Please help on these two 5 mins till due!!!!!

Answer:

c

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

\(\frac{AD}{WZ}\) = \(\frac{CD}{YZ}\) , substitute values

\(\frac{10}{46}\) = \(\frac{5}{YZ}\) ( cross- multiply )

10YZ = 230 ( divide both sides by 10 )

YZ = 23 → c

a. The probability of a pregnancy lasting 309 days or longer is approximately 0.0035.

b. Babies born on or before 240 days are considered premature.

a. The probability of a pregnancy lasting 309 days or longer can be found by calculating the z-score and using the standard normal distribution table. First, we calculate the z-score using the formula:

z = (x - μ) / σ

where x is the desired value (309 days), μ is the mean (269 days), and σ is the standard deviation (15 days). Substituting the values, we get:

z = (309 - 269) / 15 = 40 / 15 = 2.67

Next, we look up the z-score of 2.67 in the standard normal distribution table and find the corresponding probability. The table shows that the area to the left of the z-score of 2.67 is approximately 0.9965. However, we are interested in the probability of the pregnancy lasting 309 days or longer, so we subtract this value from 1:

P(X ≥ 309) = 1 - 0.9965 = 0.0035

Therefore, the probability that a pregnancy will last 309 days or longer is approximately 0.0035.

b. To find the length that separates premature babies from those who are not premature, we need to determine the value that corresponds to the lowest 3% in the distribution. This is equivalent to finding the z-score that has an area of 0.03 to its left. We look up this z-score in the standard normal distribution table and find it to be approximately -1.88.

To find the corresponding length, we use the z-score formula:

z = (x - μ) / σ

Rearranging the formula to solve for x:

x = μ + z * σ

Substituting the values, we have:

x = 269 + (-1.88) * 15 = 269 - 28.2 = 240.8

Rounding to the nearest integer, we conclude that babies born on or before 240 days are considered premature.

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The length in feet of the dog kennel is 60 feet.

Fred has 160 feet of fencing. He uses all the fencing to make the four sides of a rectangular dog kennel. The length of the dog kennel is 3 times the width.

Therefore, the length in feet of the dog kennel can be calculated as follows:

perimeter of the fencing = 2(l + w)

l = 3w

perimeter of the fencing = 2(3w + w)

perimeter of the fencing = 2(4w)

160 = 8w

divide both sides by 8

w = 160 / 8

w = 20 feet

length of the kennel = 3(20)

length of the kennel = 60 feet

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When performing a 3-D problem analysis, in general, you have three scalar equations of equilibrium. Therefore, the answer is (b) 3.

In a 3-D problem analysis, we consider forces and moments acting in three perpendicular directions: x, y, and z. For each direction, we can apply the principle of equilibrium to derive a scalar equation. The equations of equilibrium are as follows:

ΣFx = 0 (Sum of forces in the x-direction is zero)

ΣFy = 0 (Sum of forces in the y-direction is zero)

ΣFz = 0 (Sum of forces in the z-direction is zero)

These three scalar equations of equilibrium represent the conditions for a body to be in static equilibrium in three-dimensional space.

When analyzing 3-D problems, we typically have three scalar equations of equilibrium. These equations help us determine the unknown forces and moments acting on a body by setting the sums of forces and moments in each direction equal to zero. By solving these equations simultaneously, we can find the equilibrium conditions and obtain the desired solutions.

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Answer:

y+x=600

Step-by-step explanation:

Answer:

Step-by-step explanation:

first step : you put it in y form

y<600-x

then put the x so that the value of x+y do not exceed 600

since the sign is < and not ≤ then the line is dotted and not solid

Answer:

Total amount pay by Ben = $82.27 (Approx.)

Step-by-step explanation:

Given:

2 Shirts = $16 each

3 pairs of socks = $2.50 each

1 pair of jeans = $37.75 each

Sales tax = 6.5%

Find:

Total amount pay by Ben

Computation:

Total amount for shirts = 2 x 16

Total amount for shirts = $32

Total amount for socks = 3 x 2.50

Total amount for shirts = $7.50

Total amount before tax = $32 + $7.50 + $37.75

Total amount before tax = $77.25

Total amount pay by Ben = Total amount before tax[1+tax]

Total amount pay by Ben = 77.25[1+6.5%]

Total amount pay by Ben = $82.27 (Approx.)

Answer:

22.47

Step-by-step explanation:

321 x 0.07 = 22.47

7% of 321 is 22.47

Answer:

Step-by-step explanation:

43 + 24 + 57 + x = 180 degree (being sum of interior angles of a triangle)

124 + x = 180

x = 180 - 124

x = 56 degree

in small triangle

57 + 24 + z = 180 degree (sum of interior angles of a triangle )

81 + z = 180

z = 180 - 81

z = 99 degree

in big triangle

x + 43 + y = 180 degree (sum of interior angles of a triangle )

56 + 43 + y = 180

99 + y =180

y = 180 - 99

y = 81 degree

The value of x= 56°

Hope it helps you...

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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The recursive formula for Lindsey's scores is aₙ = aₙ₋₁ \(\times\) r, and the explicit formula is aₙ \(= 67 \times r^{(n-1).\)

To find the recursive and explicit formulas for the given geometric sequence, let's analyze the pattern of Lindsey's scores.

From the given information, we can observe that Lindsey's scores are increasing at the same rate.

This suggests that the scores form a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.

Let's denote the first term as a₁ = 67 and the common ratio as r.

Recursive Formula:

In a geometric sequence, the recursive formula is used to find each term based on the previous term. In this case, we can write the recursive formula as:

aₙ = aₙ₋₁ \(\times\) r

For Lindsey's scores, the recursive formula would be:

aₙ = aₙ₋₁ \(\times\) r

Explicit Formula:

The explicit formula is used to directly calculate any term of a geometric sequence without the need to calculate the previous terms.

The explicit formula for a geometric sequence is:

aₙ = a₁ \(\times r^{(n-1)\)

For Lindsey's scores, the explicit formula would be:

aₙ \(= 67 \times r^{(n-1)\)

In both formulas, 'aₙ' represents the nth term of the sequence, 'aₙ₋₁' represents the previous term, 'a₁' represents the first term, 'r' represents the common ratio, and 'n' represents the term number.

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Answer:

\(k<1, k>5\)

Step-by-step explanation:

\(3x+1=x^2+kx+2 \\ \\ x^2+x(k-3)+1=0 \\ \\ \Delta>0 \implies (k-3)^2-4(1)(1)>0 \\ \\ (k-3)^2-2^2>0 \\ \\ (k-1)(k-5)>0 \\ \\ k<1, k>5\)

Answer:

B or 2

Step-by-step explanation:

Because 2 and 4 are alternative interior angles that means that they are equal, but on the inside of the traversal (Parallels AB and CD)

Hope this helped :)

Answer:

it should be angle 2 and 4

Step-by-step explanation:

since 2 and 4 are interior angles they are the same and congruent so they have to be equal for the line to be parallel

The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.

Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.

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The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

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Answer:

Yes, Alternate Exterior Angles

Step-by-step explanation:

A testicle cuff is a ring-shaped device around the scrotum between the body and the testicles which when closed does not allow the testicles to slide through it. A common type has two connected cuffs, one around the scrotum and the other around the base of the penis. They are just one of many devices to restrain the male genitalia. A standard padlock, which cannot be removed without its key, may also be locked around the scrotum.

Answer:

There are 144 cubes in total. So 144÷36= 4 layers this is the answer.

Step-by-step explanation:

The cutoff for the lowest 12% of balances of the bank will be equal to the value $611.

To find the cutoff for the lowest 12% of balances, we can use the inverse normal distribution function to find the value x such that P(X ≤ x) = 0.12, where X is a normally distributed random variable with mean $845 and standard deviation $270. Now, since we know the values of the variables according to the question.

Plugging these values into the inverse normal distribution function, we get x = $611. This means that the cutoff for the lowest 12% of balances is $611, so any balances lower than this value will fall within the lowest 12%.

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Here's an example set of numbers:

{5, 10, 12, 15, 18, 20, 22, 22, 25, 30, 30}

Mean = sum of all numbers / total number of numbers

Mean = (5 + 10 + 12 + 15 + 18 + 20 + 22 + 22 + 25 + 30 + 30) / 11

Mean = 20

Median = the middle number when the numbers are arranged in order from smallest to largest

Median = 20 (since there are 11 numbers, the median is the 6th number, which is 20)

Mode = the most frequently occurring number in the set

Mode = 22 (since 22 appears twice in the set, which is more than any other number)

In this example, the mean and median are close together, which indicates that the data is fairly evenly distributed. However, the mode is different from the mean and median, which indicates that there is a skew in the data towards the higher end, since 22 and 30 occur twice each.

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Answer:

see below

Step-by-step explanation:

f(x)=72-12x

Domain:

Is the possible values that x can take

This is a line and x can take all values

(-∞,∞) or all real numbers

Range:

Is the possible values the output can take

This is a line and y can take all values

(-∞,∞) or all real numbers

Answer: The domain is 6, and range is 72 I believe.

Step-by-step explanation:

I really hope it helps :0

The value of the integral is 15.87.

The given integral is:∫∫R 10(x+y) dAwhere R={(x,y)∣16≤x²+y²≤25,x≤0} in rectangular coordinates.In rectangular coordinates, the equation of circle is x²+y² = r², where r is the radius of the circle and the equation of the circle is given as: 16 ≤ x² + y² ≤ 25 ⇒ 4 ≤ r ≤ 5We need to evaluate the integral over the region R using rectangular coordinates and integrate first with respect to x and then with respect to y.∫∫R 10(x + y) dA = 10∫ from 4 to 5 ∫ from -√(25-y²) to -√(16-y²) (x+y) dx dy...[since x < 0]

Now, integrating ∫(x+y) dx we get ∫(x+y) dx = (x²/2 + xy)Therefore, 10∫ from 4 to 5 ∫ from -√(25-y²) to -√(16-y²) (x+y) dx dy = 10∫ from 4 to 5 ∫ from -√(25-y²) to -√(16-y²) [ (x²/2 + xy) ] dy dx= 10∫ from 4 to 5 [∫ from -√(25-y²) to -√(16-y²) (x²/2 + xy) dy] dxNow integrating with respect to y we get∫(x²/2 + xy) dy = (xy/2 + y²/2)

Putting the limits and integrating we get10∫ from 4 to 5 [∫ from -√(25-y²) to -√(16-y²) (x²/2 + xy) dy] dx = 10∫ from 4 to 5 [(∫ from -√(25-y²) to -√(16-y²) (x²/2 + xy) dy)] dx = 10∫ from 4 to 5 [(x²/2)[y]^(-√(16-x²) )_(^(-√(25-x²))] + [(xy/2)[y]^(-√(16-x²) )_(^(-√(25-x²)))] dx = 10∫ from 4 to 5 [-(x²/2)√(16-x²) + (x²/2)√(25-x²) - (x/2)(16-x²)^(3/2) + (x/2)(25-x²)^(3/2) ] dxNow integrating with respect to x, we get10∫ from 4 to 5 [-(x²/2)√(16-x²) + (x²/2)√(25-x²) - (x/2)(16-x²)^(3/2) + (x/2)(25-x²)^(3/2) ] dx = [ (10/3) [(25/3)^(3/2) - (16/3)^(3/2)] - 5√3 - (5/3)[(25/3)^(3/2) - (16/3)^(3/2) ] ]Ans: The value of the integral is 15.87.

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The margin of error associated with the 95% confidence interval for the population mean volume is: D. 5.62.

To calculate the 95% confidence interval for the population mean volume, we can use the formula:

CI = x ± (t * (s/√n))

Where CI represents the confidence interval, x is the sample mean, t is the t-score associated with the desired confidence level (95%), s is the sample standard deviation, and n is the sample size.

In this case, x = 64 cc, s = 12 cc, and n = 20 orangutans. We need to find the t-score for a 95% confidence interval with 19 degrees of freedom (n-1). Using a t-table, we find that the t-score is approximately 2.093.

Now we can calculate the margin of error:

Margin of Error = t * (s/√n) = 2.093 * (12/√20) ≈ 5.62

Therefore, the margin of error associated with the 95% confidence interval for the population mean volume is: D. 5.62.

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Answer:

\(l = \frac{S}{\pi r} - r\)

Step-by-step explanation:

Given the surface area of a cone expressed as S = \(\pi r^{2} +\pi rl\) where r is the radius of the cone and 'l' is its slant height. To find the slant height from the formula, we will make l the subject of the formula as shown;

\(S = \pi r^{2} + \pi rl\\S = \pi r (r + l)\\\frac{S}{\pi r} = r+l\\l = \frac{S}{\pi r} - r\\\)

The final expression gives the value of the slant height.

Answer: l=s/3.14-r2

Step-by-step explanation:

did it on Edg and the 3.14 i’d supposed to be the symbol for pi hope it helps :)

Answer:

Step-by-step explanation:

The values of angles are written below,

a° = 121°

b° = 53°

c° = 87°

d° = 72°

The Inscribed Angle Theorem: This theorem states that the measure of an inscribed angle in a circle is equal to half the measure of the intercepted arc.

In other words, if an angle is formed by two intersecting chords in a circle, the measure of the angle is equal to half the sum of the measures of the arcs intercepted by the angle.

The values of angles are calculated as,

a = (2 x 108 ) - 9 5

a = 121°

b = 360 - ( 121 + 95 + 91 )

b = 53°

c = (121 + 53 ) / 2

c = 87°

d = ( 91 + 53 ) /2

d = 72°

Therefore, the values are a = 121°, b = 53°, c = 87°, and d = 72°.

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Answer:

The length of the hypotenuse is 39. In the step by step explanation I included the Pythagorean Theorem formula and how it converted to the equation here to solve the problem.

Step-by-step explanation:

a² + b² = c²

15² + 36² = 1,521

√1,521 = 39

39 = c

If you have 5 qualified candidates to fill the positions of president and vice president, then their have 20 ways to be fill the positions.

In the given question,

If you have 5 qualified candidates to fill the positions of president and vice president, then we have to find how many ways can the positions be filled.

We have total 5 qualified question.

Their have total 2 position president and vice president.

When the one position one of president filled then their one left 4 qualified candidate for the vice president position.

So the possible ways to fill the position is find by multiplying the 5 and 4. So

Possible ways=5*4

Possible ways=20

Hence, if you have 5 qualified candidates to fill the positions of president and vice president, then their have 20 ways to be fill the positions.

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The correct option d. the event can take no more than a maximum amount of time, described the  an event has a timebox.

A timebox is a set amount of time during which a work must be completed in agile software development.

Thus, when an event has a timebox, it signifies that the event can only last a certain length of time.

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The 85% confidence interval for the mean electricity usage per family is (19.6, 20.4) kWh per day.

To construct the confidence interval, we need to use the sample mean, the sample size, and the population standard deviation (which is given as 2 kWh). The formula for the confidence interval is:

Confidence interval = sample mean +/- z* (population standard deviation / square root of sample size)

Here, z* is the critical value from the standard normal distribution that corresponds to the desired level of confidence. For an 85% confidence interval, z* is 1.44 (you can find this value in a standard normal distribution table or calculator).

Plugging in the values, we get:

Confidence interval = 20 ± 1.44 x (2 / √(576))

= 20 ± 0.36

= (19.6, 20.4)

This means that we are 85% confident that the true population mean falls within this interval. In other words, we can say with reasonable certainty that the average daily electricity usage per family in the population is somewhere between 19.6 and 20.4 kWh.

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