0.8,2/3,0.67,70% in order

Answer:

x ≈ 2.76

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan78° = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{13}{x}\) ( multiply both sides by x )

x × tan78° = 13 ( divide both sides by tan78° )

x = \(\frac{13}{tan78}\) ≈ 2.76 ( to 2 dec. places )

The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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Answer:

x = 6

Step-by-step explanation:

The sides of a 30-60-99 triangle are: a) x sqrt 3, b) x, and the hypotenuse 2x

2x = 12

Answer:

Yes yes no no

Step-by-step explanation:

This image should help

Using visual interpretation of the plot trend, the scatter plot shows positive correlation.

A positive correlation is depicted by a positive slope or trend line on a scatter plot. The trend of the scatter plot slopes upward which establishes a positive association.

If the slope is otherwise negative, such that the trend line slopes downward, then we have a negative association or relationship.

Therefore, the scatter plot shows positive relationship.

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Answer:

164,340

Step-by-step explanation:

plug in 32 for n in the expression and solve.

120(32)+160,500

3840+160,500 = 164,340

hope this helps <3

Answer:

when n=32

120n + 160,500=120×32+160500=164340 is your answer.

To compute the z-score for the applicant, we can use the formula:

z = (x - μ) / σ

Where:

x is the applicant's score

μ is the mean

σ is the standard deviation

Given that the applicant's score is 21.0, the mean is 18.0, and the standard deviation is -3.0, we can substitute these values into the formula to calculate the z-score.

z = (21.0 - 18.0) / (-3.0)

z = 3.0 / -3.0

z = -1.0

Therefore, the z-score for the applicant is -1.0.

The correct option is O-10.

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The equation of the exponential equation with an asymptote of y=12 that passes through the points (3,332) and (5,5132). y = -28.295(b^x) + 12.

An exponential function with an asymptote of y = 12 has the general form y = a(b^x) + 12

where a is a non-zero constant and b is a positive constant.

To find the specific exponential function that passes through the given points, we need to solve for a and b.

Using the point (3,332), we have:

332 = a(b^3) + 12

Using the point (5,5132), we have:

5132 = a(b^5) + 12

We now have two equations with two unknowns. We can solve for a by subtracting the second equation from the first equation:

-4800 = a(b^3 - b^5)

We can then solve for b^2 by dividing both sides by a and factoring out b^2:

b^2 = (b^3 - b^5) / (-4800a)

Since b is positive, we can take the square root of both sides:

b = sqrt((b^3 - b^5) / (-4800a))

We can then substitute this expression for b into one of the original equations to solve for a. Using the first equation, we have:

332 = a(b^3) + 12

332 = a(sqrt((b^3 - b^5) / (-4800a))^3) + 12

332 = a(b^3 - b^5)^(3/2) / (-4800a) + 12

Multiplying both sides by (-4800a) and simplifying, we get:

-1593600 = a(b^3 - b^5)^(3/2) + (-4800a)(12)

-1593600 = a(b^3 - b^5)^(3/2) - 57600a

-27.67 = (b^3 - b^5)^(3/2) - 0.036a

We can now solve for a:

a = (b^3 - b^5)^(3/2) / (-27.67 + 0.036b^2)

Substituting this expression for a back into the equation for b^2, we have:

b^2 = (b^3 - b^5) / (-4800a)

b^2 = (b^3 - b^5) / (-4800[(b^3 - b^5)^(3/2) / (-27.67 + 0.036b^2)])

Simplifying, we get:

b^2 = sqrt((27.67 - 0.036b^2) / 4800)

Squaring both sides, we have:

b^4 = (27.67 - 0.036b^2) / 4800

Multiplying both sides by 4800 and rearranging, we get:

0.036b^6 + 4800b^4 - 27.67 = 0

This is a sixth-degree polynomial in b^2, which can be solved numerically using a calculator or software. We find that there are three real solutions, one of which is negative and two of which are positive. We choose the positive solution that gives the correct y-values for both given points:

b ≈ 1.3825

We can then substitute this value for b and the value we found for a into the general form of the exponential equation to get the specific equation that passes through the given points:

y = -28.295(b^x) + 12.

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No, the data do not provide the convincing evidence that proportion of teenagers texted while driving exceeds 77% as p-value is greater than the significance level

Number of teenager drives in Atlanta = 31

Number of teenager texting while driving = 26

Percent of teenager texted while driving = 77%

Use a hypothesis test for a single proportion.

Null hypothesis (H0),

The proportion of teenagers who have texted while driving is equal to 77%.

Alternative hypothesis (HA),

The proportion of teenagers who have texted while driving exceeds 77%.

Use a significance level of 0.05, which is a commonly used threshold in hypothesis testing.

Test statistic for this hypothesis test is given by,

z = (p1 - p0) / √(p0× (1 - p0) / n)

where p1 is the sample proportion,

p0 is the hypothesized proportion under the null hypothesis,

and n is the sample size.

Substitute values we get,

p1 = 26/31

   = 0.8387

p0 = 0.77

n = 31

Plugging these values into the formula, we get,

z = (0.8387 - 0.77) / √(0.77(1 - 0.77) / 31)

 = 0.09090

Using a standard normal distribution table,

p-value associated with a z-value of 0.09090 is 0.4637.

Since the p-value is greater than the significance level of 0.05,

Fail to reject the null hypothesis.

Therefore, we do not have convincing evidence that the proportion of teenagers who have texted while driving exceeds 77%.

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The solutions to the equation \(2x^{2} +3x=-8\\\) are \(x=\frac{-3+i\sqrt{55} }{4}\) and \(x=\frac{-3-i\sqrt{55} }{4}\) respectively.

What is a quadratic equation?

A second-degree algebraic equation is a quadratic equation in x.

\(ax^{2} +bx+c=0\) is the quadratic equation in standard form, where a and b are the coefficients, x is the variable, and c is the constant term.

To find the root value of x, \(x= \frac{-b}{2a}\) ± \(\frac{\sqrt{b^{2} -4ac} }{2a}\)

Given, \(2x^{2} +3x=-8\\\)

or, \(2x^{2} +3x+8=0\)

Comparing the equation \(2x^{2} +3x+8=0\) with the equation  \(ax^{2} +bx+c=0\) , we get

\(a=2, b=3, c=8\)

Then, \(x= \frac{-3}{2*2}\) ± \(\frac{\sqrt{3^{2} -4*2*8} }{2*2}\)

or,  \(x= \frac{-3}{4}\) ± \(\frac{i\sqrt{55} }{4}\)

Taking '+' sign, we get \(x=\frac{-3+i\sqrt{55} }{4}\)  and \(x=\frac{-3-i\sqrt{55} }{4}\)

Therefore, the solutions of the given equation are \(x=\frac{-3+i\sqrt{55} }{4}\) and \(x=\frac{-3-i\sqrt{55} }{4}\).

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Answer:

The answer is 5.48

Step-by-step explanation:

When rounding the hundredths (second number after the dot), you want to look at the number on the right. In this case, that number is 6.

Anytime the number to the right is more than 5, you make the number before it one number higher. Here, the 7 in 5.476 turns into 5.48.

After you've rounded, drop the number you looked at. So, no need for the 6 anymore!

That's it!

Answer:

well first we need to see the total percent of sugar solution there is.

So first we need to add 50%+68%=118%/200%

so now 62%/100% needs translated to /200%.

We get 124%/200% Now 50%/100%=100%/200% 68%/100%=136%/200%

62% would be in a total of needed of like 7 ml of the 50% sugar solution i think let me know if i am wrong

Step-by-step explanation:

Answer:

8 cubes will have paint on 3 faces

Step-by-step explanation:

8 cubes will have paint on 3 faces

4 * 4 * 3 =  48  will have paint on two  faces

[ 8 + 48 ]  /   6^3    

56  /  216  

7 / 27

What is called cube?

In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

It is also said to be a regular hexahedron.

Cube is a 3-dimensional structure with six squares/faces, and three of them meet at each vertex, and all the angles at the corner are right-angled.

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Answer:

7 cm

Step-by-step explanation:

Area of a parallelogram formula:

\(A=bh\) where b is the base length and h is the height

Plug in known values (A=112, b=16 and h=x)

\(112=16x\)

Divide both sides by 16 to isolate x

\(\frac{112}{16} = \frac{16x}{16}\\7=x\)

Therefore, x is equal to 7 cm.

I hope this helps!

Answer:

This statement is B. False

Step-by-step explanation:

You CAN tesselate six-sided regular polygons by themselves therefore, this statement is FALSE.

Hope this helped! :)

Answer:

Step-by-step explanation:

Answer:

I'm not sure, but it could be "inverse"

Step-by-step explanation:

Probabilities of each of the cards are :

A) 1/52, B) 1/16, C) 3/52, D) 1/26, E) 1/4 and F) 9/169

Given that,

A standard 52 deck of cards are shuffled.

A card is chosen from the deck, then returned to the deck and then second card is chosen.

A) a heart and then a queen.

Number of hearts = 13 and number of queen = 4

Probability of choosing a heart and then a queen = 13/52 × 4/52 = 1/52

B) a spade and then a diamond

Number of spades = 13 and number of diamonds = 13

Probability of choosing a spade and then a diamond = 13/52 × 13/52 = 1/16

C) a face card and then a club

Number of face cards = 12 and number of clubs = 13

Probability of choosing a face card and then a club = 12/52 × 13/52 = 3/52

D) a red card and then a king

Number of red cards = 26 and number of king  = 4

Probability of choosing a face card and then a club = 26/52 × 4/52 = 2/52 = 1/26

E) two black cards in a row

Number of black cards = 26

Probability of choosing two black cards in a row = 26/52 × 26/52 = 1/4

F) a numbered card and then an ace

Number of numbered cards = 36 and number of ace = 4

Probability of choosing a numbered card and then an ace = 36/52 × 4/52 = 9/169

Hence the probabilities are found.

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Step-by-step explanation:

the answer is 3/2

always remember when multiplying numbers of the same base the exponents will always be added and when dividing numbers of the same base the exponents will be minused.

Answer:

3:54

Step-by-step explanation:

1 hour and 36 minutes after 2:18 is 3:54

Answer:

b = $48000, m = $3187.5 / year

Step-by-step explanation:

The equation of a linear function is given as y = mx + b, where m is the rate of change, b is the value of y when x = 0, y = dependent variable and x = dependent variable.

Given that V = mt + b:

b = initial price of the house at 0 years = $48000

V = mt + 48000, At 8 years the house is appraised at ​$73,500

73500 = 8m + 48000

8m = 73500 - 48000

8m = 25500

m = 3187.5

Answer:

Step-by-step explanation:

The slope of line u is 9/2; the line perpendicular to that is the opposite reciprocal...opposite sign and the flip of the fraction. The perpendicular slope is -2/9

Answer:

57

Step-by-step explanation:

2166/38=57

Answer: 57

Step-by-step explanation:2188 divided by 38 =57

Answer:

2(3x + 5) = 6x + 10

⇔ 6x + 10 = 6x + 10

=> infinite solution

Step-by-step explanation:

Answer:

qr=68r/s

Step-by-step explanation:

rs=44

s=44/r

qs=68

q(44/r)=68

44q/r=68

44q=68r

q=68r/44

rs=44

r=44/s

qr=(68r/44)(44/s)=68r/s

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

Here is an example solution in Python that follows the given pseudocode:

# Prompt for and read the first term

first_term = int(input("Enter first term: "))

# Prompt for and read the common difference

common_difference = int(input("Enter common difference: "))

# Prompt for and read the number of terms

number_of_terms = int(input("Enter number of terms: "))

# Calculate the last term

last_term = first_term + (number_of_terms - 1) * common_difference

# Calculate the sum of all the terms

sum_of_terms = number_of_terms * (first_term + last_term) / 2

# Calculate the average of all the terms

average_of_terms = sum_of_terms / number_of_terms

# Display the results

print("The last term is", last_term)

print("The sum of all the terms is", sum_of_terms)

print("The average of all the terms is", average_of_terms)

If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:

The last term is 300

The sum of all the terms is 15150.0

The average of all the terms is 151.5

The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.

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We will have the following:

So, the expression in its simplest form is 4/9.

***Explanation***

First we are given the expression:

From the properties of roots, we will have that if a root contains a fraction, then we can rewrite the expression applying the root to the numerator and denominator [Separately], this is:

Since, these expressions are equivalent, then we solve for each one, that is:

Then, we simply replace in the fraction form:

Answer:

22: 2

23: -7

25: 6

26: 3

Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!

Step-by-step explanation:

For 22: 2 * 2 * 2 = 8, therefore, 2

For 23:  -7 * -7 * -7 = -343. This results in a negative number because there is is an odd number of negative numbers (follows the odd-even negative rule).

For 25: Multiply both sides of the equation by -1/2 to get z^3 = 216. The cube root of 216 is 6

For 26: Add 11 to both sides to get 2h^3 = 54. Divide both sides by 2 to get h^3 = 27. Cube root of 27 is 3.

Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!

the answer would be C since in order to determine a volume, you need the width, length and height :)

Obviously, the answer is C as you can't the volume of a solid without knowing its dimensions.

The estimated total time for all five pools is approximately 13.85 hours.

To estimate the time required to install the fifth pool using the learning curve, we can use the formula:

Time for nth unit = Time for first unit * (n^b)

Where:

Time for nth unit is the estimated time to install the nth pool

Time for first unit is the estimated time to build the first pool (30 hours)

n is the number of units (in this case, n = 5 for the fifth pool)

b is the learning curve exponent (85% learning rate corresponds to b = log(0.85) / log(2))

Let's calculate the estimated time for the fifth pool:

b = log(0.85) / log(2) ≈ -0.157

Time for fifth pool = Time for first pool * (5^b)

Time for fifth pool = 30 * (5^(-0.157))

Calculating this, we find:

Time for fifth pool ≈ 30 * 0.6764 ≈ 20.29 hours

Therefore, the estimated time required to install the fifth pool is approximately 20.29 hours.

To calculate the total time for all five pools, we need to sum the time required for each pool from the first to the fifth. Since the learning curve assumes decreasing time with increasing units, we can use a summation formula:

Total time for all units = Time for first unit * ((1 - (n^b)) / (1 - b))

Using this formula, let's calculate the total time for all five pools:

Total time for all five pools = Time for first pool * ((1 - (5^b)) / (1 - b))

Total time for all five pools = 30 * ((1 - (5^(-0.157))) / (1 - (-0.157)))

Calculating this, we find:

Total time for all five pools ≈ 30 * 0.4615 ≈ 13.85 hours

Therefore, the estimated total time for all five pools is approximately 13.85 hours.

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