The temperature outside when Colin went to bed was -4°F. When he woke up the next

morning, it was -11°F outside. Describe the change in temperature by completing the

statements.

We have been given that Mr. Collins and Ms. LaPointe are saving money to buy a new motorcycle. The total amount of money Mr. Collins will save is given by the function [tex]p(x) = 62+5x[/tex]. The total amount of money Ms. LaPointe will save is given by the function [tex]a(x) = x^2+38[/tex]. We are asked to find number of months when they have the same amount of money saved.

To solve our given problem, we will equate both equations as:

[tex]x^2+38=62+5x[/tex]

[tex]x^2-5x+38=62+5x-5x[/tex]

[tex]x^2-5x+38=62[/tex]

[tex]x^2-5x+38-62=62-62[/tex]

[tex]x^2-5x-24=0[/tex]

[tex]x^2-8x+3x-24=0[/tex]

[tex]x(x-8)+3(x-8)=0[/tex]

[tex](x-8)(x+3)=0[/tex]

[tex](x-8)=0,(x+3)=0[/tex]

[tex]x=8,x=-3[/tex]

Since time cannot be negative, therefore, after 8 months they will have the same amount of money saved.

Answer:

a

Step-by-step explanation:

bc I just took the quiz☝

Answer:

P(X ≥ 125) = 0.9812

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the normal distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

The Poisson can be approximated to the normal, with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]

Let μ = 2.5 every minute

This is the mean of the Poisson, so [tex]\lambda = 2.5n[/tex], in which n is the number of minutes.

P(X ≥ 125) over an hour

An hour has 60 minutes, so [tex]n = 60, \lambda = 2.5*60 = 150, \sigma = \sqrt{150} = 12.25[/tex]

Using continuity correction, this is [tex]P(X \geq 125 - 0.5) = P(X \geq 124.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 124.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{124.5 - 150}{12.25}[/tex]

[tex]Z = -2.08[/tex]

[tex]Z = -2.08[/tex] has a pvalue of 0.0188

1 - 0.0188 = 0.9812

So

P(X ≥ 125) = 0.9812

Answer:

441

Step-by-step explanation:

84 / 4 = 21

21 x 21 = 441

Answer:

441

Step-by-step explanation:

84/2=42

Answer:

t = pn

Step-by-step explanation:

We are to find the relationship between total cost and the number of items.

First we would represent the relationship between total cost and number of items with variables

Let the total cost = t

and the number of items = n

Total cost t is proportional to the number n of items:

t ∝ n

t = kn

where k is constant

Since it is purchased at a constant price p, the constant of proportionality would be p. the k would be replaced with p

t = pn

Answer:

18/35

Step-by-step explanation:

1 1/5 ÷ 2  1/3

Change from mixed numbers to improper fractions

1 1/5 = (5*1+1)/5 = 6/5

2 1/3 = (3*2+1)/3 = 7/3

6/5÷ 7/3

Copy dot flip

6/5* 3/7

18/35

Answer:

Step-by-step explanation:

I don't say you must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me my friend...

Answer: A

Step-by-step explanation:

Formula for inverse of a matrix is:

[tex]A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\qquad \rightarrow \qquad A^{-1}=\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]

[tex]A=\left[\begin{array}{cc}2&5\\3&8\end{array}\right] \qquad \rightarrow \qquad A^{-1}=\dfrac{1}{2(8)-5(3)}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\dfrac{1}{1}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right][/tex]

We have that  Option A is the correct option as its the correct in verse of the Matrix A

From the question we are told that:

[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]

Inverse of a Matrix

The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is A^{-1}, and A.A^{-1} = I.

Therefore the inverse of the Matrix A is

[tex]A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}[/tex]

Giving

[tex]A^{-1}= \begin{vmatrix}8 & -5 \\-3 & -2\end{vmatrix}[/tex]

In conclusion

The correct Option is Option A as its the correct in verse of the Matrix A

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In conclusion

Answer:

C. No, the program is not statistically significant because the results are likely to occur by chance.

Step-by-step explanation:

At a significance level that is smaller than 0.2, the effect is not significant.

We have a P-value of 20%, which means that we have 20% chances of getting this sample given that the method has no effect.

We then can conclude that there is not enough evidence to support the claim that the method is effective.

Answer:

[tex]w>48[/tex] pounds

Step-by-step explanation:

The customer will be charged extra if the weight of their suitcase is above 48 pounds.

Let the weight of the suitcase = w (in pounds)

Therefore, w above (greater than) 48 pounds is written mathematically as:

[tex]w>48[/tex] pounds

This is the inequality that represents w, the weight of the suitcase in pounds, that will have an extra charge.

Answer:

There is enough evidence to support the claim of the manufacturers that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

The significance level is 0.05.

The sample 1 (hybrid), of size n1=21 has a mean of 32 and a standard deviation of 6.

The sample 2 (non-hybrid), of size n2=31 has a mean of 21 and a standard deviation of 3.

The difference between sample means is Md=11.

[tex]M_d=M_1-M_2=32-21=11[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{6^2}{21}+\dfrac{3^2}{31}}\\\\\\s_{M_d}=\sqrt{1.714+0.29}=\sqrt{2.005}=1.4158[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{11-0}{1.4158}=\dfrac{11}{1.4158}=7.77[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=21+31-2=50[/tex]

This test is a right-tailed test, with 50 degrees of freedom and t=7.77, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>7.77)=0.0000000002[/tex]

As the P-value is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.

Answer: About 14.14 in^3

Step-by-step explanation:

We know that the circumference of a sphere is C=2πr. We are given that the circumference is 9.42 in. We can find the radius to get our volume.

[tex]9.42=2\pi r[/tex]

[tex]4.71=\pi r[/tex]

[tex]r=1.5\\[/tex]

Now that we know radius, we can find our volume.

[tex]V=\frac{4}{3} \pi r^3[/tex]

[tex]V=\frac{4}{3} \pi (1.5)^3[/tex]

[tex]V=14.14in^3[/tex]

Answer:

The answer is x=5.

Step-by-step explanation:

11x + 7x + 90 = 180

18x + 90 = 180

       -90    -90

= 18x = 90

 x = 5

x is 5!

Value of x is 10°.

Correct option is B.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”.

Given,

a || b

cut by transversal s and t

lines b and t have angle = 90°

The first top left angle between a, s, t = 7x

The last bottom angle between s and b = 11x

a || b, so a and t will also have angle = 90°

by the figure,

180° - 11x + 90° - 7x + 90° = 180°

360° - 18x = 180°

18x = 180°

x = 10°

Hence, 10° is value of x.

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Answer:

Step-by-step explanation:

Let x represent the random variable representing the scores in the exam. Given that the scores are normally distributed with a mean of 40 and a standard deviation of 5, the diagram representing the curve and​ the position of the​ mean, the mean plus or minus one standard​ deviation, the mean plus or minus two standard​ deviations, and the mean plus or minus three standard deviations is shown in the attached photo

1 standard deviation = 5

2 standard deviations = 2 × 5 = 10

3 standard deviations = 3 × 5 = 15

1 standard deviation from the mean lies between (40 - 5) and (40 + 5)

2 standard deviations from the mean lies between (40 - 10) and (40 + 10)

3 standard deviations from the mean lies between (40 - 15) and (40 + 15)

b) We would apply the probability for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 40

σ = 5

the probability that a randomly selected score will be greater than 50 is expressed as

P(x > 50) = 1 - P( ≤ x 50)

For x = 50,

z = (50 - 40)/5 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.98

P(x > 50) = 1 - 0.98 = 0.02

Answer:

A = 36pi in^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi 6^2

A = 36pi in^2

Radius(r)=6 inches

Area of circle=?

Now,

Area of circle=pi r ^2

=pi (6)^2

36 pi inches^2

So the right answer is 36 pi inches^2

Hope it helps

Answer:

1a) (i) 0.0537

(ii) 0.0250

(iii) 0.6188

1b) The probability that neither Kofi nor Mensah solves the problem correctly = (9/20) = 0.45

Step-by-step explanation:

The complete Question is presented in the attached image to this answer.

1a) This is a normal distribution problem with

Mean lifetime of bulbs = μ = 210 hours

Standard deviation = σ = 56 hours

(i) at least 300 hours, P(x ≥ 300)

We first standardize 300 hours

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (300 - 210)/56 = 1.61

To determine the required probability

P(x ≥ 300) = P(z ≥ 1.61)

We'll use data from the normal probability table for these probabilities

P(x ≥ 300) = P(z ≥ 1.61) = 1 - P(z < 1.61)

= 1 - 0.94630 = 0.0537

(ii) at most 100 hours, P(x ≤ 100)

We first standardize 100 hours

z = (x - μ)/σ = (100 - 210)/56 = -1.96

To determine the required probability

P(x ≤ 100) = P(z ≤ -1.96)

We'll use data from the normal probability table for these probabilities

P(x ≤ 100) = P(z ≤ -1.96) = 0.0250

(iii) between 150 and 250 hours.

P(150 < x < 250)

We first standardize 150 and 250 hours

For 150 hours

z = (x - μ)/σ = (150 - 210)/56 = -1.07

For 250 hours

z = (x - μ)/σ = (250 - 210)/56 = 0.71

To determined the required probability

P(150 < x < 250) = P(-1.07 < z < 0.71)

We'll use data from the normal probability table for these probabilities

P(150 < x < 250) = P(-1.07 < z < 0.71)

= P(z < 0.71) - P(z < -1.07)

= 0.76115 - 0.14231

= 0.61884 = 0.6188 to 4 d.p.

1b) Probability that Kofi solves the problem correctly = P(K) = (1/4)

Probability that Mensah solves the problem correctly = P(M) = (2/5)

Probability that Kofi does NOT solve the problem correctly = P(K') = 1 - P(K) = 1 - (1/4) = (3/4)

Probability that Mensah does NOT solve the problem correctly = P(M') = 1 - P(M) = 1 - (2/5) = (3/5)

To find the probability that neither of them solves the problem correctly, we first make the logical assumption that the probabilities of either of them solving the problem are independent of each other.

Hence, the probability that neither of them solves the problem correctly = P(K' n M')

P(K' n M') = P(K') × P(M') = (3/4) × (3/5) = (9/20) = 0.45

Hope this Helps!!!

Complete Question

1. Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of​ data, then compare the variation.

Bank A (single lines): 6.5, 6.6, 6.7, 6.8, 7.2, 7.3, 7.4, 7.6, 7.6, 7.7

Bank B (individual lines): 4.1, 5.4, 5.8, 6.3, 6.8, 7.8, 7.8, 8.6, 9.3, 9.7

- The coefficient of variation for the waiting times at Bank A is ----- %?

- The coefficient of variation for the waiting times at the Bank B is ----- ​%?

- Is there a difference in variation between the two data​ sets?

Answer:

a

The coefficient of variation for the waiting times at Bank A is [tex]l =[/tex]6.3%

b

The coefficient of variation for the waiting times at Bank B is [tex]l_1 =[/tex]25.116%

c

The waiting time of Bank B has a considerable higher variation than that of Bank A

Step-by-step explanation:

From the question we are told that

  For Bank A  : 6.5, 6.6, 6.7, 6.8, 7.2, 7.3, 7.4, 7.6, 7.6, 7.7

 For  Bank B : 4.1, 5.4, 5.8, 6.3, 6.8, 7.8, 7.8, 8.6, 9.3, 9.7

The sample size is  n =10

The mean for Bank A is

          [tex]\mu_A = \frac{6.5+ 6.6+ 6.7+ 6.8+ 7.2+ 7.3+ 7.4+ 7.6+ 7.6+ 7.7}{10}[/tex]

          [tex]\mu_A = 7.14[/tex]

The standard deviation is mathematically represented as

      [tex]\sigma = \sqrt{\frac{\sum|x- \mu|}{n} }[/tex]

        [tex]k = \sum |x- \mu | ^2 = 6.5 -7.14|^2 + |6.6-7.14|^2+ |6.7-7.14|^2+ |6.8-7.14|^2 + |7.2-7.14|^2+ |7.3-7.14|^2, |7.4-7.14|^2+ |7.6-7.14|^2+|7.6-7.14|^2+|7.7-7.14|^2[/tex]

[tex]k = 2.42655[/tex]

    [tex]\sigma = \sqrt{\frac{2.42655}{10} }[/tex]

    [tex]\sigma = 0.493[/tex]

The coefficient of variation for the waiting times at Bank A is  mathematically represented as  

        [tex]l = \frac{\sigma}{\mu} *100[/tex]

        [tex]l = \frac{0.493}{7.14} *100[/tex]

       [tex]l =[/tex]6.3%

Considering Bank B

     The mean for Bank B is

               [tex]\mu_1 = \frac{4.1+ 5.4+ 5.8+ 6.3+6.8+ 7.8+ 7.8+ 8.6+ 9.3+ 9.7}{10}[/tex]

              [tex]\mu_1 = 7.16[/tex]

The standard deviation is mathematically represented as      

       [tex]\sigma_1 = \sqrt{\frac{\sum|x- \mu_1|}{n} }[/tex]

    [tex]\sum |x- \mu_1 | ^2 =4.1-7.16|^2 +| 5.4-7.16|^2+ |5.8-7.16|^2 + | 6.3-7.16|^2 + |6.8-7.16|^2 + | 7.8-7.16|^2 +|7.8-7.16|^2 +|8.6-7.16|^2 + |9.3-7.16|^2 +|9.7-7.16|^2[/tex]

[tex]\sum |x- \mu_1 | ^2 =32.34[/tex]

    [tex]\sigma_1 = \sqrt{\frac{32.34}{10} }[/tex]

     [tex]\sigma_1 = 1.7983[/tex]

The coefficient of variation for the waiting times at Bank B is  mathematically represented as  

        [tex]l_1 = \frac{\sigma }{\mu} *100[/tex]

        [tex]l_1 = \frac{1.7983 }{7.16} *100[/tex]

        [tex]l_1 =[/tex]25.116%

Answer:

0 = 3x -2y -6

Step-by-step explanation:

The general form of the equation of a line is 0 = Ax + By + C

y = 3/2x -3

Subtract y from each side

0 = 3/2x -y -3

Multiply each side by 2

0 = 3x -2y -6

Answer:

f(x)=4

Step-by-step explanation:

In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)x wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.

f(x)=4(2/3)*

option D

opción D

Answer:

5   : 4

Step-by-step explanation:

4:  3.2

Multiply by 10 to get rid of the decimal

4*10 : 3.2* 10

40 : 32

Divide each side by 8 to simplify

40/8   : 32/ 8

5   : 4

Answer:it’s ZERO

Step-by-step explanation:

The discriminant of the function is zero

A relation is a function if it has only One y-value for each x-value.

The discriminant tells you where the graph of the parabola goes through the x-axis, if at all.

If the discriminant is negative there are no real zeros and the parabola does not cross or touch the x-axis;

if the discriminant is positive the parabola will go through the x axis in 2 places;

if the discriminant is 0 the parabola will touch the x-axis in 1 place.

Our discriminant is 0 since the parabola only touches the x-axis but does not go through.

Hence, the discriminant of the function is zero

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Answer:

0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost

Step-by-step explanation:

Independent events:

If two events, A and B, are independent, then:

[tex]P(A \cap B) = P(A)*P(B)[/tex]

Conditional probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: At least one tag is lost

Event B: Exactly one tag is lost.

Each tag has a 40% = 0.4 probability of being lost.

Probability of at least one tag is lost:

Either no tags are lost, or at least one is. The sum of the probabilities of these events is 1. Then

[tex]p + P(A) = 1[/tex]

p is the probability none are lost. Each one has a 60% = 0.6 probability of not being lost, and they are independent. So

p = 0.6*0.6 = 0.36

Then

[tex]P(A) = 1 - p = 1 - 0.36 = 0.64[/tex]

Intersection:

The intersection between at least one lost(A) and exactly one lost(B) is exactly one lost.

Then

Probability at least one lost:

First lost(0.4 probability) and second not lost(0.6 probability)

Or

First not lost(0.6 probability) and second lost(0.4 probability)

So

[tex]P(A \cap B) = 0.4*0.6 + 0.6*0.4 = 0.48[/tex]

Find the probability that exactly one tag is lost, given that at least one tag is lost (write it up to second decimal place).

[tex]P(B|A) = \frac{0.48}{0.64} = 0.75[/tex]

0.75 = 75% probability that exactly one tag is lost, given that at least one tag is lost

Answer:

a) [tex] z = \frac{295.2-247}{62.2}=0.772[/tex]

And using the normal distribution table or excel we got:

[tex] P(Z>0.772) = 1-P(Z<0.772) = 1-0.77994= 0.22006[/tex]

b) [tex] z = \frac{295.5 -247}{\frac{62.2}{\sqrt{16}}}= 3.119[/tex]

And we can use the normal standard table or excel in order to find the probability and we got:

[tex] P(z>3.119) =1-P(Z<3.119)= 1- 0.999093=0.000907[/tex]

Step-by-step explanation:

For this case we know that the random variable of interest is normally distributed with the following parameters:

[tex] X \sim N (\mu = 247, \sigma =62.2)[/tex]

Part a

We want to find this probability:

[tex] P(X>295.2)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{X-\mu}{\sigma}[/tex]

Replacing we got:

[tex] z = \frac{295.2-247}{62.2}=0.772[/tex]

And using the normal distribution table or excel we got:

[tex] P(Z>0.772) = 1-P(Z<0.772) = 1-0.77994= 0.22006[/tex]

Part b

We select a random sample of size n = 16 and we try to find this probability:

[tex] P(\bar X >295.2)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And replacing we got:

[tex] z = \frac{295.5 -247}{\frac{62.2}{\sqrt{16}}}= 3.119[/tex]

And we can use the normal standard table or excel in order to find the probability and we got:

[tex] P(z>3.119) =1-P(Z<3.119)= 1- 0.999093=0.000907[/tex]

Answer:

98.57

Step-by-step explanation:

3.5% over 100% X 102=3.43

102-3.43= 98.57

Answer:

(1)Equivalence Relation

(2)Not Transitive, (0,3) is missing

(3)Equivalence Relation

(4)Not symmetric and Not Transitive, (2,1) is not in the set

Step-by-step explanation:

A set is said to be an equivalence relation if it satisfies the following conditions:

(1) {(0,0), (1,1), (2,2), (3,3)}

(3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)}

The relations in 1 and 3 are Reflexive, Symmetric and Transitive. Therefore (1) and (3) are equivalence relation.

(2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)}

In (2), (0,2) and (2,3) are in the set but (0,3) is not in the set.

Therefore, It is not transitive.

As a result, the set (2) is not an equivalence relation.

(4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}

(1,2) is in the set but (2,1) is not in the set, therefore it is not symmetric

Also, (2,0) and (0,1) is in the set, but (2,1) is not, rendering the condition for transitivity invalid.

Answer:

answer is in exaplation

Step-by-step explanation:

cosA

+

cosA

1+sinA

=2secA

Step-by-step explanation:

\begin{lgathered}LHS = \frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=\frac{cos^{2}A+(1+sinA)^{2}}{(1+sinA)cosA}\\=\frac{cos^{2}A+1^{2}+sin^{2}A+2sinA}{(1+sinA)cosA}\\=\frac{(cos^{2}A+sin^{2}A)+1+2sinA}{(1+sinA)cosA}\\=\frac{1+1+2sinA}{(1+sinA)cosA}\end{lgathered}

LHS=

1+sinA

cosA

+

cosA

1+sinA

=

(1+sinA)cosA

cos

2

A+(1+sinA)

2

=

(1+sinA)cosA

cos

2

A+1

2

+sin

2

A+2sinA

=

(1+sinA)cosA

(cos

2

A+sin

2

A)+1+2sinA

=

(1+sinA)cosA

1+1+2sinA

/* By Trigonometric identity:

cos² A+ sin² A = 1 */

\begin{lgathered}=\frac{2+2sinA}{(1+sinA)cosA}\\=\frac{2(1+sinA)}{(1+sinA)cosA}\\\end{lgathered}

=

(1+sinA)cosA

2+2sinA

=

(1+sinA)cosA

2(1+sinA)

After cancellation,we get

\begin{lgathered}= \frac{2}{cosA}\\=2secA\\=RHS\end{lgathered}

=

cosA

2

=2secA

=RHS

Therefore,

\begin{lgathered}\frac{cosA}{1+sinA}+\frac{1+sinA}{cosA}\\=2secA\end{lgathered}

1+sinA

cosA

+

cosA

1+sinA

=2secA

Answer:

 Z = 0.8528 < 2.576

The calculated value Z = 0.8528 < 2.576 at 0.01 level of significance

Null hypothesis is Accepted at 0.01 level of significance.

There is no significance difference between the means

Step-by-step explanation:

Given data

size of the sample 'n' = 11

mean of the sample x⁻ =20.5

Mean of the Population μ = 18.7

Standard deviation of Population σ = 7

Test statistic

                  [tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

                  [tex]Z = \frac{20.5 -18.7}{\frac{7}{\sqrt{11} } }[/tex]

                  [tex]Z = \frac{1.8}{2.1105}[/tex]

                  Z = 0.8528

critical Value

[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01}{2} } = Z_{0.005} = 2.576[/tex]

The calculated value Z = 0.8528 < 2.576 at 0.01 level of significance

Null hypothesis is Accepted at 0.01 level of significance.

There is no significance difference between the means

Answer:Answer:

B. 18.7 ± 9.7

Step-by-step explanation:

Answer:

One mask=$4

One pack of glove=$2

Step-by-step explanation:

Let mask=m

Let glove=g

4m+g=18 (1)

4m+3g=22 (2)

From (1)

g=18-4m

Substitute g=18-4m into equation (2)

4m+3g=22

4m+3(18-4m)=22

4m+54-12m=22

4m-12m=22-54

-8m=-32

Divide both sides by -8

m=4

Substitute m=4 into equation (1)

4m+g=18

4(4)+g=18

16+g=18

g=18-16

g=2

One mask=$4

One pack of glove=$2

Answer:

Step-by-step explanation:

Answer:

18.84mm^2

Step-by-step explanation:

Surface area of a cylinder can be found with the following formula:

2πrh+2πr^2

r is radius

h is height

Plug our values in

2π1(2)+2π(1)^2

2π(2)+2π(1)

4π+2π

6π

6(3.14)

18.84

Answer:

A cup of water can hold a cup of water (or about 250 mL)

Step-by-step explanation:

anything between 1 and 4 cups should be an acceptable answer

If this helps, please consider giving me brainliest

Answer:

I'm gonna go with 250 ML

Step-by-step explanation:

One liter is a little more than 1 quart.

250 mL = 0.25 L