-2/5+4/5 drop the corrects sum on the number line

Option A is correct i.e. No, she should divide 1 / 2 by 2 to get 1 / 4.

No, Lucky's claim is not correct. The walking path is 1 / 2 miles long and is divided into 2 equal sections. Therefore, each section of the walking path is:

(1 / 2) miles ÷ 2 = 1 / 4 miles

This is equivalent to 0.25 miles, not 1 mile. Therefore, Lucky's claim that each section of the walking path is 1 mile long is incorrect

Therefore, option A is correct i.e. No, she should divide 1 / 2 by 2 to get 1 / 4.

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1  35.56

2  914.6

3 76595.6

The theoretical probability of a fair coin landing on heads is 0.5. After flipping a coin 14 times, the experimental probability of landing on heads is 0.5 (7/14). The experimental probability matches the theoretical probability, indicating a fair coin.

The theoretical probability of a fair coin landing on heads is 0.5, since there are two equally likely outcomes (heads or tails) and only one of them is heads.

When flipping a coin 14 times, the possible outcomes are heads or tails, and each flip is independent of the others. The frequency of each outcome can be recorded as follows

Heads: 7

Tails: 7

The experimental probability of landing on heads is the number of times that heads occurred divided by the total number of flips

Experimental probability of landing on heads = 7/14 = 0.5

The experimental probability of landing on heads (0.5) is equal to the theoretical probability of landing on heads (0.5), which suggests that the coin used in the experiment is fair.

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Using De Morgan's law and the associative law of disjunction, the simplified expression for [(p∧q') → r']' is p' ∨ q ∨ r.

The solution to the logical expression [(p∧q') → r']', can be solved as follows:

1. Applying De Morgan's law to the expression [(p∧q') → r']':

[(p∧q') → r']' = [(p∧q')' ∨ r]

2. De Morgan's law is applied again to the negated conjunction (p∧q')':

(p∧q')'= (p' ∨ q) ∨ r

Then, the inner parentheses are removed using the associative law of disjunction, and then the expression is simplified thus: p' ∨ q ∨ r

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x=3.42851536

to be 100% honest with you, this was kind of a guess and check, i'm sure there is some method i am forgetting from highschool, but it's been way too long since i've done this kind of problem

To calculate the confidence interval, we'll use the formula:

CI = sample proportion ± z* (standard error)

where:

- sample proportion = p_hat = 23/50 = 0.46 (proportion of students in the sample who used tutoring and found it beneficial)

- z = 1.96 (for a 95% confidence level)

- standard error = sqrt(p_hat * (1 - p_hat) / n) = sqrt(0.46 * 0.54 / 50) = 0.101

Plugging these values into the formula, we get:

CI = 0.46 ± 1.96 * 0.101

CI = [0.263, 0.657]

Therefore, we can say with 95% confidence that the true proportion of Mesa students who have used tutoring and found it beneficial is between 0.263 and 0.657.

Invest in stocks and bonds directly by purchasing them through a brokerage account. Indirect investments  can be made through mutual funds.

Assets acquired or invested  to build wealth and save money based on hard-earned income or appreciation. Investing primarily means getting extra income or income from an investment over a certain period of time.  Stocks, bonds and cash are the three main types of investments.

Stocks - represent ownership in a company and their value varies depending on market demand and company performance. Stocks may offer potential growth over the long term, but they also carry more risk than other  investments.  

Bonds - are essentially loans that investors make to governments or companies, usually offering a fixed interest payment and repayment of principal at maturity. Bonds generally offer lower yields than stocks, but are considered  less risky.

Cash - refers to investments that are highly liquid and can be easily converted to cash, such as savings accounts, money market accounts, and certificates of deposit (CDs). Cash investments usually have lower returns than stocks and bonds, but  are considered  the least risky types of investments.

You can invest in stocks and bonds directly by buying them through a brokerage account. This can be done online or through a financial advisor. Financial investments can be made directly through a bank or credit union. Such investments  can be invested indirectly through investment funds. A mutual fund is  money from many investors  managed by a professional investment manager. A mutual fund invests in a diversified portfolio that includes stocks, bonds or cash, depending on the fund's investment objective. Investors can buy shares of  mutual funds, and the value of the shares will rise or fall based on the performance of the underlying investments.

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Answer: 2

Step-by-step explanation:

Tara would be required to repay the debt in 90.42 days, or roughly 90 days and 10 hours.

The simple interest is calculated as,

Simple interest = Principal x Rate x Time

Where the loan's principal, interest rate, and term are represented by the variables principal, rate, and time, respectively.

In this case, the maturity value, which includes the principal and interest, is $2,572.92 and the principal is $2,500. The rate is 8.75%. Let's begin by computing the interest on the loan:-

Interest = Maturity value - Principal

Interest = $2,572.92 - $2,500

Interest = $72.92

Calculate the interest below,

Interest = Principal x Rate x Time / 365

$72.92 = $2,500 x 0.0875 x Time / 365

$72.92 x 365 = $2,500 x 0.0875 x Time

Time = $72.92 x 365 / ($2,500 x 0.0875)

Time = 90.42 days

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Answer:

Step-by-step explanation:

The measure of angles m∠1,m∠2, and m∠3 are 133°, 47°, and 43° respectively

47° and m∠1 are on a straight line and their sum is equal to 180° so;

m∠1 + 47° = 180° {sum of angles on a straight line}

m∠1 = 180° - 47° {subtract 47° from both sides}

m∠1 = 133°

47° and m∠2 are vertical angles hence they are equal so;

m∠2 = 47°

m∠2 and m∠3 are complementary angles so their sum is equal to 90°

m∠3 + 47° = 90°

m∠3 = 90° - 47°

m∠3 = 43°

In conclusion, the measure of angles m∠1,m∠2, and m∠3 are 133°, 47°, and 43° respectively

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The standard deviation of the given set of numbers is calculated as:  6.833

Standard deviation is defined as a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

We are given the data as: 88, 100, 85, 82

Thus:

To find the standard deviation of a set of numbers, first find the mean (average) of the set of numbers:

(88 + 100 + 85 + 82)/4 = 88.75

Second, for each number in the set, subtract the mean and Add the square the result:

(88 - 88.75)² + (100 - 88.75)² + (85 - 88.75)² + (82 - 88.75)² = 186.75

Standard deviation = √(186.75/4)

= 6.833

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The measure of the angles are A = 33 degrees, B = 107.5 degrees and 39.5 degrees

from the question, we have the following parameters that can be used in our computation:

The triangle

The measure of angle C is calculated using

c² = a² + b² - 2ab * cos(C)

So, we have

14² = 21² + 12² - 2 * 21 * 12 * cos(C)

Evaluate

196 = 585 - 504 * cos(C)

Subtract and divide

cos(C) = 0.7718

Take the arc cos

C = 39.5 degrees

Using the list of options, we have

A = 33 degrees, B = 107.5 degrees and 39.5 degrees

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Answer:

You didn't tell us what S is equal to, but just do this: 15-S=__

Step-by-step explanation:

Answer: To calculate the monthly payment, we need to use the formula for the equal monthly installment for a loan with constant payments and interest:

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

where:

P = monthly payment

r = monthly interest rate

PV = present value (the initial loan amount)

n = total number of payments

In this case, PV = $3500, n = 60, and r = 1.75% per month.

First, we can calculate the monthly interest rate by dividing the annual rate by 12:

r = 1.75% / 100% / 12 = 0.0175/12

Plugging in the values, we get:

P = (0.0175/12 * $3500) / (1 - (1 + 0.0175/12)^-60)

P = $69.92 (rounded to two decimal places)

So the monthly payment is $69.92.

To calculate the total interest paid, we can subtract the initial loan amount from the total of all payments:

Total interest = (P * n) - PV

Total interest = ($69.92 * 60) - $3500

Total interest = $195.20

So the total interest paid is $195.20.

Step-by-step explanation:

Answer: The total interest paid is $1186.

Step-by-step explanation: The first step is to calculate the monthly interest rate:

1.75% per month can be written as 0.0175 in decimal form.

Next, we can use the formula for the monthly payment of a loan:

P = r(PV) / [1 - (1+r)^(-n)]

Where:

P = monthly payment

r = monthly interest rate

PV = present value of the loan

n = total number of payments

Plugging in the given values, we get:

P = 0.0175(3500) / [1 - (1+0.0175)^(-60)]

= 78.10

Therefore, your monthly payments are $78.10.

To calculate the total interest paid, we can multiply the monthly payment by the number of payments and subtract the original loan amount:

Total interest = (60 x 78.10) - 3500

= 4686 - 3500

= $1186

Therefore, the total interest paid is $1186.

From the ANOVA table, we can see that the F-statistic is 114.89 and the p-value is less than 0.001.

To conduct the F-test, we first need to calculate the sum of squares for regression, error, and total, as well as their respective degrees of freedom. We can then use these values to complete an ANOVA table, which summarizes the results of the F-test.

The ANOVA table for this problem would look like this:

Source of Variation Degrees of Freedom Sum of Squares Mean Square F p-value

Regression 1 3,703,333 3,703,333 114.89 <0.001

Error 4 696,667 174,167  

Total 5 4,400,000  

In this ANOVA table, the regression and error degrees of freedom are 1 and 4, respectively, since there is one independent variable and six data points.

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the equation of the line that passes through the point (2,1/4) is: y = (1/8)x

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

To find the equation of the line that passes through (2,1/4), we need to find the values of m and b.

We are not given the slope, so we will need to use another point to find it. Let's choose the point (0,0) as another point on the line. Then, we can find the slope as:

m = (1/4 - 0) / (2 - 0) = 1/8

Now, we can use the slope and the point (2,1/4) to find the y-intercept:

1/4 = (1/8)(2) + b

b = 0

Therefore, the equation of the line that passes through the point (2,1/4) is: y = (1/8)x.

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Answer:

To find the surface area of the figure, we need to break it down into its component shapes and calculate their surface areas, then add them up.

The figure can be divided into a rectangular prism (the bottom part) and two triangular prisms (the top part).

The rectangular prism has dimensions 32 m × 26 m × 12 m. Its surface area is:

2(32 × 26) + 2(32 × 12) + 2(26 × 12) = 2(832 + 384 + 312) = 2(1528) = 3056 m²

Each of the two triangular prisms has base 32 m, height 15 m, and slant height 17 m (using the Pythagorean theorem). The surface area of each triangular prism is:

2(1/2)(32)(15) + 2(1/2)(32)(17) + 2(1/2)(15)(17) = 480 + 544 + 255 = 1279 m²

Therefore, the total surface area of the figure is:

3056 + 1279 + 1279 = 5614 m²

Rounding to the nearest tenth, the surface area is 5614.0 m².

The calculated value of the probability using the given parameters is 0.0154

From the question, we have the following parameters that can be used in our computation:

n = 4

x = 3

p = 1/6

The probability is then calculated as

P(x = x) = nCr * p^x * (1 - p)^(n - x)

Substitute the known values in the above equation, so, we have the following representation

P(x = 3) = 4C3 * (1/6)^3 * (1 - 1/6)

Evaluate

P(x = 3) = 0.0154

Hence, the probability is 0.0154

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Answer:

4/3 × (4 5/6 - 1/2) is greater.

Step-by-step explanation:

What is inside the parenthesis is the same in both expressions. So what makes them different is multiplying by 3/4 or by 4/3.

Multiplying by 3/4 will make the value smaller. It is essentially "a shrink" multiplier.

On the other hand, 4/3 is bigger than one. If you times something by 1 it stays the same. If you multiply by something greater than 1 the answer will be bigger than the starting number.

Since these are actual numbers, we can just do it.

3/4(4 5/6 - 1/2)

= 3/4(4 5/6 - 3/6)

= 3/4(4 2/6)

= 3/4(4 1/3)

= 3/4(13/3)

= 13/4

= 3.25

4/3(4 5/6 - 1/2)

= 4/3(4 5/6 - 3/6)

= 4/3(4 2/6)

= 4/3(4 1/3)

= 4/3(13/3)

= 52/9

= 5.7777...

Reasoning it out definitely seems like less work!

The exact values of the given trigonometric functions are:

cos(330) = [tex]\sqrt{3}/2[/tex] or 0.866

sin(330) = 1/2 or 0.5

To find the trigonometric values of cos(330) and sin(330) exactly, we can use the unit circle and the properties of the trigonometric functions.

In the unit circle, the angle of  330 degrees is equivalent to -30 degrees or [tex]-\pi/6[/tex] radians. Since cosine is an even function, we know that [tex]cos(-\theta) = cos(\theta)[/tex], so we can find cos(-30).

Using the special triangles and the reference angle of 30 degrees, we can determine the exact values:

cos(-30) = cos(30) = [tex]\sqrt{3}/2[/tex]

Similarly, the sine of -30 degrees is the same as the sine of 30 degrees:

sin(-30) = sin(30) = 1/2

Therefore, the exact values are:

cos(330) = cos(-30)= cos(30) = [tex]\sqrt{3}/2[/tex] or 0.866

sin(330) = sin(-30)= sin(30)= 1/2 or 0.5

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By using addition, we find that the number in the top brick of the pyramid with a base of -3 and -5 is -8,

The pyramid is of two layers with base of two bricks numbered as -3 and -5. and the third brick is on the top of them whose value is unknown.

Using the rule that the missing number in any brick is the sum of the two bricks below it, we can work our way up the pyramid

The bottom layer has two bricks with values of -3 and -5, so the brick above them must be the sum of these two values

x = -3 + (-5) = -8.

Therefore, the value in the top brick of the pyramid is -8

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--The given question is incomplete, the complete question is given

" In the pyramid of 3 bricks, the missing number in any brick is the sum of the two bricks below it. What is the number in the top brick 'X'? the number on two bricks at base is -3 and -5."--

Answer:

Step-by-step explanation:

You want the solution to the system of equation using the addition method:

We can multiply the first equation by 0.02 and add it to the second:

  0.02(x) +(0.08x +0.02y) = 0.02(y +600) +(470)

  0.10x +0.02y = 0.02y +482 . . . . . . . . . simplify

  0.10x = 482 . . . . . . . . . . . . . . . . . . . . subtract 0.02y

  x = 4820 . . . . . . . . . . . . . . . . . . . . multiply by 10

  y = x -600 = 4820 -600 = 4220

The amount invested at 8% is $4820; the amount invested at 2% is $4220.

__

Additional comment

You will notice that we solved the equations using "addition" by adjusting coefficients so one variable (y) had the same coefficient on each side of the equal sign. That term was then subtracted from both sides, eliminating the variable. The point of the "method of addition" is to eliminate one variable, which is what we did.

More conventionally, we might rearrange the first equation to x - y = 600 before multiplying by 0.02 and doing the addition. That also eliminates the y-variable.

The calculator result shown in the attachment is also a form of elimination by the addition method.

Answer: D

Step-by-step explanation:

A.  2(2x + 1) = 4x + 2

    4x +2 = 4x +2     because it's the same on both sides you have infinite answers

B. 3x + 7 = x

    2x=  -7

      x = -7/2      one answer

C. 3x + 6 = x + 2

      2x = -4

        x= -4/2 = -2    one answer

D. 5x + 1 = 5x - 3       if you bring 5x over it cancels out

        1 = -3                this is what you are left with and it's not true so this one has no solution

Answer:

54 neighbors received cookies from Grace.

Step-by-step explanation:

We can be 95% confident that the true mean skull width falls within the interval of 123.8 mm to 143.2 mm.

To construct a confidence interval estimate of the mean skull width, we can use the following formula:

CI =  x ± t(α/2, n-1) * s/√n

where:

x = sample mean

t(α/2, n-1) = t-value from t-distribution table with α/2 level of significance and (n-1) degrees of freedom

s = sample standard deviation

n = sample size

First, we need to calculate the sample mean, sample standard deviation, and sample size:

x = (128.3 + 138.3 + 125.7 + 131.8 + 143.2 + 134.9 + 139.1 + 128.7) / 8 = 133.5

s = sqrt[((128.3-133.5)² + (138.3-133.5)² + ..+ (128.7-133.5)²) / (8-1)] = 6.28

n = 8

Next, we need to find the t-value from the t-distribution table with α/2 = 0.025 (since we want a 95% confidence interval) and (n-1) = 7 degrees of freedom. The t-value is 2.365.

Substituting these values into the formula, we get:

CI = 133.5 ± 2.365 * 6.28 / sqrt(8) = (123.8, 143.2)

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It takes 16 minutes until there are 2 grams of the element remaining.

Given that, an element with a mass of 600 grams decays by 29.5% per minute.

Remaining element is 2 grams.

According to the question,

600(1-29.5%)ˣ=2

600×0.705ˣ=2

0.705ˣ=2/600

0.705ˣ=0.00333

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form:

x=log(0.00333)/log(0.705)

x=16.35

x≈16

Therefore, it takes 16 minutes until there are 2 grams of the element remaining.

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Answer:  37

Step-by-step explanation:

all of the external angles of a polygon add up to 360

2x+x+10+x+18+3x+x-1+x =360

9x +27 = 360

x = 37

The roots of the given quadratic functions are -

x = (- 6 ± √42)/2

Given is that Inga is solving the quadratic equation -

2x² + 12x - 3 = 0

The quadratic equation is given as -

2x² + 12x - 3 = 0

We can write the roots of the equation as -

x = {- 12 ± √(144 + 24)}/4

x = (- 12 ± √168)/4

x = (- 12 ± 2√42)/4

x = (- 6 ± √42)/2

Therefore, the roots of the given quadratic functions are -

x = (- 6 ± √42)/2.

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