In quadrilateral ABCD, AD || BC
What must the length of segment AD be for the
quadrilateral to be a parallelogram?
B
8 units
O 16 units
3x + 7
5x - 9
31 units
62 units
С
D

Answer:

Step-by-step explanation:

A, B and C must be real numbers, and A and B are not both zero (which would cause division by zero in the calculation of the slope).

Answer:

a) Alternative hypothesis: the use of the coupons is isgnificantly higher than 10%.

Null hypothesis: the use of the coupons is not significantly higher than 10%.

The null and alternative hypothesis can be written as:

[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]

b) Point estimate p=0.13

c) At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.

Eagle should not go national with the  promotion as there is no evidence it has been succesful.

Step-by-step explanation:

The question is incomplete.

The sample data shows that x=13 out of n=100 use the coupons.

This is a hypothesis test for a proportion.

The claim is that the proportion of coupons use is significantly higher than 10%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]

The significance level is 0.05.

The sample has a size n=100.

The point estimate for the population proportion is the sample proportion and has a value of p=0.13.

[tex]p=X/n=13/100=0.13[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{100}}\\\\\\ \sigma_p=\sqrt{0.0009}=0.03[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.13-0.1-0.5/100}{0.03}=\dfrac{0.025}{0.03}=0.833[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>0.833)=0.202[/tex]

As the P-value (0.202) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the proportion of coupons use is significantly higher than 10%.

Answer:

Presumably the first graph solely based on its shape.

Graph A is showing the exponential function. Then the correct option is A.

The mathematical expression f(x)= [tex]e^x[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data. In graph A we can see that the values are varying exponentially from the second quadrant to the first quadrant.

Hence, the correct option is A.

To know more about exponential functions follow

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Answer:

12/25

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(x)=-x+4

f(-2)=-(-2)+4

f(-2)=+2+4

f(-2)=6

Answer:

6

Step-by-step explanation:

-(-2)+4=___

+(+2)+4=6

Answer:

C. -2

Step-by-step explanation:

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

Simply use 2 xy values and plug them into the formula:

m = (-4 - 0)/(5 - 3)

m = -4/2

m = -2

Answer:

-2

Step-by-step explanation:

Since we have two points we can use the slope formula

m = (y2-y1)/(x2-x1)

  = (10-6)/(-2-0)

  =4/-2

  -2

Answer:

The answer is option D.

3u + 1 + 7y

All the terms here are different and cannot be combined

Hope this helps you

Answer:

6

Step-by-step explanation:

=> -x+4

Given that x = -2

=> -(-2)+4

=> 2+4

=> 6

Answer:

6

Step-by-step explanation:

You just have to input -2 into the statement and then solve

= -(-2) + 4

= 2+ 4

= 6

Answer:

180 fb*lb

45 ft*lb

Step-by-step explanation:

We have that the work is equal to:

W = F * d

but when the force is constant and in this case, it is changing.

 therefore it would be:

[tex]W = \int\limits^b_ a {F(x)} \, dx[/tex]

Where a = 0 and b = 30.

F (x) = 0.4 * x

Therefore, we replace and we would be left with:

[tex]W = \int\limits^b_a {0.4*x} \, dx[/tex]

We integrate and we have:

W = 0.4 / 2 * x ^ 2

W = 0.2 * (x ^ 2) from 0 to 30, we replace:

W = 0.2 * (30 ^ 2) - 0.2 * (0 ^ 2)

W = 180 ft * lb

Now in the second part it is the same, but the integral would be from 0 to 15.

we replace:

W = 0.2 * (15 ^ 2) - 0.2 * (0 ^ 2)

W = 45 ft * lb

Following are the calculation to the given value:

Given:

[tex]length= 30 \ ft\\\\mass= 0.4 \ \frac{lb}{ft}\\\\edge= 80 \ ft \\\\[/tex]

To find:

work=?

Solution:

Using formula:

[tex]\to W=fd[/tex]

[tex]\to W=\int^{30}_{0} 0.4 \ x\ dx\\\\[/tex]

[tex]= [0.4 \ \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{4}{10} \times \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{2}{10} \times x^2]^{30}_{0} \\\\= [\frac{1}{5} \times x^2]^{30}_{0} \\\\= [\frac{x^2}{5}]^{30}_{0} \\\\= [\frac{30^2}{5}- 0] \\\\= [\frac{900}{5}] \\\\=180[/tex]

Therefore, the final answer is "[tex]180\ \frac{ lb}{ft}[/tex]".

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Answer:

The  UCL  is  [tex]UCL = 0.054[/tex]

The LCL  is  [tex]LCL \approx 0[/tex]

Step-by-step explanation:

From the question we are told that  

     The quantity of each sample is  n =  30

     The  average of defective products is  [tex]p = 0.025[/tex]

Now  the upper control limit [UCL] is  mathematically represented as

      [tex]UCL = p + 3 \sqrt{\frac{p(1-p)}{n} }[/tex]

substituting values  

      [tex]UCL = 0.025 + 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]

      [tex]UCL = 0.054[/tex]

The  upper control limit (LCL) is mathematically represented as

       [tex]LCL = p - 3 \sqrt{\frac{p(1-p)}{n} }[/tex]

substituting values  

      [tex]LCL = 0.025 - 3 \sqrt{\frac{0.025 (1-0.025)}{30} }[/tex]

       [tex]LCL = -0.004[/tex]

        [tex]LCL \approx 0[/tex]

Answer:

Step-by-step explanation:

The diagonal of the parallelogram ABCD divides it into 2 equal triangles. Considering triangle ABC, it means that the area of the parallelogram would be

2 × area of triangle ABC

Writing the vertices of triangle ABC,

A(−1,3,3), B(0,5,7), C(1,2,6)

We would determine the length of each side of the triangle.

AB = √(0 - - 1)² + (5 - 3)² + (7 - 3)^2

AB = √(1 + 4 + 16) = √21

BC = √(1 - 0)² + (2 - 5)² + (6 - 7)²

BC = √(1 + 9 + 1) = √11

AC = √(1 - - 1)² + (2 - 3)² + (6 - 3)²)

AC = √(4 + 1 + 9) = √14

We would apply the heron's formula for determining the area of a triangle

Area = √s(s - a)(s - b)(s - c)

Where

s = (a + b + c)/2

a = AB, b = BC, c = AC

s = (√21 + √11 + √14)/2 = 5.82

s - a = 5.82 - √21 = 1.24

s - b = 5.82 - √11 = 2.5

s - c = 5.82 - √14 = 2.08

Area = √(5.82 × 1.24 × 2.5 × 2.08) = 6.126

Therefore, area of parallelogram ABCD is

6.126 × 2 = 12.252

Answer:

6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement

Step-by-step explanation:

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^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Poisson distribution with a mean of 1 crack per 100 ft.

So [tex]\mu = \frac{ft}{100}[/tex], in which ft is the length of the pavement.

What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement

500ft, so [tex]\mu = \frac{500}{100} = 5[/tex]

This is P(X = 8).

[tex]P(X = 8) = \frac{e^{-5}*5^{8}}{(8)!} = 0.0653[/tex]

6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement

Answer:

The answer is

Step-by-step explanation:

f(x) = 2x² + 1

g(x) = 3x - 5

To find f - g(x) subtract g(x) from f(x)

That's

f-g(x) = 2x² + 1 - (3x - 5)

= 2x² + 1 - 3x + 5

= 2x² - 3x + 6

Hope this helps you

Answer:

This question should be worth atleast 20 points

Step-by-step explanation:

a. For the vertex, input the funtion into the calculator, and see where the turning piont is, that is the vertex.

b. Solve using this vormula.

x= (-b ±[tex]\sqrt{b^2 - 4ac}[/tex])/2a

you will get two asnwrs, both are correct.

Answer:

There will be no transaction

Step-by-step explanation:

Given:

Displayed ask price = $20.05 for 100 shares

Displayed bid price = $20 for 150 shares

Explain:

If a limit order to buy = 50 shares for $20.02

Computation:

Displayed bid will be not accepted because, displayed bid price is for 150 shares not 100 shares

Limited order will be also not accepted.

So, there will be no transaction.

Answer:

C. -3/2

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes.

We know that line m is perpendicular to line l.

Line l has a slope of 2/3. To find the slope of line m, find the negative reciprocal of 2/3.

Negative: switch the sign

2/3 --> -2/3

Reciprocal: switch the numerator (top number) and denominator (bottom number)

-2/3 --> -3/2

Line m has a slope of -3/2 and C is correct.

Answer:

C

Step-by-step explanation:

perpendicular lines have negative reciprocal slope

Answer:

So then our significance level is [tex]\alpha=0.05[/tex] and we need to remember these two conditions:

1) If the p value [tex]p_v <\alpha[/tex] we have enough evidence to reject the null hypothesis at the significance level given

2) If the p value [tex]p_v \geq \alpha[/tex] we have enough evidence to FAIL reject the null hypothesis at the significance level given

And baed on the options we see that the only possibility would be:

d. 0.015

Step-by-step explanation:

We want to know for which value we would REJECT the null hypothesis.

So then our significance level is [tex]\alpha=0.05[/tex] and we need to remember these two conditions:

1) If the p value [tex]p_v <\alpha[/tex] we have enough evidence to reject the null hypothesis at the significance level given

2) If the p value [tex]p_v \geq \alpha[/tex] we have enough evidence to FAIL reject the null hypothesis at the significance level given

And baed on the options we see that the only possibility would be:

d. 0.015

Answer:

C. c = (xv - x) / (v - 1).

Step-by-step explanation:

v = (x + c) / (x - c)

(x - c) * v = x + c

vx - vc = x + c

-vc - c = x - vx

vc + c = -x + vx

c(v + 1) = -x + vx

c = (-x + vx) / (v + 1)

c = (-x + xv) / (v + 1)

c = (xv - x) / (v + 1)

So, the answer should be C. c = (xv - x) / (v + 1).

Hope this helps!

Answer:

Length of the arc LM = 15.7 cm

Step-by-step explanation:

To determine the length of the arc LM we have to find the circumference of the the big circle then divide by the ratio of the angle or go straight to use the radians as the angle and look for the length.

Radius= 30cm

π= 3.142

Value of the angle is in radians

360° = 2π

π = 180

π/6 = 180/6

π/6= 30

Value of the angle is 30°

Length of the arc = 2πr * 30/360

Length of the arc = 2πr/12

Length of the arc = πr/6

Length of the arc = 30π/6

Length of the arc =5π

Length of the arc = 5*3.142

Length of the arc = 15.71

Approximately Length of the arc

= 15.7cm

Answer:

B. 15.7cm

Step-by-step explanation:

Answer:

Five

Step-by-step explanation:

Pivot columns are said to be columns where pivot exist and a pivot exist in the first nonzero entry of each row in a matrix that is in a shape resulting from a Gaussian elimination.

Suppose A = 5 × 7 matrix

So; if A columns span set of real numbers R⁵

The number of pivot columns that A must have must be present in each row. In a  5 × 7 matrix ; we have 5 rows and 7 columns . So , since A must be present in each row, then :

The matrix must have five pivot columns and we can infer that about  the statements that "A has a pivot position in every row"  and "the columns of A spans R⁵" are logically equivalent.

Answer:

Option I and II

Step-by-step explanation:

I. Assuming this represents a random sample from the population, the sample mean is an unbiased estimator of the population mean.

II. Because they're robust, t procedures are justified in this case.

The t procedures are utilized because they are used as a hypothesis testing tool, which allows for testing of an hypothesis applicable to a population where in this case we are testing the null hypothesis about the population mean.

Answer:

The probability that the weight of a randomly selected steer is between 920 and 1730 lbs

P(920≤ x≤1730) = 0.7078

Step-by-step explanation:

Step(i):-

Given mean of the Population = 1100 lbs

Standard deviation of the Population = 300 lbs

Let 'X' be the random variable in Normal distribution

Let x₁ = 920

[tex]Z = \frac{x-mean}{S.D} = \frac{920-1100}{300} = - 0.6[/tex]

Let x₂ = 1730

[tex]Z = \frac{x-mean}{S.D} = \frac{1730-1100}{300} = 2.1[/tex]

Step(ii)

The probability that the weight of a randomly selected steer is between 920 and 1730 lbs

P(x₁≤ x≤x₂) = P(Z₁≤ Z≤ Z₂)

                  = P(-0.6 ≤Z≤2.1)

                  = P(Z≤2.1) - P(Z≤-0.6)

                 = 0.5 + A(2.1) - (0.5 - A(-0.6)

                 =  A(2.1) +A(0.6)               (∵A(-0.6) = A(0.6)

                 =  0.4821 + 0.2257

                 = 0.7078

Conclusion:-

The probability that the weight of a randomly selected steer is between 920 and 1730 lbs

            P(920≤ x≤1730) = 0.7078

Answer:

0.7975

Step-by-step explanation:

Answer:

410 bagels

Step-by-step explanation:

If the weights of the moving averages are 0.6, 0.3, 0.1. We will determine the forecast for week 8 using week seven's sales with a 0.6 weight, week six's sales with a 0.3 weight, and week five's sales with a 0.1 weight:

[tex]S_8=0.6S_7+0.3S_6+0.1S_5\\S_8=0.6*400+0.3*430+0.1*410\\S_8=410\ bagels[/tex]

The forecast for week 8 is 410 bagels.

Answer:(x+1)(x+2)(x-3)

Because..

Answer:

Step-by-step explanation:

We khow that the volume of a prism the product of the base and the height

We have a hole inside it so we must khow what is the geometrical form of this whole to calculate its volum then substract from the total volume

Sample Answer:

I found the volume of the large rectangular prism. Then I found the volume of the small rectangular prism. I subtracted the volume of the smaller prism from the volume of the larger prism.

Answer:

(A)4 + 4 + 4 = 12

Step-by-step explanation:

Each of Nika's cake needed 17/4 cups of flour. Now, we know that:

[tex]\dfrac{17}{4}=4.25 \approx 4[/tex]

Therefore, for three loaves of bread, the best estimate of the number of cups of flour Nika used is:

4 + 4 + 4 = 12

The correct option is A.

Answer:

The correct answer is A.)4 + 4 + 4 = 12

Answer:

11.3 cm

Step-by-step explanation:

(see attached for reference)

using the Pythagorean theorem

hypotenuse ² = length ² + length ²

16² = L² + L²

16² = 2L²   (express 2 = (√2)²

16² = (√2)²L²  

16² = (√2L)²  

16 = √2L

L = 16 /√2

L = 11.3 cm

11.3

use Pythagoras theorem give each side is "a"

a^2+a^2=16^2

2*a^2=256

a^2=256/2=128

a=sqrt(128)=11.3 sqrt=square root

Answer:

Required probability is 0.9748

Step-by-step explanation:

given data

mean [tex]\mu[/tex] = 117.7-cm

standard deviation [tex]\sigma[/tex] = 2.2-cm

sample size n = 29

solution

we consider here random variable which represents here length of rod= x

so get here first z that is express as

[tex]Z = \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]    

put here value with x value 118.5-cm

[tex]Z = \dfrac{118.5-117.7}{\dfrac{2.2}{\sqrt{29}}}[/tex]

Z = 1.9582

p value is 0.9748

so required probability is 0.9748