Problem solving visual pattern, please help me! Youd be a life saver

The observed proportion is 20/45 (since 20 out of 45 names had already dropped the course).

To find the test statistic value for the hypothesis test, we need to calculate the z-score.

Given that Dr. J claims 40% of his college algebra class will drop his course by midterm, we can calculate the expected proportion of students who would drop the course. Since he selected 45 names at random, the expected number of students who would have dropped the course can be calculated as follows:

Expected number of students who would have dropped the course = (40/100) * 45

Next, we calculate the standard deviation of the expected proportion:

Standard deviation = sqrt((40/100) * (60/100) / 45)

The test statistic value (z-score) is then calculated as:

Test statistic value = (Observed proportion - Expected proportion) / Standard deviation

Here, the observed proportion is 20/45 (since 20 out of 45 names had already dropped the course).

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Answer: Even = -4

Step-by-step explanation:

2-4 = -2

-2-2 = -4 which is even

Answer:

It's even.

Step-by-step explanation:

2-4-2=-4

PEMDAS

2-4=-2

-2-2=-4

The gateway arch in st. Louis, MO is approximately 630 ft tall, the same height of the Nickels would be in a stack is 98474.

Height of Gateway Arch in St. Louis, MO = 630ft tall

We are asked, how many nickels would be in a stack of the same

height when 1 nickel is 1.95 mm thick.

Convert height in ft to mm

1 ft = 304.8 mm

630ft = X

After Cross Multiply,

630ft × 304.8mm/1ft

= 192024 mm.

To find how many nickel would be in a stack of the same height

= Total thickness/ Thickness of 1 US dime

= 192024 mm/1.95mm

= 98473.8

≈98474 nickels

Therefore, the number of nickel that would be in a stack of the same height is 98474.

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Answer:

5 scarves

Step-by-step explanation:

8x5=40

Answer:

B. 16/25

Step-by-step explanation:

6

10

+

4

100

=  

6 × 10

10 × 10

+

4

100

=  

60

100

+

4

100

=  

60 + 4

100

=  

64

100

=  

64 ÷ 4

100 ÷ 4

=  

16

25

Answer:

\(\huge\boxed{\sf \frac{16}{25} }\)

Step-by-step explanation:

\(\displaystyle \frac{6}{10} +\frac{4}{100}\)

To equalize the denominator, we will have to multiply the fraction 6/10 by 10.

\(\displaystyle =\frac{6 \times 10}{10 \times 10} +\frac{4}{100} \\\\\ =\frac{60}{100} +\frac{4}{100}\)

Now, that the denominator is equal, we can add both the fractions.

\(\displaystyle= \frac{60+4}{100} \\\\=\frac{64}{100}\)

Divide both numerator and denominator by 2.

\(\displaystyle = \frac{64 \div 2}{100 \div 2} \\\\= \frac{32}{50}\)

Divide again.

\(\displaystyle= \frac{32 \div 2}{50 \div 2} \\\\= \frac{16}{25} \\\\\rule[225]{225}{2}\)

The length of the diagonal of the parallelogram is 10 cm using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

In the question, we observe that the diagonal of the parallelogram will form a right-angled triangle with the adjacent side of length 8cm and 6cm.

thus by Pythagoras rule;

the length of the diagonal = √(6² + 8²) cm

the length of the diagonal = √(36 + 64) cm

the length of the diagonal = √100 cm

the length of the diagonal = 10 cm

In conclusion, by proper application of Pythagoras rule we have derived the length of the diagonal of the parallelogram to be 10 cm.

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The cost of one computer is £600 and the cost of one printer is £800.

Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.

Let the cost of a computer be x and the cost of a printer be y.

Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)

4x + 5y = 6000 ---------------------- (2)

Solving equations (1) and (2) simultaneously:x = 600y = 800

Therefore, the cost of a computer is £600 and the cost of a printer is £800..

:Therefore, the cost of one computer is £600 and the cost of one printer is £800.

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Answer:

I cannot answer this question because it is not complete. Please use complete sentences and questions.

Answer:

4 months

Step-by-step explanation:

if she paid the 15 already subtract it from the 155. Once you that you get 140 and if you break that inton groups of 35 *division* than you get 4. As in 4 months

Answer:

35x + 15 + 155

35x = 155 - 15

It will take 4 months to pay off the debt.

B

C

E

Answer: 72.5

Step-by-step explanation:

120% = 120/100 = 1.2

1.2*x = 87

x = 87/1.2 = 72.5

Answer:

Yes, you showed your work.

Step-by-step explanation:

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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Answer:

Given :

The length of a rectangle is 4 cm more than its width

The area of the rectangle is 96 cm²

To Find :

Width of the rectangle.

Solution :

Let the length of the rectangle be x cm.

Let the breadth of the rectangle be y cm.

Case 1:

➣

➣  _____(1)

Case 2 :

We have the formula for area of the rectangle as follows :

Where,

l = length → x cm

b = breadth → y cm.

➣

➣

Substitute, x = 96/y in equation 1,

➣

➣

➣

➣

➣

Divide by minus sign,

➣

➣

➣

➣

➣

➣

➣

As per assumption, y = breadth of the rectangle.

•°• y = -12 is not acceptable.

Substitute, y = 8 in equation 1,

➣

➣

➣

➣

Step-by-step explanation:

The cost for 866 miles will be $53.31.

The car car averages 32 mpg and gas costs $1.97 per gallon.

Therefore,. the cost for 866 miles will be:

= 866/32 × $1.97

= 27.0625 × $1.97

= $53.31

The cost is $53.31.

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XYZ corporation can expect to have 1000 defective widgets out of the 100,000 widgets produced.

If 1% of the widgets produced by XYZ corporation are defective, then the expected number of defective widgets in a sample of 100,000 widgets can be calculated as follows:

Expected number of defective widgets = 1% x 100,000 = 0.01 x 100,000 = 1000

Therefore, XYZ corporation can expect to have 1000 defective widgets out of the 100,000 widgets produced. However, it is important to note that this is just an expected value, and the actual number of defective widgets may vary from this value due to random variation.

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The value of the function f(-3) in f(x) = -2x² + 3x - 6 is -33

from the question, we have the following parameters that can be used in our computation:

f(x) = -2x² + 3x - 6

To find the value of f(-3). we set x = -3

Using the above as a guide, we have the following equation

f(-3) = -2(-3)² + 3(-3) - 6

Evaluate the expression

f(-3) = -33

Hence, the solution is f(-3) = -33

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Answer:

30 ft

Step-by-step explanation:

6 x 5 = 30

you multiply 6 times 5 and you get 30

Step-by-step explanation:

Answer: 13

Step-by-step explanation:

Answer:

750 meters

Step-by-step explanation:

120 meters/4 seconds = 30 meters per second

30 meters per second * 25 seconds = 750 meters

(you could calculate 3 * 25 first to get 75 and then add the zero at the end. It's the faster way.)

Answer:

x = 750 m

Step-by-step explanation:

Write and solve a equation of ratios:  

  120 m          4 sec

-------------  =  -------------

       x              25 sec

Inverting this equation yields

      x             25 sec

-------------- = -------------

  120 m          4 sec

Cross-multiplication yields (4 sec)x = (120 m)(25 sec).  This yields:

      3000 m-sec

x = --------------------  = 750 meters

           4 sec

Note that the same result can be obtained by multiplying (120 m) by (25/4).

Answer:

f(x)= -2x+190

Step-by-step explanation:

In this problem, the lower limit of integral is -3 and the upper limit of integration is 3.

We can use the formula for the surface area of a solid of revolution generated by a curve revolving around a given axis. The formula is S = 2π ∫ a b y dx, where a and b are the lower and upper limits of integration, and y is the height of the curve at x. In this problem, the lower limit of integration is -3 and the upper limit of integration is 3. Substituting y = 1/16(e^8x + e^-8x) into the equation gives S = 2π ∫ -3 3 (1/16(e^8x+e^-8x)) dx. Integral this expression gives S = 10512π.

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In the case of the electronic chess game, with a useful life that follows an exponential distribution with a mean of 30 months, we need to determine the length of service time after which the percentage of failed units will approximately equal 50 percent. The options provided are 9 months, 16 months, 21 months, and 25 months.

For the major television manufacturer, the service life of its 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. We are asked to calculate the probability of service lives of at least five years.

1. Electronic Chess Game:

The exponential distribution is characterized by a constant hazard rate, which implies that the percentage of failed units follows an exponential decay. The mean of 30 months indicates that after 30 months, approximately 63.2% of the units will have failed. To find the length of service time when the percentage of failed units reaches 50%, we can use the formula P(X > x) = e^(-λx), where λ is the failure rate. Setting this probability to 50%, we solve for x: e^(-λx) = 0.5. Since the mean (30 months) is equal to 1/λ, we can substitute it into the equation: e^(-x/30) = 0.5. Solving for x, we find x ≈ 21 months. Therefore, the length of service time after which the percentage of failed units will approximately equal 50 percent is 21 months.

2. LED Televisions:

The service life of 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. To find the probability of service lives of at least five years, we need to calculate the area under the normal curve to the right of five years (60 months). We can standardize the value using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. Substituting the values, we have z = (60 - 72) / 0.5 = -24. Plugging this value into a standard normal distribution table or using a calculator, we find that the probability of a service life of at least five years is approximately 1.0000 (or 100% with four digits after the decimal point).

Therefore, the probability of service lives of at least five years for 50-inch LED televisions is 1.0000 (or 100%).

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Let be a 3×3 diagonalizable matrix whose eigenvalues are 1=1, 2=3, and 3=−4. If 1=[100],2=[110],3=[011] are eigenvectors of corresponding to 1, 2, and 3, respectively, then factor into a product −1 with diagonal, and use this factorization to find 5. We have: A^5 = [-1 -1023 0; 0 -1 0; 0 0 1024]

We have three eigenvectors for the given matrix as:

v1 = [1 0 0]T

v2 = [1 1 0]T

v3 = [0 1 1]T

Since the matrix is diagonalizable, we can form a diagonal matrix D and invertible matrix P such that A = PDP^-1, where the columns of P are the eigenvectors of A.

Thus, we have:

P = [v1 v2 v3] = [1 1 0; 0 1 1; 0 0 1]

D = diag(1, 3, -4)

To factor -1 with diagonal, we need to find a diagonal matrix D1 such that D = -D1^2. Since the diagonal entries of D are all nonzero, we can choose D1 = diag(sqrt(-1), sqrt(-3), sqrt(4)) = diag(i, sqrt(3)i, 2i). Then, we have:

-D1^2 = [-1 0 0; 0 -3 0; 0 0 -4]

Finally, we can use the factorization A = PDP^-1 = -PD1^2P^-1 to find A^5 as:

A^5 = (-PD1^2P^-1)^5 = -PD1^2P^-1PD1^2P^-1PD1^2P^-1PD1^2P^-1PD1^2P^-1

= -PD1^10P^-1 = -Pdiag(i^10, (sqrt(3)i)^10, (2i)^10)P^-1

= -Pdiag(1, -1, 1024)P^-1

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A logical implication is considered true if the antecedent (p or q or r) implies the consequent (q or p or r), meaning that if the antecedent is true, then the consequent must also be true.

The six possible logical implications between pairs of propositions p, q, and r are:

A logical implication is considered true if the antecedent (p or q or r) implies the consequent (q or p or r), meaning that if the antecedent is true, then the consequent must also be true. However, the converse of the implication may not be true, meaning that if the consequent is true, the antecedent may not be true.

Whether or not any of p, q, and r are logically equivalent to another depends on the specific logical relationships between them. Logical equivalence occurs when two propositions have the same truth value, meaning that they are both true or both false, regardless of the truth values of the other propositions.

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When we replace σ with the sample standard deviation (s), we introduce a new source of variability and the sampling distribution becomes is a. t-distribution.

This is because the sample standard deviation is an estimate of the population standard deviation, and therefore introduces a new source of variability into the sampling distribution.

The t-distribution is used to account for this additional variability and is used when the sample size is small or the population standard deviation is unknown. The t-distribution is similar to the normal distribution but has fatter tails to account for the additional variability.

Hence Option A is correct.

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