At basketball practice, Nicole's team practiced defense for 1 hour and 55 minutes and offense for 1 hour and 20 minutes. If the practice ended at 8:55 P.M., what time did it start?

Given:

Length of escalator = 26 ft

Angle of depression = 41 degrees

To find:

The horizontal distance x the escalator covers to the nearest tenth of a foot.

Solution:

In a right angle triangle,

\(\cos \theta=\dfrac{Base}{Hypotenuse}\)

Using this formula for the given triangle, we get

\(\cos 41^\circ=\dfrac{x}{26}\)

\(26\cos 41^\circ=x\)

\(26(0.7547)=x\)

\(19.6222=x\)

Round the value to the nearest tenth.

\(x\approx 19.6\)

Therefore, the escalator covers 19.6 ft horizontally.

Answer:

Part A:

The Standard Form equation of a line has the following formula:

Ax+By=C, where A, B, and C are integers, and A is non-negative.

We will assume that when renting a boat Sam paid fixed cost and rental charge per day.

y = the total rent

x = the number of days

Sam rented a boat at $225 for 2 days would mean:

y = 225 when x = 2 or if we plug into Ax+By=C:

2A + 225B = C since A is non-negative we divide both sides by A

2 + (B/A)225 = C/A

He rents the same boat for 5 days, he has to pay a total rent of $480 means:

y = 480 when x = 5 days

5A + 480B = C since A is non-negative we divide both sides by A

5 + (B/A)480 = C/A

Now we have:

2 + (B/A)225 = C/A

5 + (B/A)480 = C/A

Lets denote s = B/A  and t = C/A. Now we can write the following system of equations:

2 + 225s = t

5 + 480s = t

........

click here to see the system of equations solved for s and t

........

s = -1/85

t = -11/17 = -55/85

Now we can go back to:

B/A = -1/85 and C/A = -55/85

A = 85, B = -1, C = -55

The standard equation is:

85x - y = -55

Part B:

Using the equation 85x - y = -55 we solve for y

.......

click here to see the equation solved for y

........

y = 85x + 55

or in function notion y = f(x)

f(x) = 85x + 55

Part C:

The graph of y = 85x + 55 is:

Step-by-step explanation:

Answer:

y = 225/2x + 2

Step-by-step explanation:

Find AB , AC , DE and DF. If the ratios DE/AB and DF/AC are equal , then the triangles are similar

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔDEF

Now , the corresponding sides are

DE/AB and DF/AC

Now , corresponding sides of similar triangles are in the same ratio.

On simplifying , we get

DE/AB = DF/AC

Hence , the triangles are similar

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Answer:

1. 27/100

2. 9/100

Step-by-step explanation:

1  Move the decimal enough places to the right to get a whole number.

2. Note the number of places you moved the decimal

3. Take 10 to the power of the number you got in step 2

4. Divide the number in step 1 by the number in step 2

5. Simplify if possible

Example
1. 0.27 ==> 27 by moving the decimal point 2 places to the right

2. Number of places moved = 2

3. 10² = 100

4. 26/100 is the fraction

5. cannot simplify further

The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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Answer:

Maria's book was 8 days late

Step-by-step explanation:

According to the information given, you can write an equation that states that 15¢ multiply for the number of days that the book was late plus $2 is equal to $3.20:

0.15x+2= 3.20

x= number of days that the book was late

Now, you have to solve for x:

0.15x= 3.20-2

0.15x= 1.20

x= 1.20/0.15

x= 8

The book was 8 days late.

The formula of  g(u) in terms of u is g(u) = (-12u + 2) / 8 by equation  -12u + 3 = 8v + 1.

To find a formula for g(u) in terms of u, we need to solve the given equation for v and express it in terms of u.

Starting with the equation: -12u + 3 = 8v + 1

Rearranging the terms, we have:

8v = -12u + 3 - 1

8v = -12u + 2

Dividing both sides of the equation by 8:

v = (-12u + 2) / 8

Therefore, the formula for g(u) in terms of u is:

g(u) = (-12u + 2) / 8

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If the length of one side of the rhombus is 6m and the radius of the rhombus as 4 m then the area of the rhombus is 24 m².

What is the area of the rhombus?

The Area of a Rhombus = A = ½ × d1 × d2,

Where d1 and d2 are the diagonals of the rhombus.

The area of a rhombus can be found using the formula:

Area = (diagonal 1 x diagonal 2) / 2

or

Area = (base x height) / 2

We are given the length of one side of the rhombus as 6 m, which means the length of the other side is also 6 m since all sides of a rhombus are congruent. We are also given the radius of the rhombus as 4 m, which is half the length of the diagonal.

Using the Pythagorean theorem, we can find the length of the other diagonal:

diagonal 2 = 2(radius) = 2(4) = 8 m

Now we can use the formula to find the area of the rhombus:

Area = (diagonal 1 x diagonal 2) / 2

Area = (6 m x 8 m) / 2

Area = 24 m²

Therefore, the area of the rhombus is 24 m².

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Answer:

11z + 11

Step-by-step explanation:

Answer:

If Luca wants to leave a 16% tip on the total amount including the tax, he should pay $32.24.

Step-by-step explanation:

First, you have to calculate the 4% of the bill and add that amount to the total of the bill to determine the total amount including the tax:

193.75¨*4%=7.75

193.75+7.75=201.5

Now, you have to calculate 16% of the amount including the tax:

201.5*16%=32.24

According to this, the answer is that if Luca wants to leave a 16% tip on the total amount including the tax, he should pay $32.24.

Answer:

$201.50

Step-by-step explanation:

just took the. test

A correlational study is an experiment that can be conducted to determine if there is a mean relationship (slope) between two variables

An experiment that can be conducted to determine if there is a mean relationship (slope) between two variables is known as correlation analysis. Correlation analysis is performed to determine whether a relationship exists between two variables, as well as the strength of that relationship.

A correlational study can be performed in which two variables are measured at the same time for all individuals, and the correlation coefficient is calculated. For instance, a study may look at the relationship between the number of hours studied and the score earned on a test in a group of students.

The goal is to determine whether there is a linear relationship between the two variables (hours studied and test score), and the strength of that relationship.

If the correlation coefficient is high (close to +1 or -1), it suggests a strong relationship between the two variables. If the correlation coefficient is close to zero, it implies no relationship between the variables.

If the correlation coefficient is negative, it means that the two variables are inversely related.

In conclusion, a correlational study is an experiment that can be conducted to determine if there is a mean relationship (slope) between two variables.

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The P-value for the hypothesis test is approx. 0.7064.

To find the P-value for the hypothesis test, we need to perform a two-sample proportion test. The formula to calculate the test statistic for this test is given by:

\(\[ z = \frac{{(\hat{p}_1 - \hat{p}_2) - 0}}{{\sqrt{\hat{p}(1 - \hat{p})\left(\frac{1}{{n_1}} + \frac{1}{{n_2}}\right)}}} \]\)

where \(\hat{p}_1\) and \(\hat{p}_2\) are the sample proportions, \(\hat{p}\) is the combined sample proportion, \(n_1\) and \(n_2\) are the sample sizes, and 0 is the hypothesized difference in proportions.

In this case, we have \(n_1 = 50\), \(x_1 = 8\) (number of successes in sample 1), \(n_2 = 50\), and \(x_2 = 7\) (number of successes in sample 2).

First, we calculate the sample proportions:

\(\[ \hat{p}_1 = \frac{x_1}{n_1} = \frac{8}{50} = 0.16 \]\)

\(\[ \hat{p}_2 = \frac{x_2}{n_2} = \frac{7}{50} = 0.14 \]\)

Next, we calculate the combined sample proportion:

\(\[ \hat{p} = \frac{x_1 + x_2}{n_1 + n_2} = \frac{8 + 7}{50 + 50} = 0.15 \]\)

Then, we calculate the standard error:

\(\[ SE = \sqrt{\hat{p}(1 - \hat{p})\left(\frac{1}{{n_1}} + \frac{1}{{n_2}}\right)} = \sqrt{0.15(1 - 0.15)\left(\frac{1}{50} + \frac{1}{50}\right)} \approx 0.0529 \]\)

Finally, we calculate the test statistic:

\(\[ z = \frac{(\hat{p}_1 - \hat{p}_2) - 0}{SE} = \frac{(0.16 - 0.14) - 0}{0.0529} \approx 0.3772 \]\)

To find the P-value, we look up the test statistic in the standard normal distribution table. In this case, the P-value is the probability of observing a test statistic greater than 0.3772 or less than -0.3772.

Consulting the table, we find that the P-value is approximately 0.7064. Therefore, the P-value for the hypothesis test is approximately 0.7064.

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Answer: Standard Deviation.

Step-by-step explanation:

DescriptionIn insights, the standard deviation is a proportion of the measure of variety or scattering of a lot of qualities. A low standard deviation demonstrates that the qualities will in general be near the mean of the set, while an elevated expectation deviation shows that the qualities are spread out over a more extensive territory.

The value of (ΣX)² for the scores 1, 5, 2 is:  

64

It is the representation of the sum of infinite or many values. And it is represented by the following symbol:

∑xi

The value of (ΣX)² for the scores 1, 5, 2 can be found by first finding the summation of the scores and then squaring the result.

Steps to follow:

Step 1: Find the summation of the scores.
            ΣX = 1 + 5 + 2 = 8

Step 2: Square the summation.
            (ΣX)² = 82 = 64

Therefore, the value of (ΣX)² for the scores 1, 5, 2 is 64.

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As per the concept of compound interest, it take 62.915 years for the account to earn $7500

Compound interest:

The general formula to calculate the compound interest is written as,

A = P(1 + r/n)^nt

where

A = Accrued amount (principal + interest)

P = Principal amount

r = Annual nominal interest rate as a decimal

n = number of compounding periods per unit of time

t = time in decimal years;

Given,

Compounding frequency = Quarterly

Interest rate = 1.75%

Opening balance = $2500

Final amount = $7500

Now, we have to calculate the time time for the person to achieve the final amount,

First, convert R as a percent to r as a decimal

r = R/100

r = 1.75/100

r = 0.0175 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(7,500.00/2,500.00) / ( 4 × [ln(1 + 0.0175/4)] )

t = ln(7,500.00/2,500.00) / ( 4 × [ln(1 + 0.004375)] )

t = 62.915 years

Therefore, the  time required to get a total amount of $7,500.00 with compounded interest on a principal of $2,500.00 at an interest rate of 1.75% per year and compounded 4 times per year is 62.915 years.

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Answer:

DF = 13.3

KF = 7.2

Step-by-step explanation:

Because of the parallel sides, triangles DEF and LKF are similar by AA.

Then DE/KL = DF/LF = EF/KF.

25/15 = DF/8 = 12/KF

15DF = 8 * 25

DF = 13.3

25KF = 15 * 12

KF = 7.2

Answer:

g(x) = 2ˣ ⁻ ⁵ + 3

Step-by-step explanation:

When doing transformations, any time you are going left and right, you do on the inside. It also has to be the opposite sign. That's why we do - 5 with the x.

Translating horizontally deals with changes along the x-axis. That's why it affects the x.

Any time it's on the outside, we go up and down. Aka the + 3.

Answer:

Step-by-step explanation:

l is line. It has no beginning and end point.

AB is a ray. It has a beginning point and has no end point.

CD is a segment and it has both beginning and end point.

∠1 is an angle.

a, b are parallel lines and t is transversal.

Answer: with what???

Using division of fractions, the equivalent expression is:

B. \(\frac{4}{d - 6}\).

To divide two fractions, we multiply the first by the inverse of the second.

In this problem, we have that:

Applying the multiplication, we have that:

\(\frac{2(d - 3)}{(d + 8)(d - 6)} \times \frac{2(d + 8)}{d - 3} = \frac{4}{d - 6}\).

Hence option B is correct.

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Answer:

30yd^3

Step-by-step explanation:

dimensions are 3*5*2 (count the number of blocks) so multiply to get 30 yd^3

Answer:

It is C

Step-by-step explanation:

Khan Academy I use it trust me

Answer:

19 orders of tea

57 orders of collee

Step-by-step explanation:

find 1/4 of the 76

76/4=19

multiply by 3

19x3=57

48.5 feet

1) Sketching this we have:

2) As the point here is how much string was left out, then let's use a trigonometric ratio to find out that hypotenuse since height is always perpendicular (90º with the ground).

3) Hence, that kite's string is 48.5 feet long

The capacitance of the other cylinders are 2174. 94cm³ and 1208. 30cm³.

Capacity of a cylinder is seen as its volume

Volume of a cylinder = πr²h

The heights of the cylinders are

a. 3cm

b. 9cm

c. 5cm

Let's find the radius

Capacity = 3. 142 × r² × 3

725 = 3. 142 × r² × 3

r² = \(\frac{725}{3. 142 * 3}\)

r² = \(\frac{725}{9. 426}\)

r² = 76. 91

r = √76. 91

r = 8. 77cm

Radius of the cylinders = 8. 77cm

For cylinder with height of 9cm

Capacitance = πr²h

Capacitance = 3. 142 × 8. 77 × 8. 77 × 9

Capacitance = 2174. 94 cm³

For cylinder with height of 5cm

Capacitance = 3. 142 × 8. 77 × 8. 77 × 5

Capacitance = 1208. 30 cm³

Thus, the capacitance of the other cylinders are 2174. 94cm³ and 1208. 30cm³.

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Answer:

The answer would be x= 4, hope this helps!

The value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded), we need at least 5 terms in the series of cos(x). We will use Taylor's theorem to derive this result.

Taylor's theorem, also known as the Taylor series theorem, is a mathematical formula used to represent functions as a sum of infinitely many derivatives in order to approximate them over a certain interval.

This formula allows us to derive the value of a function at a point using information about its derivatives at that point.

In essence, Taylor's theorem is a tool used in calculus to model complex functions that cannot be easily solved.

Using Taylor's theorem to solve the question:

We know that the Taylor series expansion of cos(x) is given by the formula:

cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...

To get an accurate value of cos(x), we need to keep adding terms in the series until the absolute value of the next term is less than our required accuracy.

Using |x| ≤ 1/12 and rounding to 12 decimal places, we have an error tolerance of 0.000000000001.

Therefore, we need to find the smallest value of n such that \(|x^(n+1)/(n+1)!| ≤ 0.000000000001,\)

where x = 1/12.

Substituting x = 1/12,

we have |(1/12)^(n+1)/(n+1)!| ≤ 0.000000000001

Using a calculator, we can find that n = 4 satisfies this inequality.

Therefore, we need at least 5 terms in the series of cos(x) to compute the value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded).

Conclusion:

To calculate the value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded), we need at least 5 terms in the series of cos(x). We used Taylor's theorem to derive this result.

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Answer:

According to my the answer is 32

Step-by-step explanation:

cuz 4 ÷ 1/8 becomes 4×8/1

which is 32