Find the length of a rectangle with a perimeter of 32 meters and a width of 5 meters

Answer:

4 x 13

Step-by-step explanation:

GCD of 28 and 24 is 4

28 = 4 x 7

24 = 4 x 6

u take the 4 out

4 (7 + 6)

4 x 13

The product of two factors using the GCF and the distributive property is 4(13).

The largest integer of highest degree that is an exact divisor of each of two or more integers.

The greatest common divisor of 24 and 28

24=2×2×2×3

28=2×2×7

We can see that the 2 and 2 is common in 24 and 28

The GCD of 28 and 24 is=2×2= 4

For the distributive property we have

28 = 4 x 7

24 = 4 x 6

we take the 4 out

4 (7 + 6)

=4 x 13

Therefore the GCD is 4 and by distributive property product is 4(13).

To learn more about the product visit:

https://brainly.com/question/10873737

To answer the questions, let's go step by step:

Calculate the OLS estimates of ß0 and ß1, and the R²:

The OLS estimates can be obtained using the following formulas:

ß1 = Cov(x, y) / Var(x)

ß0 = y_bar - ß1 * x_bar

where Cov(x, y) is the sample covariance between x and y, Var(x) is the sample variance of x, y_bar is the sample average of y, and x_bar is the sample average of x.

Given the information:

Sample average of y = 20

Sample average of x = 20

Sample variance of y = 20

Sample variance of x = 10

Sample covariance of y and x = 10

Using the formulas, we get:

ß1 = Cov(x, y) / Var(x) = 10 / 10 = 1

ß0 = y_bar - ß1 * x_bar = 20 - (1 * 20) = 0

The coefficient of determination, R², can be calculated as the square of the coefficient of correlation, r. Since r is equal to the covariance between x and y divided by the product of their standard deviations, we have:

r = Cov(x, y) / (std(x) * std(y)) = 10 / (√10 * √20) ≈ 0.707

Therefore, R² = r² = 0.707² ≈ 0.5

Estimate the variance of the error term, σ², and Var(ß1):

The variance of the error term, σ², can be estimated as:

σ² = (SSR / (n - k))

where SSR is the sum of squared residuals, n is the number of observations, and k is the number of predictors (including the intercept).

Var(ß1) can be estimated as:

Var(ß1) = σ² / (n * Var(x))

where Var(x) is the sample variance of x.

Since the sample variance of x is given as 10, we need to know the number of observations (n) and the number of predictors (k) to calculate σ² and Var(ß1).

Test the null hypothesis that x has no effect on y against the alternative that x has an effect on y at the 5% and 1% significance levels:

To test this hypothesis, we can perform a t-test for the coefficient ß1. The null hypothesis is that ß1 = 0, indicating that x has no effect on y.

The t-statistic for ß1 can be calculated as:

t = ß1 / se(ß1)

where se(ß1) is the standard error of ß1.

To determine statistical significance, we compare the t-statistic to the critical values at the desired significance levels (5% and 1%). If the t-statistic is larger than the critical value, we reject the null hypothesis.

However, since we haven't calculated the standard error of ß1, we cannot perform the t-test without that information.

Suppose we add the term ß2z to the original model, and x and z are negatively correlated. The likely bias in the estimates of ß1 obtained from the simple regression of y on x, if ß2 < 0, is that it will be upwardly biased.

This is known as the omitted variable bias. When an additional variable (z) that is correlated with the independent variable (x) but omitted from the regression is negatively correlated with x, the coefficient of x (ß1) tends to be biased upward. In this case, since ß2 is negative, it leads to an upward bias in ß1.

Based on question 4, when R² = 0.75 from regressing y on x and z, we don't have enough information to calculate the t-statistic for the coefficient on z. The t-statistic is typically calculated using the standard error of the coefficient estimate, which we don't have. Therefore, we cannot determine whether z is statistically significant based on the given information.

Based on question 4, if x is highly correlated with z in the sample and z has large partial effects on y, the bias in question 4 would tend to be small. When x and z are highly correlated, the omitted variable bias tends to be smaller because the correlation between the omitted variable (z) and the included variable (x) reduces the bias. Additionally, if z has a large partial effect on y, it can help explain the variation in y that is not accounted for by x alone, further reducing the bias in the estimate of ß1.

Considering the expression of a line, the slope intercept form is y= -x+2.

A linear equation o line can be expressed in the form y = mx + b

where

This is known as the slope-intercept form. This form is one of the most common forms used to represent the equation of a line and can be used to find the equation of a line when given the slope of the straight line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis).

In this case, the line is x+y=2. Expressed in the form y = mx + b, you get:

y= 2 -x     or     y= -x +2

Finally,  x+y=2 in slope intercept form is y= -x+2.

Learn more about slope-intercept form:

https://brainly.com/question/1884491

https://brainly.com/question/6202710

#SPJ1

Answer:

Kayla's age is 20

Step-by-step explanation:

20*3=60

Answer:

Make a line using points (0,0) (1,6) and (-1,-6)

Step-by-step explanation:

Okay, so your first point will be (0,0) at the origin because in your equation there is no y-intercept.

For your next point, we have to use Rise/Run, or slope, to find our next point. In y=mx+b, m is the slope. So for y=6x, 6/1 is our slope.

So from the origin, we go up 6 and to the right once. This will give us the point (1,6)

Incase you need another point, we can also go down 6 and left 1. This gives us the point (-1,-6)

Hopefully this helps! Leave a comment if it does, and ask your teacher to see if it's right! <3

Answer:1815 euros left

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

4x>48

x>12ans.this is the correct answer

Answer:

Hello you are a b**ch

Step-by-step explanation:

I just want some points thanks.

The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

Learn more about Graphical method

brainly.com/question/29193266

#SPJ11

If the car goes to the top of spike's peak and back, the mileage of the car is 16 miles per gallon

The mileage of car in uphill = 12 miles per gallon

The mileage of car in downhill = 24  miles per gallon

The total distance traveled in up hill = 48 miles

The number of gallon of gas used = 48/12

= 4 gallon

The total distance traveled in down hill = 48 miles

The number of gallon of gas used = 48 / 24

= 2 gallon

Total distance traveled = 48 + 48

= 96 miles

Total number of gallons of gas = 4 + 2

= 6 gallon

The mileage = Total distance / The number of gallon

= 96 / 6

= 16 miles per gallon

Therefore, the mileage of the car is 16 miles per gallon

Learn more about mileage here

brainly.com/question/3124860

#SPJ4

a) If Kindra starts with $61 in her savings account, an inequality to represent how much she needs to save is 61 + x > 1500.

b) Kindra needs to save $1439 to have $1500.

a) The aim of this task is to find out how much Kindra should save to have at least $1500,

Kindra has $61 and she wants to save $1500. An inequality to represent how much she needs to save is 61 + x > 1500.

b) With x representing the amount she needs to save to have at least $1500,

Solving for how much she needs to save = 61 + x ≥ 1500

x ≥ 1439 (Subtracting 61 from both sides of the equation)

Kindra needs to save $1439 to have $1500.

The inequality in symbol form and the inequality in the number line is given below.

To learn more about inequality, click here:

brainly.com/question/30228778

#SPJ4

The appropriate limits of integration for finding the area between the functions defined by x = −1 and x = − y^3 − 3y^2 are y = -2 and y = 0.

To find the limits of integration, we need to determine the intersection points of the given functions. Equating x = −1 and x = − y^3 − 3y^2, we get:

−1 = − y^3 − 3y^2

Rearranging and simplifying, we get:

y^3 + 3y^2 - 1 = 0

We can solve this cubic equation to get the three roots, but we are only interested in the real root between y = -2 and y = 0. We can use numerical methods or a graphing calculator to find that the real root is approximately -1.7549.

Therefore, the appropriate limits of integration for finding the area between the given functions are y = -2 and y = 0. The integral to find the area is:

A = ∫^0_-2 [(− y^3 − 3y^2) + 1] dy

Simplifying and evaluating the integral, we get:

A = 49/12.

For more questions like Function click the link below:

https://brainly.com/question/16008229

#SPJ11

An 1 οr perhaps an even integer will be drawn back 75% οf the times frοm the set οf 1, 2, 3 and 4. Thus, Prοbability P(nοt even) is 75%.

Prοbability is the likelihοοd that sοmething will οccur οr the prοbability that sοmething will happen. Prοbability is the measure οf hοw prοbable it is that a cοin will land heads up after being tοssed intο the air.

As prοbabilistic arguments sοmetimes prοduce οutcοmes that appear cοntradictοry οr illοgical, prοbability is usually regarded as amοng the mοst challenging tοpics οf mathematics.

P(1) = 1/4(there is one card with a 1)

P(even) = 2/4 = 1/2 (there are 2 cards with even numbers out of 4)

Therefore,

P( 1 or even) =P(1) + P(even)

= 1/4 + 1/2

= 3/4

To express the answer as a percentage, we can multiply by 100:

P(1 or even) = 3/4 × 100%

=> 75%

To know more about probability visit:

brainly.com/question/30034780

#SPJ1

You pick a card at random. card 1, card 2 and card 3

What is P(not even)?

Write your answer as a fraction or percentage.

Answer:

Passive

Step-by-step explanation:

Active voice means that a sentence has a subject that acts upon its verb. Passive voice means that a subject is a recipient of a verb's action.

The Correct answer is A. (-4,1) ordered pair generated by this model should be discarded because the values are unreasonable.

In algebra, a quadratic equation (from Latin quadratus 'rectangular') is any equation that can be rearranged in well-known form as ax²+bx+c=0 Where x represents an unknown value, and a, b, and c constitute recognized numbers.

One supposes usually that a ≠ zero; the one's equations with a = zero are taken into consideration degenerate because the equation then will become linear or even simpler. The numbers a, b, and c are the coefficients of the equation and can be prominent with the aid of calling them, respectively, the quadratic coefficient, the linear coefficient, and the consistent or loose time period.

The values of x that satisfy the equation are referred to as answers to the equation, and roots or zeros of the expression on its left-hand aspect. A quadratic equation has at most two answers. If there is handiest one solution, one says that it's miles a double root. If all the coefficients are real numbers, there are both actual solutions, a single actual double root, or two complicated answers which can be complicated conjugates of each other.

To learn more about Quadratic Equation visit here:

brainly.com/question/17177510

#SPJ4

Complete Question:

Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. which ordered pair generated by this model should be discarded because the values are unreasonable?

The probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.

The probability that the digit 7 doesn't appear among 100 digits where each digit is one of (0-9) and all sequences are equally likely is given by the probability that all 100 digits are chosen from the set {0, 1, 2, 3, 4, 5, 6, 8, 9}. There are 10 choices for each digit, so there are 10^100 possible sequences of 100 digits. The number of sequences that don't contain the digit 7 is 9^100. Therefore, the probability that the digit 7 doesn't appear among 100 digits is: P(7 doesn't appear) = (9^100) / (10^100) = 9 / 10

Therefore, the probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.

To learn more about probability,

Visit; brainly.com/question/30034780

#SPJ4

Answer:

18

Step-by-step explanation:

y=mx + b

m is the slope.

Therefore, 18 should be the slope

e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

For more questions like P-value click the link below:

https://brainly.com/question/14790912

#SPJ4

The actual lower and upper bounds of an interval in a grouped frequency distribution are called the class limits.

In a grouped frequency distribution, data is grouped into intervals or classes to simplify the presentation and analysis of data. Each interval has an upper limit and a lower limit that define its boundaries. The lower limit represents the smallest value within the interval, while the upper limit represents the largest value within the interval.

The class limits are important in determining the range and boundaries of each interval. They help organize the data into meaningful groups and allow for the calculation of various statistical measures such as frequencies, percentages, and cumulative frequencies within each interval. The class limits play a vital role in constructing histograms, frequency polygons, and other graphical representations of the grouped data.

To learn more about frequency.

Click here:brainly.com/question/29739263?

#SPJ11

The probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg is approximately 1.

Given, the mean maximum oxygen uptake for elite athletes is 60 ml/kg and the standard deviation is 6.4 ml/kg. We can use the standard normal distribution to find the probability of an athlete having a maximum oxygen uptake of at least 50 ml/kg.

First, we need to find the z-score corresponding to a maximum oxygen uptake of 50 ml/kg:

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than or equal to -1.56, which is approximately 0.06.

However, we are interested in the probability of an athlete having a maximum oxygen uptake of at least 50 ml/kg, which is equivalent to finding the probability of a standard normal random variable being greater than or equal to -1.56. This probability can be found by subtracting the probability of being less than -1.56 from 1:

Therefore, the probability that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg is approximately 1, meaning it is highly likely that an elite athlete has a maximum oxygen uptake of at least 50 ml/kg.

Learn more about Probability:

https://brainly.com/question/24756209
#SPJ4

The five sets given in the problem were analyzed to determine if they are subspaces of c[−1, 1]. It was found that the first, second, and fourth sets are subspaces of c[−1, 1], while the third and fifth sets are not subspaces of c[−1, 1].

Subspaces of c[−1, 1] can be determined by checking if they satisfy the following three conditions:

The following are the subspaces of c[−1, 1]:

(a) The set of functions f in c[−1, 1] such that f(−1) = f(1).

This is a subspace of c[−1, 1].

Let f and g be two functions in the set. Then, (f+g)(−1) = f(−1) + g(−1) = f(1) + g(1) = (f+g)(1).

Thus, the set is closed under addition. Also, if k is a scalar and f is a function in the set, then

(kf)(−1) = kf(−1) = kf(1) = (kf)(1).

Thus, the set is closed under scalar multiplication.

Finally, the zero function in c[−1, 1] satisfies f(−1) = f(1) and hence belongs to the set.

Therefore, the set is a subspace of c[−1, 1].

(b) The set of odd functions in c[−1, 1]. This is a subspace of c[−1, 1].

Let f and g be two odd functions in the set. Then, (f+g)(−x) = f(−x) + g(−x) = −f(x) − g(x) = −(f+g)(x).

Thus, the set is closed under addition.

Also, if k is a scalar and f is an odd function in the set, then,

(kf)(−x) = kf(−x) = −kf(x) = (kf)(x).

Thus, the set is closed under scalar multiplication.

Finally, the zero function in c[−1, 1] is odd and hence belongs to the set.

Therefore, the set is a subspace of c[−1, 1].

(c) The set of continuous nondecreasing functions on [−1, 1]. This is not a subspace of c[−1, 1].

For example, the functions f(x) = x and g(x) = 2x − 1 are both continuous and non-decreasing on [−1, 1], but their sum f+g is not nondecreasing on [−1, 1].

(d) The set of functions f in c[−1, 1] such that f(−1) = 0 and f(1) = 0. This is a subspace of c[−1, 1].

Let f and g be two functions in the set. Then,

(f+g)(−1) = f(−1) + g(−1) = 0 + 0 = (f+g)(1).

Thus, the set is closed under addition.

Also, if k is a scalar and f is a function in the set, then,

(kf)(−1) = k(f(−1)) = 0 = (kf)(1).

Thus, the set is closed under scalar multiplication.

Finally, the zero function in c[−1, 1] satisfies f(−1) = 0 and f(1) = 0 and hence belongs to the set.

Therefore, the set is a subspace of c[−1, 1].

(e) The set of functions f in c[−1, 1] such that f(−1) = 0 or f(1) = 0. This is not a subspace of c[−1, 1].

For example, the functions f(x) = x and g(x) = −x are both in the set, but their sum f+g is not in the set because

(f+g)(−1) = 0 and (f+g)(1) = 0, but

(f+g)(0) = 0 + 0 = 0,

which means that f+g is not in the set.

Therefore, out of the five sets given in the problem, only the first, second, and fourth sets are subspaces of c[−1, 1].

Learn more about subspaces visit:

brainly.com/question/28384717

#SPJ11

The equation of parabola in the intercept form that passes through (0,-18) with x intercepts of 9 and 1 is y = -2(x-9)(x-1)  .

In the question,

it is given that ,

the parabola passes through (0,-18) and has x intercepts as 9 and 1 .

The intercept form of the equation of parabola is given by

y = a(x-p)(x-q)   , where a is the constant

and p , q are the x intercepts  .

Given that the parabola has x intercepts as 9 and 1 , So

equation becomes

y = a(x-9)(x-1)          .....(i)

Since parabola passes through the points (0,-18) ,

hence , point should satisfy the equation ,

So putting y = -18 and x=0 , we get

-18 = a(0-9)(0-1)

-18 = a(-9)(-1)

-18 = 9a

a = -2

Substituting a= -2 in equation (i) ,

we get the equation of parabola as y = -2(x-9)(x-1) .

Therefore , the equation of parabola in the intercept form that passes through (0,-18) with x intercepts of 9 and 1 is y = -2(x-9)(x-1)   .

The given question is incomplete , the complete question is

Write an equation of the parabola in intercept form that passes through (0,-18) with x-intercepts of 9 and 1 .

Learn more about Parabola here

https://brainly.com/question/17555460

#SPJ1

Answer:

-1+13=4v

12=4v

v=3

....

.............

The volume common to two spheres, each with radius r, if the distance between their centres is r/2 is V = (11/12)×π×r³.

The attached diagram shows 2 circumferences with radius r and separated centres by r/2.

Let´s call circumferences  1 and 2; by symmetry, rotating area A will produce a volume V₁ identical to a V₂, Obtained by rotating area B ( both around the x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) × r × x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) × r × x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) × r × (r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

To know more about volume, here

https://brainly.com/question/22907480

#SPJ4

The right answer is option A, which reads "four times one-third" multiplied by the number of one-third cup servings in four cups.

You can multiply, reduce, add, or take this away in mathematics. An expression is put together as follows: Verb, numeric value, and math operator A mathematical formulation is composed of numbers, variables, and procedures (such as addition, subtraction, multiplication or division etc.) Opposing phrases and phrases is possible. An exponential function is any mathematical declaration that has variables, integers, or an mathematical operation. As an instance, the phrase 4m + 5 consists of both the terms 4m and 5, as well as the supplied equation's variable m, each of which is divided by the mathematical sign +.

given

the expression = "  number of one-third cup servings in 4 cups "

= four times one-third

= 4*1/3

The right answer is option A, which reads "four times one-third" multiplied by the number of one-third cup servings in four cups.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

A vertical line has points with all the same x-values. So if the line intersects (a,b) and (c,d), then a must equal c.

Answer:

1=23, 2=157, 3=23

Step-by-step explanation:

1 is alternate to 3 so if 1 is 23 then 3 is also 23 . as you know angles on a straight line add up to 180° and 2 and 3 are angles on a straight line. so subtract 23 from 180 to get 157°

The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.

Each payment will have to be $300