Sarah left Minneapolis heading east on the interstate at a speed of 65 mph. Her sister followed her on the same route, leaving two hours later and driving at a rate of 75 mph. How long, in hours, will it take for Sarah's sister to catch up to Sarah?

The coordinates of the vertices for the image of the triangle U′V′W′ is

U′(1, 1), V′(−4, 0), W′(−1, 4)

To rotate a point 90 ° clockwise about the origin, we can apply the transformation (x, y) → (y, -x)

So applying this transformation to each vertex of triangle UVW we get

U(−1, 1) → U' = (1, 1)

V(0, −4) → V' = ( -4, 0)

W(−4, −1) → W' = (-1, 4)

Therefore the coordinates of the vertices for the image triangle U'V'W' are U′(1, 1), V′(−4, 0), W′(−1, 4)

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A sample size that would give the standard deviation of \(\bar{x}\) equal to 0.8 years is 1,227.

In Mathematics and Statistics, a sample size that would result in a standard deviation of 0.8 years can be calculated by using the mathematical equation (formula):

Sample size, n = (zσ/ME)²

Where:

By assuming a confidence level of 95% with a z-score of 1.96, we would substitute the given parameters into the formula for sample size as follows;

Sample size, n = (zσ/E)²

Sample size, n = (1.96 × 14.3/0.8)²

Sample size, n = (28.028/0.8)²

Sample size, n = (35.035)²

Sample size, n = 1,227.45 ≈ 1,227.

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Complete Question:

Suppose the standard deviation of the ages of all Florida panthers is 14.3 years. Let \(\bar{x}\) be the mean age for a sample of a certain number of Florida panthers. What sample size will give the standard deviation of \(\bar{x}\) equal to 0.8 years?

Round the solution up to the nearest whole number, if necessary.

a)

Recall, the sum of the angles in a triangle is 180 degrees. This means that

For triangle ABC,

angle A + angle B + angle C = 180

For triangle DEF,

angle D + angle E + angle F = 180

From the information given,

In triangle ABC,

angle A = 30

angle B = 52

Thus,

30 + 52 + angle C = 180

82 + angle C = 180

Subtracting 82 from both sides of the equation,

82 - 82 + angle C = 180 - 82

angle C = 98 degrees

In triangle DEF,

angle D = 22

angle E = 50

Thus,

22 + 50 + angle F = 180

72 + angle F = 180

Subtracting 72 from both sides of the equation,

72 - 72 + angle F = 180 - 72

angle F = 108 degrees

Tasheena's grade percentage in the class so far is approximately 71.00935%.

The percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

To compute Tasheena's grade percentage in the class so far, we can calculate the weighted average of her scores based on the weightage of each component of the final grade.

Given:

Quizzes: 15% weightage

Exams: 55% weightage

Projects: 25% weightage

Attendance: 5% weightage

Tasheena's scores:

Quizzes: 117 out of 150 points

Exams: 74, 86, and 91 on the first three exams (each worth 100 points)

Projects: 29 out of 25 possible points

Attendance: Perfect attendance

Let's calculate Tasheena's grade percentage:

Quizzes:

Tasheena's quiz score percentage = (117 / 150) * 100 = 78%

Exams:

Tasheena's exam average = (74 + 86 + 91) / 3 = 83.67

Tasheena's exam score percentage = (83.67 / 100) * 55 = 46.017%

Projects:

Tasheena's project score percentage = (29 / 25) * 100 = 116%

Attendance:

Tasheena's attendance score percentage = 100% (since she had perfect attendance)

Now, let's calculate the weighted average of Tasheena's scores:

Weighted average = (Quizzes weightage * Quiz score percentage) + (Exams weightage * Exam score percentage) + (Projects weightage * Project score percentage) + (Attendance weightage * Attendance score percentage)

= (15% * 78%) + (55% * 46.017%) + (25% * 116%) + (5% * 100%)

= 11.7% + 25.30935% + 29% + 5%

= 71.00935%

Hence, Tasheena's grade percentage in the class so far is approximately 71.00935%.

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The saving $100 at the end of each quarter for 15 years in an ordinary annuity that earns 5.4% interest, compounded quarterly, the Smith family would have $29,161.66 to travel the world.

An ordinary annuity is a stream of regular payments that are paid at the end of each period, such as quarterly, annually, or monthly. The Smith family intends to invest in an ordinary annuity to save money for a trip around the world.To compute the future value of a regular annuity,

the following formula is used:FV= PMT [ (1+r/n)^n*t - 1 ] / (r/n)where FV = future value, PMT = payment amount, r = interest rate per compounding period, n = number of compounding periods per year, and t = number of years of the investment.The Smith family's ordinary annuity has a 5.4% interest rate, compounded quarterly. As a result, the quarterly interest rate is: 5.4% / 4 = 1.35%.

The interest rate per compounding period is then converted to decimal form: 1.35% / 100 = 0.0135.The number of compounding periods per year is calculated by dividing the annual interest rate by the quarterly interest rate: 5.4% / 1.35% = 4.The number of payments the Smith family would make over a period of 15 years is: 15 years * 4 payments/year = 60 payments.

Finally, the future value of the annuity is calculated using the formula:FV= PMT [ (1+r/n)^n*t - 1 ] / (r/n) = PMT [(1+0.0135)^60 - 1]/ (0.0135)If the Smith family wants to save $100 at the end of each quarter, the calculation is as follows:FV = $100 [ (1+0.0135)^60 - 1 ] / (0.0135) = $29,161.66

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(a) x -5 -3 0 2 4

   y 4 0 -6 -10 -14

(d) x -14 -10 -6 0 4

   y 4 2 0 -3 -5

These tables could be used to verify that the functions they represent are inverses of each other

To verify if two functions are inverses of each other, we need to check if the composition of the two functions gives the identity function.

In other words, if f and g are two functions, then we need to check if f(g(x)) = x and g(f(x)) = x for all x in their domains.

We can create two tables, one for f and one for g, and use them to compute the compositions.

If the compositions give the identity function, then the functions are inverses of each other.

Based on this, the two tables that could be used to verify that the functions are inverses of each other are:

(a) x -5 -3 0 2 4

    y  4 0 -6 -10 -14

(d) x -14 -10 -6 0 4

    y 4    2   0 -3 -5

We can use the values in these tables to compute the compositions f(g(x)) and g(f(x)) and check if they give the identity function.

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Given:-

To find:-

Answer:-

In the given right angled triangle, we may use the trigonometric ratios. We can see that the measure of the longest side is "x" which is hypotenuse and it needs to be find out. The perpendicular in this case is "2" .

We may use the ratio of sine here as , we know that in any right angled triangle,

\(\implies\sin\theta =\dfrac{p}{h} \\\)

And here , p = 2 and h = x , so on substituting the respective values, we have;

\(\implies \sin\theta = \dfrac{2}{x} \\\)

Again here angle is 60° . So , we have;

\(\implies \sin60^o =\dfrac{2}{x} \\\)

The measure of sin45° is √3/2 , so on substituting this we have;

\(\implies \dfrac{\sqrt3}{2}=\dfrac{2}{x} \\\)

\(\implies x =\dfrac{2\cdot 2}{\sqrt3}\\\)

Value of √3 is approximately 1.732 . So we have;

\(\implies x =\dfrac{4}{1.732} \\\)

\(\implies \underline{\underline{\red{\quad x = 2.31\quad }}}\\\)

Hence the value of x is 2.31 .

Answer:

The length of side x to the nearest tenth is 2.3.

Step-by-step explanation:

From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : √3 : 2.  Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:

We have been given the side opposite the 60° angle, so:

\(\implies b\sqrt{3}=2\)

Solve for b by dividing both sides of the equation by √3:

\(\implies b=\dfrac{2}{\sqrt{3}}\)

The side labelled "x" is the hypotenuse, so:

\(\implies x=2b\)

Substitute the found value of b into the equation for x:

\(\implies x=2 \cdot \dfrac{2}{\sqrt{3}}\)

\(\implies x=\dfrac{4}{\sqrt{3}}\)

\(\implies x=2.30940107...\)

\(\implies x=2.3\; \sf (nearest\;tenth)\)

Therefore, the length of side x to the nearest tenth is 2.3.

The unit circle has the co-ordinates (-√2/2, -√2/2)

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: The unit circle and the point makes an angle of 225

we know the co-ordinates of any point on the unit circle is given by

x=cost and y=sint where t is the angle that line passing through the origin containing the point makes with x-axis

Thus x=cos225

           =-√2/2

and y=sin225

        =-√2/2

Hence, The required point is given by co-ordinates (-√2/2, -√2/2)

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Answer: 4

Step-by-step explanation: because he needs to divided by 2

Answer:

Step-by-step

Assuming that "43" is 4:3,  

21/3 = 7

4 * 7 = 28

There are 28 offensive players.ation:

Answer:28 defensive players

Step-by-step explanation:

The value of A when we rewrite 6^x as A^x/4 is 3/2

An algebraic expression can simply be defined as a mathematical expression that consists of terms, factors, constants, coefficients and variables.

They are also known as expressions made up of arithmetic operations, such as;

From the information given, we have that;

The function is given as;

6^x

Here, the coefficient or rather the base is 6

To determine the value of A when ^^x is given as A^x/4

The value of A would be;

6/4 = 3/2

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Answer: 25/100

Step-by-step explanation:

it 25%

Answer:

b

Step-by-step explanation:

since 5 is 1/2 of 10, 10 is 1/2 of 20, and so on and so forth.

Answer:

B

Step-by-step explanation:

Every number on A is half what the corrisponding number on B

Answer:

\(\huge\boxed{\sf x = -2}\)

Step-by-step explanation:

\(\sf x-5= 43 -10(x+7)\\\\Resolving \ Parenthesis\\\\x-5 = 43 - 10x -70\\\\x-5 = -10x +43-70\\\\x-5 = -10x -27\\\\Combining \ like \ terms\\\\x+10x = -27+5\\\\11x = -22\\\\Dividing \ both \ sides \ by \ 11\\\\x = -22/11\\\\x = -2\)

Hope this helped!

~AnonymousHelper1807

(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula

P(X=x|B) = P(X=x and B)/P(B).

Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:

P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.

Therefore, the conditional PMF P X∣B (x) is given by:

P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13

(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.

(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.

(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:

P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...

(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.

(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.

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Answer: 4

Step-by-step explanation: since there are 4 squares 16/4 is 4

Answer: To find the distance of a chord from the center of a circle, we need to use the following formula:

Distance from center = sqrt(r^2 - (c/2)^2)

Where r is the radius of the circle and c is the length of the chord.

In this case, the radius of the circle is 3.7cm and the length of the chord is 7cm.

So, substituting these values in the formula, we get:

Distance from center = sqrt(3.7^2 - (7/2)^2)

= sqrt(13.69 - 12.25)

= sqrt(1.44)

= 1.2 cm

Therefore, the distance of the chord from the center of the circle is 1.2 cm.

Step-by-step explanation:

Answer:

The answer is 90.

Step-by-step explanation:

90 is in the middle

Answer:

d

Step-by-step explanation:

cause i said so

Answer:

100 ml of 5% solution

200 ml of  20% solution

Step-by-step explanation:

x = amount of 5% solution

y = amount of 20% solution

System of equations:

x + y = 300

.05x + .20y = 300(.15)

Solve by substitution:  let y = 300 - x

.05x + .2(300-x) = 300(.15)

.05x + 60 - .20x = 45

-.15x = -15

x = 100, therefore y = 200

The data in the table can be modeled by this linear equation in slope-intercept form: y = 8x - 5.

The slope is 8, which means the wages earned increases at rate of 8 dollars per hour as the time increases.

The y-intercept is -5 and it represent the initial wages earned.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (24.00 - 8.00)/(3 - 1)

Slope (m) = 16.00/2

Slope (m) = 8

At data point (1, 3), a linear equation in slope-intercept form for this line can be calculated as follows:

y - y₁ = m(x - x₁)

y - 3 = 8(x - 1)

y = 8x - 8 + 3

y = 8x - 5

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Answer:

7%

Step-by-step explanation:

32.50--100%

2.25--x%

x=2.25×100%/32.5 it is approximately equal to 7%

Answer:

65.4

Step-by-step explanation:

60*.09 = 5.4

60+5.4 = 65.4

Answer:

C(t) = 6/55

Step-by-step explanation:

Given:

t = 10

Work:

\(C(t)= \frac{4 +2t}{120+10t} \\\\C(t)= \frac{4 +2(10)}{120+10(10)}\\\\C(t)= \frac{4 +20}{120+100}\\\\C(t)= \frac{24}{220}\\\\C(t)=\frac{6}{55}\)

The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1