{7}{12}\)

   ≈ 469.1 yd² ( to 1 dec. place )

Answer:

I don't know

Step-by-step explanation: