if a customer in a department Store once an $45 item and uses 35% off coupon at checkout a) how much is their discount? b) how much will they pay for the item after the discount?

WY = a = 4

ZY = b = 3

As WYZ is forming a right angle triangle, therefore, we can use pythagorean theorem to find the value of c

a2+b2=c2 (4)2+(3)2=C2 16+9=C2 C2=25

Taking square root on both sides

√c2= √25 c=5

The value of c is 5 units.

The value of c is 5 units

The complete question is an illustration of a right-triangle, where the equation to calculate the value of c is:

c^2 = a^2 + b^2

The equation becomes

c^2 = 3^2 + 4^2

Evaluate the exponents

c^2 = 9 + 16

Evaluate the sum

c^2 = 25

Take the square root of both sides

c =5

Hence, the value of c is 5 units

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Answer:

There are 8568 ways to combine the shoes.

Step-by-step explanation:

In this case Connie wants to create smaller subsets from a larger group of things, therefore we must do a combination, which can be applied by using the following formula:

[tex]C_{(n,r)} = \frac{n!}{r!*(n - r)!}[/tex]

In our case n = 18, which is the total number of shoes and r = 5, which is the subset she wants to create.

[tex]C_{(18,5)} = \frac{18!}{5!*(18 - 5)!} = \frac{18!}{5!*13!} = \frac{18*17*16*15*14*13!}{5!*13!}\\C_{(18,5)} = \frac{18*17*16*15*14}{5*4*3*2} = 8568[/tex]

There are 8568 ways to combine the shoes.

The number of ways can she choose which shoes to take is 8,568.

Given that,

Based on the above information, the calculation is as follows:

[tex]= \frac{n!}{k!(n-k)!} \\\\= \frac{18!}{5!13!} \\\\= \frac{18\times 17\times 16\times\15\times \times 14}{5\times 4\times 3\times2\times 1}[/tex]

= 8,568

Therefore we can conclude that The number of ways can she choose which shoes to take is 8,568.

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Answer:

(n- 2/3)²

Step-by-step explanation:

We have:

It can be put as:

Here we consider n = a and -2/3 = b, then

Now we add 4/9 to a given binomial to make it perfect square:

So, added 4/9 and got a perfect square (n- 2/3)²

Answer:

Hey there!

The product of these two fractions would equal 15.

Hope this helps :)

Answer:

Hi! The answer to your question is 7 11/14 or rounded will be 15

Step-by-step explanation:

So first let’s take the whole numbers which is 4 and 3 if we add them up we will get 7.

Now we do LCD (least common denominator)

4/14+7/14=11/14

So the answer is 7 11/14 or 15

(In mixed number the answer is 7 11/14 and in whole the answer is 15)

Hope this helps! :)

Answer:

Step-by-step explanation:

The question is incorrect. Here is the correct question.

Verify the identity sin²t / cos t = sect - cost

Given the identity sin²t / cos t = sect - cost, to verify means we are to check if both sides are equivalent. To do that we are going to start the proof from any sides of the equation and solve until we get to the function at the opposite side.

Starting with the left hand equation (LHS)

sin²t / cos t ...1

From trigonometry identity,  sin²t+ cos²t = 1

sin²t = 1- cos²t ... 2

Substituting eqn 2 into 1 we have:

= 1- cos²t/cost

= 1/cost -  cos²t/cost

= 1/cost - cost

Also from trig. identity, 1/cost = sect

On replacing this identity in the resulting equation we will have;

= sect - cost (which is equivalent to the RHS)

This shows that sin²t / cos t = sect - cost (Identity Proved!)

Answer:

Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.

Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.

Step-by-step explanation:

Question:

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

30

∑  (−3i+5)

i=1

Answer:

The first three terms are : 2, -1 and -4

The last term is: -85

The sum of the sequence is: -1245

Step-by-step explanation:

Given;

==================================

30

∑  (−3i+5)                    -------------------(i)

i=1

==================================

Where the ith term aₙ is given by;

[tex]a_{i}[/tex] = [tex]-3i + 5[/tex]         -------------------(ii)

(a) Therefore, to get the first three terms ([tex]a_1, a_2, a_3[/tex]), we substitute i=1,2 and 3 into equation (ii) as follows;

[tex]a_{1}[/tex] = [tex]-3(1) + 5[/tex] = 2

[tex]a_2 = -3(2) + 5 = -1[/tex]

[tex]a_3 = -3(3) + 5[/tex][tex]= -4[/tex]

Since the sum expression in equation (i) goes from i=1 to 30, then the last term of the sequence is when i = 30. This is given by;

[tex]a_{30} = -3(30) + 5 = -85[/tex]

(b) The sum [tex]s_n[/tex] of an arithmetic sequence is given by;

[tex]s_n = \frac{n}{2}[a_1 + a_n][/tex]   -----------------(iii)

Where;

n = number of terms in the sequence = 30

[tex]a_1[/tex] = first term = 2

[tex]a_n[/tex] = last term = -85

Substitute the corresponding values of n, [tex]a_1[/tex] and [tex]a_n[/tex] into equation (iii) as follows;

[tex]s_n = \frac{30}{2}[2 + (-85)][/tex]

[tex]s_n[/tex] = 15[-83]

[tex]s_n[/tex] = -1245

Answer:

The reciprocal is cosecant that is option B

The reciprocal function of sine is cosecant.

It is the opposite of a function meaning by if a function is f(x) then the reciprocal function will be 1/f(x).

They are real function which relates with the angle of a right angle triangle to ratios of two sides.

We have to find the reciprocal function of sine.

f=sine

Reciprocal of f=1/sine

=cosecant

Hence the reciprocal of sine is cosecant.

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Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

In the absence of answer choices, let's find the expression for the volume.

Given: Volume = length×width×height

V = lwh

length =(2a + 11)

width =(5a – 12)

height= (a + 6)

V =  (2a + 11)(5a – 12) (a + 6)

Expand the first two brackets using distributive property

V = (10a² -24a +55a - 132)(a + 6)

Collect like terms

V = (10a² + 31a -132)(a + 6)

Expand the two brackets using distributive property

V = 10a³ + 31a² - 132a + 60a² + 186a - 792

Collect like terms

V = 10a³ + 91a² + 54a - 792

The expression that represents the volume of the box = 10a³ + 91a² + 54a - 792

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

Answer:

angle of bc= 180-168= 12°

length of bc= 12/360 × π × diameter

= 12/360 × 22/7 × 21

= 12/360 × 66

= 2,20 cm (b)

Answer:

4.167(10²)

Step-by-step explanation:

Step 1: Put number into proper decimal form

416.7 = 4.167

Step 2: Figure out exponent

Since we are moving the decimal places 2 places to the right, our exponent is 2

Answer:

4.167 × 10^2

Step-by-step explanation:

= 4.167 × 10^2

(scientific notation)

= 4.167e2

(scientific e notation)

= 416.7 × 10^0

(engineering notation)

(one)

= 416.7

(real number)

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▹ Answer

20 - 12 or 8 (depending on what you need to find)

▹ Step-by-Step Explanation

4(5 - 3)

Distribute 4 * 5 and 4 * -3

This will give 20 - 12

If you are looking for the final answer, it would be 8.

Hope this helps!

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Answer:

the 3 one is the correct answer

Step-by-step explanation:

Answer: RS and SU

Step-by-step explanation:

Skew lines are lines that don't have points connected and are not parrelel to each other.

The only lines that are both not parrelel  and have unconnected points are the lines RS and SU

Answer:

Step-by-step explanation:

Hello!

Full text:

Listed below are amounts of court income and salaries paid to the town justice. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P value using  α  = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines?

Court Income: 65.0, 402.0, 1567.0, 1132.0, 273.0, 251.0, 112.0, 156.0, 34.0

Justice Salary: 31, 46, 91, 56, 47, 60, 26, 27, 18

a. What are the null and alternative hypotheses?

To test if there is a linear correlation between the court income and the justice salary, you have to use the following hypotheses:

H₀: ρ = 0

H₁: ρ ≠ 0

b. Construct a scatterplot.  See attachment.

c. The linear correlation coefficient r is: _____.

[tex]r= \frac{sumX_1X_2-\frac{(sumX_1)(sumX_2)}{n} }{\sqrt{[sumX_1^2-\frac{(sumX_1)^2}{n} ][sumX_2^2-\frac{(sumX_2)^2}{n} ]} }[/tex]

n= 9; ∑X₁= 3992; ∑X₁²= 4078308; ∑X₂= 409; ∑X₂²= 2232; ∑X₁X₂= 262123

r= 0.86

d. The P value is: _____.

This test is two-tailed and so is its p-value. I've calculated it using a statistics software:

p-value: 0.0027

e. Based on the results, does it appear that justices might profit by levying larger fines?

Using the p-value approach, the decision rule is:

If the p-value ≤ α, reject the null hypothesis.

If the p-value > α, do not reject the null hypothesis.

The calculated p-value is less than the significance level, then the decision is to reject the null hypothesis.

At a 5% significance level you can conclude that there is a linear correlation between the "court income" and the "Justice salary"

I hope this helps!

Answer:

A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Step-by-step explanation:

We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.

Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                          P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of chocolate chips = [tex]\frac{\sum X}{n}[/tex] = 1238.2

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = 94.3

            n = sample of car drivers = 16

            [tex]\mu[/tex] = population mean number of chips in a bag

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.131 < [tex]t_1_5[/tex] < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.131) = 0.95

P( [tex]-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.131 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.131 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                   = [ [tex]1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] , [tex]1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }[/tex] ]

                                   = [1187.96, 1288.44]

Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Answer:

x = -3/2

Step-by-step explanation:

0 = 4x² + 12x + 9

4x² + 12x + 9 = 0

(2x + 3)² = 0

2x + 3 = 0

2x = -3

x = -3/2

Hope this helps! :)

Answer:

1/5

Step-by-step explanation:

Your equation is written in the form y=mx+b, where m is the slope and b is the y-intercept.

m=1/5, so the slope is 1/5

Answer:

57

Step-by-step explanation:

The range of a data set is

Largest data value - Smallest data value

62 - 5

= 57

The range of the data set is 57 pounds.

Answer:

[tex]\boxed{\red{57}}[/tex]

Step-by-step explanation:

[tex]\blue {range \: \: of \: \: a \: \: data \: \: set \: \: means}[/tex]

you have to subtract the smallest value from the largest value in the data set.

[tex]\boxed{\green{largest \: \: value - smallest \: \: value}} \\ \boxed{\green{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 62 - 5}} \\ \: \: \: \: \: \: \: \: \boxed{\pink{ =57}}[/tex]

Answer:

Option (4)

Step-by-step explanation:

From the graph attached,

A dotted line passes through two points (3, 1) and (-3, -3)

Let the equation of the given line is,

y = mx + b

where 'm' = slope of the line

b = y-intercept

Slope of a line passing through [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

For the given points,

m = [tex]\frac{1+3}{3+3}[/tex]

m = [tex]\frac{2}{3}[/tex]

y-intercept 'b' = -1

Therefore, equation of the given line will be,

[tex]y=\frac{2}{3}x-1[/tex]

Since graphed line is a dotted line so it's representing an inequality(having < or > sign)

And the shaded part is below the dotted line,

Inequality will be,

y < [tex]\frac{2}{3}x-1[/tex]

Therefore, Option (4) will be the answer.

Answer:

D

Step-by-step explanation:

Correct:)

Answer:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

Step-by-step explanation:

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.

The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.

The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.

The difference between sample means is Md=-9.4.

[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/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{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]

The critical t-value for a 99% confidence interval is t=2.678.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.

[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]

The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:

[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

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▹ Answer

(3x + 4) * (4x - 5)

▹ Step-by-Step Explanation

12x² + x - 20

Rewrite

12x² + 16x - 15x - 20

Factor out

4x(3x + 4) - 15x - 20

4x(3x + 4) - 5(3x + 4)

Factor

(3x + 4) * (4x - 5)

Hope this helps!

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Answer:

Step-by-step explanation:

Given the parametric equation points x = 5t, y = 6t − 1  when t = 2

From x = 5t, t = x/5. Substituting t = x/5 into the second equation y = 6t − 1 we will have;

y = 6(x/5) - 1

y = 6/5 x - 1

The derivative of y with respect to x i.e dy/dx = 6/5 - 0. (Note that differential of any constant is zero).

dy/dx = 6/5

d²y/dx² = d/dx(dy/dx)

d²y/dx² = d/dx(6/5)

Since 6/5 is a constant, the derivative of 6/5 with respect to x will be zero.

d²y/dx² = 0.

Since the first derivative and the second derivative are both constant then, the slope m at the given parameter will be 6/5.

m = dy/dx = 6/5

The concavity is the value of the second derivative at the given value of the parameter.

The concavity d²y/dx² = 0.

Answer:

c. Not significant at .055

Step-by-step explanation:

When a pair of dice is rolled, we have 6²=36 possible outcomes. Only 2 of these outcomes have a total score of 11:

Then, we can calculate the probability of getting 11 as the quotient between the successs outcomes and the total outcomes.

Then, the probability of getting 11 is:

[tex]P=\dfrac{X}{N}=\dfrac{2}{36}=0.055[/tex]

This probability is not equal or less than 0.05, so it is not significant at 0.055.

Answer:

The calculated value |Z|  = 1.325  < 1.881 at 0.03 level of significance

Null hypothesis is accepted

Alternative hypothesis is rejected

A researcher wants to study the average miles run per day for marathon runners is 25

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 36

Given mean of the sample x⁻ = 22.8 miles

Given mean of the Population 'μ' = 25

Given standard deviation of the Population 'σ' = 10

Null hypothesis:-H₀: μ = 25

Alternative Hypothesis:H₁:μ ≠ 25

Level of significance  = 3 % or 97%

The critical value  Z₀.₉₇ = 1.881

Step(ii):-

Test statistic

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

          [tex]Z = \frac{22.8 - 25}{\frac{10}{\sqrt{36} } }[/tex]

          Z = -1.325

       |Z| = |-1.325| = 1.325

The calculated value |Z|  = 1.325  < 1.881 at 0.03 level of significance

Null hypothesis is accepted

Alternative hypothesis is rejected

conclusion:-

A researcher wants to study the average miles run per day for marathon runners is 25

Answer:

B. (x + 5)(x + 1)

Step-by-step explanation:

Since our roots are x = -5 and x = -1, we have:

x + 5 = 0

x + 1 = 0

Put that into quadratic binomials:

(x + 5)(x + 1)

Answer:

more info is needed

Step-by-step explanation:

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.36

For the alternative hypothesis,

P < 0.36

a) This is a left tailed test due to the inequality sign in the alternative hypothesis.

b)Considering the population proportion, probability of success, p = 0.36

q = probability of failure = 1 - p

q = 1 - 0.36 = 0.64

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 545

n = number of samples = 1673

P = 545/1673 = 0.33

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.33 - 0.36)/√(0.36 × 0.64)/1673 = - 2.56

c)We would determine the P-value from the normal distribution table. From the normal distribution table, the area below the test z score in the left tail 0.00523

P value = 0.00523

d) Since alpha, 0.05 > than the p value, 0.00523, then we would reject the null hypothesis.

e) The null hypothesis is the claim that 36​% of adults have heard of the new electronic reader.

Answer:

56, see step-by-step.

Step-by-step explanation:

1. AB is parallel to CD.                                1. Given

  BC is parallel to DE.

  m<BAC=64 and m<CBA =56

2. m<BAC + m<CBA + m<BCA =180       2. The angles in a triangle add up to       180

3. 64+ 56+ m<BCA=180 3. Substitution property of equality.

4. 120 + m<BCA=180 4. Addition property of equality.

5. m<BCA=60 5. Subtraction property of equality.

6. BC is a transversal that cuts through parallel lines AB and CD.

6. Def. of transversal.

7. m<CBA = m<BCD 7. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

8. m<BCA+m>BCD+m<DCE= 180. 8. Angle addition postulate

9. 60+56+m<DCE=180. 9.substitution.

10. 116 + m<DCE =180 10. Addition property of equality.

11. M<DCE =64 11. Subtraction property of equality.

12. DC is a transversal that cuts through parallel line BC and DE.

12. Def of transversal.

13. m<EDC= m<BCD 13. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

14. m<EDC= 60. 14. Substitution property of equality.

15. m<EDC+m<DCE+m<Dec=180. 15. Angle addition postulate

16. 56+64+m<dec = 180.16 Substitution property of equality.

17. 120+ m<dec = 180. Addition property of equality.

18. m<dec = 60 18. Subtraction property of equality.

Answer:

273 Touchdowns

Step-by-step explanation:

You divide the amount of confetti cannons set off by the amount of confetti cannons set off every time there is a touchdown scored. So in this case 181818 ÷ 666