Write the equation of the line that passes through (5,-2) and is perpendicular to y=x-3.

Step-by-step explanation:

To determine whether 360 is prime, composite, or neither, we need to check if it has any factors other than 1 and itself.

We can start by finding the prime factorization of 360:

First, we can divide 360 by 2 to get 180:

360 ÷ 2 = 180

Next, we can divide 180 by 2 to get 90:

180 ÷ 2 = 90

We can continue dividing by 2 until we can no longer divide evenly:

90 ÷ 2 = 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 is a prime number, so we have found the prime factorization of 360:

360 = 2 × 2 × 2 × 3 × 3 × 5

Therefore, we can see that 360 is composite because it has more than two factors. We can write it as the product of its prime factors as shown above.

In summary, the number 360 is composite and its prime factorization is:

360 = 2 × 2 × 2 × 3 × 3 × 5

a) For the integral ∫01^3 1/x^p dx to converge, p > 0. Evaluating the integral for those values of p gives ∫01^3 1/x^p dx = -1/(p-1).
b) For the integral ∫[infinity]^e 25/x^(lnx)^p dx to converge, p > 1. Evaluating the integral for those values of p gives

∫[infinity]^e 25/x^(lnx)^p dx = -25/(p-1).

Convergence and divergence. The improper integral is said to converge if the limit is both real and a limited integer.

For more such questions on integral converges, visit:

brainly.com/question/29558996

#SPJ11

The numerical value of x is 3.

The Midsegment Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

This simply means that:

The middle segment = half the third side

From the image:

Using the Midsegment Theorem

x + 10 = 1/2 × (x + 23)

Solve for x

Multiply both sides by 2

2( x + 10 ) = 1/2 ×2 (x + 23)

2( x + 10 ) = x + 23

2x + 20 = x + 23

2x - x = 23 - 20

x = 3

Therefore, the value of x is 3.

Learn more about Midsegment Theorem here: brainly.com/question/30066983

#SPJ1

Answer: 30

Step-by-step explanation:

I think 0.o

Let's represent the total distance that Mira plans to run with "x".

According to the problem, 2 miles is 40% of the total distance, so we can write:

2 = 0.4x

To find the value of "x", we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.4:

2 ÷ 0.4 = x

Simplifying the left side gives us:

5 = x

Therefore, Mira plans to run a total of 5 miles.

Answer:

c. 36 people

pls mrk me brainliest

Answer:

The answer would indeed be C. 36 people.

Answer:

37 customers preferred cake.

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

To find out how many customers preferred cake, we need to multiply the total number of customers (105) by the percentage of customers who preferred cake (35%):

(35% = 0.35)

Rounding this to the nearest whole number gives us 37. Therefore, approximately 37 customers preferred cake.

Answer:

35% of 105 is 36.75. ( Rounded up 37). So 37 customers preferred cake the most

Answer:

I think it has an area of 4 and a perimeter of 8, i'm not totally sure but I thought I'd try to help

Answer:

area:4

perimeter:8ft

Step-by-step explanation:

when doing the area, you have to MULTIPLY the length by the width. For example, length:5ft width:7ft so to find the area you have to multiply both and get the answer of 35. so for the sum you have is 2 × 2 = 4

for perimeter, you have to ADD all the sides so if you have a square with all sides of 4 you add them all up which = 16. so for your sum, add them all up = 8ft

Hope it helps I'm not that good at explaining :)

Answer:

≈ 9.9 feet

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. Let x be the distance from the house to the base of the ladder. Then:

x^2 + 15^2 = 18^2

Simplifying and solving for x, we get:

x = sqrt(18^2 - 15^2) = 9.9 feet (rounded to the nearest tenth)

Therefore, Jaquira should place the base of the ladder approximately 9.9 feet away from the house.

The right formula to figure out how much money was saved, s, in dollars when getting this desk on sale is: s = 0.2(380) (380) This calculation accounts for  desk being 20% less expensive than it was originally.

which translates to a 20% discount for the consumer. So, we must multiply the original price by the discount %, which in this case is 0.2, in order to determine the amount saved. The equation in Option A that best captures the presented circumstance is accurate. A desk is on sale for $380, which is 20% off the original price. Which equation can be used to determine the amount of money saved, s, in dollars, when purchasing this desk on sale accounts for  desk being 20% less expensive than it was originally. The equation in Option A that best captures the presented circumstance is accurate.

learn more about equation  here:

https://brainly.com/question/29657988

#SPJ4

Answer: The correct answer is:

The y-intercept is 3.79, which means a student with no absences is predicted to have a GPA of 3.79.

Explanation:

To determine the relationship between the number of absences and the GPA, the student can use linear regression analysis. The regression line can be obtained using software such as Excel or R. The y-intercept of the regression line represents the predicted value of the response variable (GPA) when the predictor variable (number of absences) is zero.

Using technology, the y-intercept for this data set is found to be 3.79. This means that a student with zero absences is predicted to have a GPA of 3.79. Therefore, the correct answer is that the y-intercept is 3.79 and it does make sense to interpret it in this context.

Step-by-step explanation:

The Binomial Distribution applet will calculate the probability of the basketball player making 2 or less shots, and it turns out to be equal to 0.8425.

Using the Binomial Distribution Applet, we can find the probability that the basketball player makes 2 shots or less by inputting the given information into the applet. The number of trials is 3, the probability of success is 0.54, and the number of successes we are looking for is 2 or less.

Here are the steps to finding the probability using the Binomial Distribution Applet: Input the number of trials as 3, Input the probability of success as 0.54, Input the number of successes as 2, Click the "Calculate" button

The applet will then calculate the probability of the basketball player making 2 or less shots, which is 0.8425. Therefore, the answer to the question is 0.8425.

Know more about probability here:

https://brainly.com/question/30034780

#SPJ11

Answer:

Height*width*depth= volume

Corsica adds 3/32 = 0.09375 ounces of water to the bucket per second.

To find how many ounces of water are added to the bucket per second, we need to rearrange the given equation to solve for the rate of change of the water, which is the change in the amount of water per unit of time.

Starting with:

3W = 32S

We can divide both sides by S:

3W/S = 32

Now we can see that the left-hand side represents the amount of water (in ounces) added per second, since W/S is the rate of change of the water with respect to time.

Therefore, we can conclude that Corsica adds 3/32 = 0.09375 ounces of water to the bucket per second.

Learn more about ounces

https://brainly.com/question/29374025

#SPJ1

However, the response would be (x - 2 + 2i2)(x - 2 - 2i2) if you are searching for factors with real coefficients.

A polynomial is a mathematical expression made up of variables, factors, one or more terms, and non-negative integer exponents used in addition, subtraction, multiplication, and multiplication. Any mathematical object, including numbers, variables, and even functions, can be represented by the variables in a polynomial. In the polynomial equation 3x2 + 2x - 5 as an illustration, the coefficients are 3, 2, and -5, the variable is x, and the exponent is 2. This polynomial has the terms 3x2, 2x, and -5, each of which is denoted by a plus or negative sign. Monomials have one term, binomials have two terms, trinomials have three terms, and so on. Polynomials can be categorized based on how many terms they contain.

given

The solution to the first question is "none of the above," as the signs of the terms in a polynomial are not what determine the signs of the factors.

(x - 2i)(x + 2i) is one of the prime factors of x2 - 4x + 12, where I is the imaginary number.

However, the response would be (x - 2 + 2i2)(x - 2 - 2i2) if you are searching for factors with real coefficients.

To know more about polynomials visit:

https://brainly.com/question/11536910

#SPJ1

The probability that a red ball was selected more than 20 times when 25 balls are randomly selected from the jar with replacement is 0.037.

Given that a jar contains 30 red balls and 20 white balls. Also, 25 balls are randomly selected from the jar with replacements. We need to find the probability that a red ball was selected more than 20 times.

The binomial probability distribution function can be represented as follows:
[tex]P(X = k) = \ ^nC_k . p^k . q^{(n-k)}[/tex]
where n is the number of trials, k is the number of successes,

p is the probability of success,

q = 1 - p is the probability of failure.
Here, the probability of selecting a red ball is 30/50 = 3/5.

So, the probability of selecting a white ball is 2/5.
Here, we have n = 25 trials, p = 3/5, q = 2/5.

Let X be the number of times a red ball is selected. Then we need to find P(X > 20).
So, P(X > 20) = 1 - P(X ≤ 20)
= 1 - Σ P(X = k), k = 0 to 20
[tex]= 1 - \sum \ ^nC_k . p^k . q^{(n-k)}[/tex], k = 0 to 20
[tex]P(X = k) = \ ^nC_k . p^k . q^{(n-k)}[/tex]

[tex]P(X > 20) = 1 - \sum \ ^nC_k . p^k . q^{(n-k)}[/tex], k = 0 to 20

= [tex]1 - { \ ^nC_0 . p^0 . q^{(n-0)} + \ ^nC_1 . p^1 . q^{(n-1)} + \ ^nC_2 . p^2 . q^{(n-2)} + ... + \ ^nC_{20} . p^{20} . q^{(n-20)}}[/tex]
= 1 - {1 . (3/5)^0 . (2/5)^25 + 25 . (3/5)^1 . (2/5)^24 + 300 . (3/5)^2 . (2/5)^23 + ... + 1.623 x 10^10 . (3/5)^20 . (2/5)^5}
= 1 - 0.963
= 0.037

Therefore, the probability that a red ball was selected more than 20 times when 25 balls are randomly selected from the jar with replacement is 0.037.

To know more about the "probability": https://brainly.com/question/24756209.

#SPJ11

We οbserve that the line segment AM frοm vertex A tο midpοint M οf base BC alsο bisects BC, since M is the midpοint οf BC. Therefοre, we have AM = BM = MC = BC/2.

An isοsceles triangle is type οf triangle that has the twο sides οf equal length. In isοsceles triangle,  angles οppοsite equal sides are alsο equal in measure. The third side οf isοsceles triangle is called base.

Tο prοve this, we can cοnsider the fοllοwing diagram οf an isοsceles triangle ABC with base BC:

       A

       / \

     /     \

   /         \

 / h          \

 B------------C

where h is the altitude tο the base BC and M is the midpοint οf the base BC. We want tο shοw that the line segment AM is alsο the median tο the base BC.

First, we οbserve that the triangle ABC is isοsceles, sο the twο legs AB and AC are cοngruent. Therefοre, the altitude h frοm vertex A tο base BC bisects BC, which means that BM = MC = BC/2.

Secοnd, we οbserve that the line segment AM frοm vertex A tο midpοint M οf base BC alsο bisects BC, since M is the midpοint οf BC. Therefοre, we have AM = BM = MC = BC/2.

Thus, we have shοwn that the altitude tο the base and the median tο the base οf an isοsceles triangle are the same line segment, which cοmpletes the prοοf.

To know more about Median visit:

brainly.com/question/3515636

#SPJ1

Answer: 0.2 square meters.

Step-by-step explanation:

We are given the equation:

3600b² = hw

We need to find the value of b, given that h = 168 cm and w = 60 kg.

First, we need to convert the height from centimeters to meters:

h = 168 cm = 1.68 m

Substituting the given values:

3600b² = (1.68)(60)

3600b² = 100.8

b² = 100.8/3600

b² = 0.028

Taking the square root of both sides:

b = √0.028

b ≈ 0.167

Rounding to the nearest tenth:

b ≈ 0.2

Therefore, the body surface area of a person who is 168 centimeters tall and weighs 60 kilograms is about 0.2 square meters.

To find the multiplication equation that shows how the denominators of 3/4 and 1/2 are related, we can simply multiply the two denominators together:

3/4 x 1/2 = 3/8

Therefore, the denominators are related by the equation 4 x 2 = 8.

To write 1/2 as an equivalent fraction with a denominator of 4, we need to multiply both the numerator and denominator by the same factor that will transform the denominator of 2 to a denominator of 4.

Using the multiplication equation we found earlier, we can see that we need to multiply both the numerator and denominator of 1/2 by 2 (since 2 x 2 = 4). This gives us:

1/2 x 2/2 = 2/4

Therefore, 1/2 can be written as an equivalent fraction with a denominator of 4 as 2/4.

To know more about multiplication equations:

https://brainly.com/question/20687498

#SPJ4

The greatest inflation rate was 1.78% in year1 and year2

When you have a lot of repetitive calculations to do, it is convenient to let a spreadsheet do it. Copying the given data to the spreadsheet ensures we have made no data entry errors.

The inflation rate is calculated as ...

 (year 2 price)/(year 1 price) -1 . . . . . expressed as a percentage

[tex]\frac{74.30}{73.00}=1.0178\\\\\frac{76.015}{75}=1.0135\\\\\frac{89.25}{88}=1.0142[/tex]

The attachment shows the results of this calculation as applied to the economies in the order shown. The least-to-greatest order is shown in the right-most column.

The complete question is-

The CPI basket price for two consecutive years in five different economies are given. Determine the rate of inflation for each economy. Then order the tiles from least to the greatest inflation rate.

Year 1 = $73.00

Year 2 = $74.30

Year 1 = $75.00

Year 2 = $76.15

Year 1 = $88.00

Year 2 = $89.25

Year 1 = $72.50

Year 2 = $73.75

Year 1 = $79.00

Year 2 = $80.25​

learn more about the inflation rate,

https://brainly.com/question/30112292

#SPJ4

Answer: 2° Celsius.

Step-by-step explanation:

a)   there is a strong positive correlation between the variables based on the given correlation coefficient and critical value

To interpret correlation values, the Table of Critical Values must be used. In this case, the correlation be reasonable to conclude that the data come from a r X. Table of critical values Sample Size, n Critical Value Sample Size, n Critical Value 5 0.880 16 0.941 6 0.888 17 0.944 7 0.898 18 0.946 8 0.906 19 0.949 9 0.912 20 0.951 10 0.918 21 0.952 11 0.923 22 0.954 12 0.928 23 0.956 13 0.932 24 0.957 14 0.935 25 0.959 15 0.939 30 0.960. The correlation coefficient is found between -1 and 1. Correlation values near 1 indicate a strong positive correlation, while those near -1 indicate a strong negative correlation. Correlation values near zero, on the other hand, indicate no correlation between the variables. In this case, we can interpret that the correlation is significant because it falls outside of the range of -0.880 and 0.880. We can see that the correlation value of 0.918 is higher than the critical value of 0.880 for the sample size of 10 from the given table of critical values. As a result, it can be concluded that there is a strong positive correlation between the variables based on the given correlation coefficient and critical value.

  Learn more about correlation

  brainly.com/question/15690353

  #SPJ4

Answer:

Step-by-step explanation:

As per question, point B is the midpoint of AC.

According to definition of midpoint, AB = BC:

The length of AB is:

Answer:

AB = 18

Step-by-step explanation:

To find:-

Answer:-

We are here given that points A , B and C are collinear and B is the midpoint of AC . From the data provided in the question we have;

Since B is the midpoint of AC, it will divide AC into two equal parts namely AB and BC. And these parts will be equal to one another. ( By Euclid's first axiom, Things which are half of the same thing are equal to one another.)

So we have;

[tex]\sf:\implies AB = BC \\[/tex]

[tex]\sf:\implies 3x = 4x - 6 \\[/tex]

[tex]\sf:\implies 3x -4x = -6 \\[/tex]

[tex]\sf:\implies -x = -6 \\[/tex]

[tex]\sf:\implies\red{ x = 6} \\[/tex]

Finally plug in the value of x, in the given expression of AB as ,

[tex]\sf:\implies AB = 3(x) \\[/tex]

[tex]\sf:\implies AB = 3(6) \\[/tex]

[tex]\sf:\implies \red{AB = 18} \\[/tex]

Hence the value of AB is 18 .

The width of the rectangle is 3/2 cm and the length is 17 cm.

The formula for the area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width. To solve this problem, we can rearrange the formula to solve for W: W = A / L. In this case, A = 6 cm and L = 2W + 11 cm. Substituting these values, we get W = 6 / (2W + 11). We can solve this equation by dividing both sides by 2W to get 1/W = 6 / (2W + 11) * 1/2W. Simplifying, we get 1/W = 3 / (11 + 2W). Subtracting 3/11 from both sides, we get -2/11 W = -3/11. Finally, we can solve for W by dividing both sides by -2/11 to get W = 3/2 cm.

Therefore, the width of the rectangle is 3/2 cm, and the length of the rectangle is 2W + 11 = 11 + 6 = 17 cm.

Learn more about rectangle here:

https://brainly.com/question/29123947

#SPJ4

The population of the town after 12 years Aand in 24 years will be approximately 34,461 and 79,171 respectively.

If the population doubles every 10 years, then we can use the formula for exponential growth to find the population after a certain number of years:

P = P₀ x 2^(t/T)

where:

P₀ = initial population = 15,000

P = population after t years

T = doubling time = 10 years

t = number of years

Using this formula, we can find the population after 12 years:

P = 15,000 × 2^(12/10)

P = 34,461

Therefore, the population of the town after 12 years will be approximately 34,461.

Similarly, we can find the population after 24 years:

P = 15,000 ×  2^(24/10)

P = 79,171

Therefore, the population of the town after 24 years will be approximately 79,171.

Learn more about exponential growth here:

https://brainly.com/question/12490064

#SPJ1

Answer:

520.37 cm

Step-by-step explanation:

apply equation:

x = 736.97(0.7061) = 520.374517
Notice 70.61% is the same as 0.7061 (just divide by 100)

now you need to round to 2 DP

x ≈ 520.37

so the 70.61% of 736.97cm is  520.37 cm

Answer:

241/84

Step-by-step explanation:

Answer:

144 feet²

Step-by-step explanation:

12 x 12 = 144

Sally's turtle walked a total of 30 feet altogether on Wednesday.

To determine the total distance the turtle went, we need to know the distances between the beginning line and points T and M.

According to the diagram, there are 12 feet between the beginning line and point T and 8 feet between the starting line and point M.

The turtle travels a distance of: when it moves from the starting line to point T and then returns to point M.

Distance between the beginning line and point T plus the distances between point T and point M and point M from the starting line equals 12 + 10 + 8 = 30 feet.

So, on Wednesday, Sally's turtle travelled a total of 30 feet.

To know more about distance visit:

https://brainly.com/question/17273444

#SPJ9

The distance between the two points from the geometrical formula for that purpose is 6.2.

The distance between two points in geometry is the length of the straight line segment that connects the two points. It is calculated using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Using the formula;

d= √(x2 - x1)^2 + (y2 - y1)^2

d = √(7.5 - 3)^2 + (6.25 - 2)^2

d = √20.25 + 18.06

d = 6.2

Learn more about distance between two points:https://brainly.com/question/2669795

#SPJ1

The length οf the secοnd lane is apprοximately 160 meters, and the width is apprοximately 74 meters. Sο the cοrrect οptiοn is D.

We can start by nοticing that the given equatiοn [tex]x^2/6241 + y^2/1296 = 1[/tex]is the equatiοn οf an ellipse cantered at the οrigin, with a majοr axis οf length 2a = 279 = 158 and a minοr axis οf length 2b = 236 = 72. This is the equatiοn οf the innermοst lane.

Tο find the equatiοn οf the secοnd lane, we need tο add 1 meter tο bοth sides οf the equatiοn, since each lane is apprοximately 1 meter apart. This gives:

[tex]x^2/6241 + y^2/1296 = 2^2[/tex]

Simplifying, we get:

[tex]x^2/6241 + y^2/1296 = 4[/tex]

This is the equatiοn οf an ellipse with the same center as the first ellipse, but with a majοr axis οf length 2(a+1) = 280 = 160 and a minοr axis οf length 2(b+1) = 237 = 74.

Therefοre, the length οf the secοnd lane is apprοximately 160 meters, and the width is apprοximately 74 meters. Sο the cοrrect οptiοn is D.

Learn more about  equatiοn

https://brainly.com/question/29273511

#SPJ1