Please help me to do this task (I really need an answer) ​

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Answer:

18 chicken wings

Step-by-step explanation:

28.5/15=1.9

34.2/1.9=18

18 chickens were bought for $34.30.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Number of chicken bought = 15

Cost of 15 chickens = $28.50

This means,

15 chickens = $28.50

1 chicken = 28.50/15

1 chicken = $1.9

Now,

The number of chickens bought with $34.20.

= 34.20 ÷ 1.9

= 18

Thus,

18 chickens were bought for $34.30.

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SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

CONCLUSION:

The final answer is:

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

a) Since Kenji's time has a lower Z-score's than Nedda, he is considered a better runner relative to his competition.

b) Since her time has the lowest Z-score, Rachel is the fastest runner with respect to her class.

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

a. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?

We have to see their z-scores.

Whoever has the lower z-score is in the lower percentile of times, that is, runs faster.

Kenji:

A junior high school class ran one mile with a mean of nine minutes and a standard deviation of two minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes.

So Kenji's z-score is found when \(X = 8.5, \mu = 9, \sigma = 2\). So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{8.5 - 9}{2}\)

\(Z = -0.25\)

Nedda:

A high school class ran one mile with a mean of seven minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in eight minutes.

So Nedda's z-score is found when \(X = 8, \mu = 7, \sigma = 4\). So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{8 - 7}{4}\)

\(Z = 0.25\)

Since Kenji's time has a lower Z-score's than Nedda, he is considered a better runner relative to his competition.

b. Who is the fastest runner with respect to his or her class? Explain why.

Whoever has the lower z-score.

We have the z-scores for Kenji and Nedda, and we have to find Rachel's z-score.

An elementary school class ran one mile with a mean of 12 minutes and a standard deviation of three minutes. Rachel, a student in the class, ran one mile in seven minutes.

So Rachel's z-score is found when \(X = 7, \mu = 12, \sigma = 3\)

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{7 - 12}{3}\)

\(Z = -1.67\)

Since her time has the lowest Z-score, Rachel is the fastest runner with respect to her class.

The deductible amount shown in the policy for both comprehensive and collision coverages is: D. $250

Danny and Sara's insurance quote includes coverage for their 2015 sports car and 2018 minivan.

The policy has various coverages, limits, and premiums for each vehicle. Let's break it down:

Bodily injury liability:

2015 sports car: $50,000 per person, $100,000 per occurrence, with a premium of $59.10

2018 minivan: $50,000 per person, $100,000 per occurrence, with a premium of $57.50

Property damage liability:

2015 sports car: $50,000 per occurrence, with a premium of $45.90

2018 minivan: $50,000 per occurrence, with a premium of $49.50

Medical payments: Not provided

Comprehensive coverage:

2015 sports car: $5,000 actual cash value, with a premium of $42.30 and a $250 deductible

2018 minivan: $5,000 actual cash value, with a premium of $38.90 and a $250 deductible

Collision coverage:

2015 sports car: Actual cash value, with a premium of $90.80 and a $250 deductible

2018 minivan: Actual cash value, with a premium of $85.60 and a $250 deductible

Additional Coverages:

6. Towing and labor: $2.00 for both vehicles

Loss of use: $20.00 for both vehicles, $1000 max, and $50 per day

Uninsured motorist bodily injury coverage is declined.

The total six-month premium for all vehicles is not provided in the quote.

The deductible amount shown in the policy for both comprehensive and collision coverages is:

D. $250

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Answer:

  70 ft

Step-by-step explanation:

You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.

Each inch represents 10 feet, so 7 inches will represent ...

  7 × 10 ft = 70 ft

The gym is 70 ft wide.

__

Additional comment

You can also write and solve an equation that shows the measures are proportional:

  actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)

Multiplying both sides of this proportion by 7 in, we have ...

  gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft

Explanation:

This is known as a cyclic quadrilateral since all four points are on the circle's edge, and the quadrilateral is entirely inside the circle (no parts of the quadrilateral spill outside the circle). Another term is "inscribed quadrilateral"

Since we have an inscribed quadrilateral, this means the opposite angles of the quadrilateral are supplementary.

B+D = 180

120+x = 180

x = 180-120

x = 60

Answer:

Step-by-step explanation:

To be rational means to be able to express the result as the ratio of two whole numbers.

a) 4/7 + (-1/3) = 12/21 - 7/21 = 5/21 so rational

b) √(4) • 2/5 = ±2 • 2/5 = ±4/5 so both solutions are rational

It should be greater not lesser

Step-by-step explanation:

3x -20= -2x +10

or,5x=30

or,X=30/5

or,X=6

Y= -2×6 + 10

= -2

therefore solution is (6, -2)

Answer :

⠀

Explanation :

⠀

Solution :

where,

⠀

We know that,

\( {\longrightarrow \bf \qquad (AC) {}^{2} = (AB) {}^{2} +( BC) {}^{2} }

\)

⠀

Now, we will substitute the given values in the formula :

\( {\longrightarrow \sf \qquad (AC) {}^{2} = (8) {}^{2} +( 6) {}^{2} }\)

⠀

We know that, (8)² = 64 and (6)² = 36. So,

\( {\longrightarrow \sf \qquad (AC) {}^{2} = 64 + 36 }\)

⠀

Now, adding 64 and 36 we get :

\( {\longrightarrow \sf \qquad (AC) {}^{2} = 100 }\)

⠀

Now, we'll take the square root of both sides to remove the square from AC :

\( {\longrightarrow \sf \qquad \sqrt{(AC) {}^{2}} = \sqrt{100} }\)

⠀

\( {\longrightarrow \sf \qquad AC = \sqrt{100} }\)

⠀

We know that, square root of 100 is 10 .

\( {\longrightarrow \bf \qquad AC = 10 }\)

⠀

So,

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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Answer:

609

Step-by-step explanation:

Step 1: Write expression

45 - 7b + 14 + 17b

Step 2: Simplify expression

10b + 59

Step 3: Substitute b

10(55) + 59

550 + 59

609

Answer:

400 apple pies

Step-by-step explanation:

To solve for the number of apple pies baked by her, let's solve using equations and solving them by substitution method.

\(\textcolor{steelblue}{\text{\textcircled{1} Define the variables}}\)

Let the number of apple pies and chicken pies baked be a and c pies respectively.

\(\textcolor{steelblue}{\text{\textcircled{2} Form equations}}\)

Total pies baked= 560

a +c= 560 -----(1)

Total pies sold= ½(560)

\( \frac{60}{100} \text{a} \: + \frac{25}{100} \text{b} = 280\)

0.6a +0.25b= 280 -----(2)

\(\textcolor{steelblue}{\text{\textcircled{3} Solve by substitution}}\)

Since we are only interested in the value of a, we should eliminate the term c by making c the subject of equation. This ensures that after substitution, the equation will be in terms of a only.

From (1):

c= 560 -a -----(3)

Substitute (3) into (2):

0.6a +0.25(560 -a)= 280

Expand:

0.6a +140 -0.25a= 280

Simplify:

0.35a +140= 280

0.35a= 280 -140

0.35a= 140

Divide both sides by 0.35:

a= 140 ÷0.35

a= 400

\(\textcolor{steelblue}{\text{\textcircled{4} Concluding statement}}\)

Thus, she baked 400 apple pies.

Answer:

Range { 2,3,4,5}

Step-by-step explanation:

The range is the output values

Range { 2,3,4,5}

Answer:

56 coins

Step-by-step explanation:

28 divided by 1/2 is 56

Answer:

(-5, 101) or (1, -7)

Step-by-step explanation:

The gradient of a function is zero when its first differential is zero

Taking first derivative of y = x³ + 6x² - 15x + 1

we get
\(\dfrac{dy}{dx} = \dfrac{d}{dx}(x^3+6x^2-15x\:+\:1)\)

\(= \dfrac{d}{dx}(x^3)+ \dfrac{d}{dx}(6x^2) - \dfrac{d}{dx}(15x)\:+\: \dfrac{d}{dx}(1)\\\\\)

\(= 3x^2 + 2(6x) - 15 + 0\\\\\\= 3x^2 + 12x - 15x\\\)

Set this first differential to 0, find the solution set for x

\(3x^2 + 12x - 15x =0\)

This is a quadratic equation which will have 2 solutions for x.

First divide throughout by 3
\(= > x^2 + 4x - 5 = 0\)

Factor the term:
\(= > x^2 + 4x - 5 = 0\\\\== > (x -1)(x + 5) = 0\\== > x - 1 =0 \text { or } x + 5 =0\\\\\)

This means x = 1 or x = -5 is the solution set

To find the y value corresponding to these values of x, plug in each of these x values in the original equation and solve for y

Plug in x = 1 into equation x³ + 6x² - 15x + 1

=> 1³ + 6(1)² - 15(1) + 1

=> 1 + 6 - 15 + 1

=> -7

So one point is (1, -7)

Looking at the choices we can eliminate the first and  last choices

Looking at choices 2 and 3 we see that only one of them has x = -5 which is the other solution value. This is the second choice

So the correct answer is second choice
(-5, 101) or (1, -7)

Note we did not have to go through the pain of computing y for x = -5

Answer:

what's that

Step-by-step explanation:

Answer:

899.2/ 900

Step-by-step explanation:

Answer:

7.2 hours.

Step-by-step explanation:

Search up "30% of 24"

Answer:

You sleep 7.2 hours.

Step-by-step explanation:

nsnsnsla

The value of x from the given figure is given as follows:

144º.

An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.

The two opposite rays in this problem have the measures given as follows:

Hence the equation to find the value of x is given as follows:

x + x/4 = 180

x + 0.25x = 180

1.25x = 180

x = 180/1.25

x = 144º.

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Answer:

6.61 mph

Step-by-step explanation:

Speed of current; c = 2 mph

Total time to travel upstream and back; t = t1 + t2 = 4 hours

Let x represent speed of the boat in still water

Then the actual speed of the boat when going upstream is x - 2, and the actual speed when going downstream downstream is x + 2.

We know that; distance = speed x time, Thus;

For the upstream trip;

12 = (x - 2)t1

t1 = 12/(x - 2)

For the downstream trip;

12 = (x + 2)t2

t2 = 12/(x +2)

Adding both equations, we have;

t1 + t2 = (12/(x - 2)) + (12/(x +2))

4 = (12/(x - 2)) + (12/(x +2))

Multiply through by (x - 2)(x + 2)

4(x - 2)(x + 2) = 12(x + 2) + 12(x - 2)

4x²- 16 = 12x + 24 + 12x - 24

4x² - 16 = 24x

4x² - 24x - 16 = 0

Using quadratic formula, we have;

x ≈ 6.61 mph

Answer:

Confidence Interval = (1.41, 1.59)

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.

The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.

Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).

In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:

a + b + c = 180

Substituting the given values, we get:

(6x-1) + 20 + (x+14) = 180

Simplifying and solving for x, we get:

7x + 33 = 180

7x = 147

x = 21

Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:

angle a = (6x-1) = (6*21-1) = 125 degrees

angle b = 20 degrees

angle c = (x+14) = (21+14) = 35 degrees

Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

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Answer:

2 hours

Step-by-step explanation:

I'm pretty sure its 2 hrs. If she did not take any breaks, she would have made it in 2 hrs due to her taking a 2 hr break. If its not 2 hours,  its 3. But I am 99% sure its 2 hrs.    

7

Step-by-step explanation:

4/12 which simplifies down to 1/3 meaning 1 pack is 3 dollars each . well 21/3 is 7

Number of baseball card packs  purchased for $21 is equals to 7.

" A proportion is defined as when two or more ratios of the given number are equivalent to each other."

Formula used

a, b, c, d are in proportion

Therefore , \(\frac{a}{b} =\frac{c}{d}\)

According to the question,

Number of baseball card packs purchased in $12 = 4

Number of baseball card packs purchased in $21 = x

As per the definition of proportion we have,

   \(\frac{4}{12} = \frac{x}{21}\)

⇒12 × x = 4 × 21

⇒       x =  (4 × 21) /12

⇒       x = 7 baseball card packs

Hence, number of baseball card packs  purchased for $21 is equals to 7

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The number of people in the set C ∩ D (customers who purchased both cats and dogs) is obtained by adding the overlap of D and C (3) with the overlap of all 3 circles (1), resulting in a total of 4 individuals.

The correct answer is 4.

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to analyze the overlapping regions in the Venn diagram.

Given information:

- Circle C (cats): 15

- Circle D (dogs): 21

- Circle F (fish): 12

- Overlap of C and F: 2

- Overlap of F and D: 0

- Overlap of D and C: 3

- Overlap of all 3 circles: 1

- Number outside of circles: 14

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to consider the overlapping region between circles C and D.

From the information given, we know that the overlap of D and C is 3. Additionally, we have the overlap of all 3 circles, which is 1. The overlap of all 3 circles includes the region where customers have purchased cats, dogs, and fish.

To calculate the number of people in the set C ∩ D, we add the overlap of D and C (3) to the overlap of all 3 circles (1). This gives us 3 + 1 = 4.

Therefore, from the options given correct one is 4.

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Answer: 4

Step-by-step explanation:

trust me bro

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

Answer:

I think its telling you to done o and up and like 2y 1x

Step-by-step explanation: