If a box has a length of 12 inches, a width of 10 inches and a height of 6 inches, what is the surface area?

Answer:

a)x2+5x+6

x2+(3+2)x+6

x2+3x+2x+6

x(x+3)+2(x+3)

(x+3)(x+2)

b)z2+8z+12

z2+(6+2)z+12

z2+6z+2z+12

z(z+6)+2(z+6)

(z+6)(z+2)

A circular utility tunnel 8 feet in diameter has a 6-foot-wide walkway across its bottom. The radius of the circular utility tunnel is 4 feet and the diameter is 8 feet. The walkway is 6 feet wide which means that the diameter of the walkway is 6 feet.

So, the radius of the walkway is 3 feet. The worker is 6 feet 2 inches tall which is 74 inches. The worker could only walk down the center of the walkway without ducking if his height plus the distance from the center of the walkway to the top of the utility tunnel is less than the radius of the walkway. This can be calculated as follows:

The radius of the walkway = 3 feet distance from the center of the walkway to the top of the utility tunnel

= (8 ft / 2) - 6 ft

= 1 ft

The total distance from the center of the walkway to the top of the utility tunnel = 3 ft + 1 ft

                                                                                                                                     = 4 ft

The worker's height = 6 feet 2 inches = 74 inches

Therefore,

the worker's height + distance from the center to the top = 74 inches + 4 feet (converted to inches)

                                                                                               = 74 inches + 48 inches

                                                                                               = 122 inches

Since the total distance from the center of the walkway to the top of the utility tunnel is 4 feet or 48 inches, and the worker's height plus the distance from the center to the top is 122 inches, which is greater than the radius of the walkway, the worker would have to duck in order to walk down the center of the walkway.

Therefore, the answer is no.

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With the Application of normal distribution conclusion can be All students missed at least one day of school per semester

what is normal distribution?

The normal distribution is a type of probability function that describes the distribution of a variable's values. Since most of the observations cluster around the middle peak of the curve, it is symmetric. When values of the distribution are far from the mean, the probability for those values narrow off evenly in both directions.

solution:

mean - ( standard deviation ) = 4 - 1 = 3

All students missed at least one day of school per semester

Therefore,  conclusion can be All students missed at least one day of school per semester

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Answer:

the ordered pair (0, 1/6)

Step-by-step explanation:

To reflect a function across the y-axis, we replace every occurrence of x with -x. Therefore, the function g(x) is given by:

g(x) = f(-x) = 1/6(2/5)^(-x)

To find an ordered pair on g(x), we need to choose a value of x and evaluate g(x). For example, if we choose x = 0, then:

g(0) = 1/6(2/5)^(-0) = 1/6

Therefore, the ordered pair (0, 1/6) is on the graph of g(x).

The total time that Marwa spent exercising on her first day is 1 hour and 30 minutes.

To calculate the total time Marwa spent exercising, we need to add the time it took for jogging and walking.

The time taken for jogging can be calculated using the formula: time = distance/speed. Marwa jogged for 1.5 km at a speed of 6.0 km/h. Thus, the time taken for jogging is 1.5 km / 6.0 km/h = 0.25 hours or 15 minutes.

The time taken for walking can be calculated similarly: time = distance/speed. Marwa walked for 3.0 km at a speed of 4.0 km/h. Thus, the time taken for walking is 3.0 km / 4.0 km/h = 0.75 hours or 45 minutes.

To calculate the total time, we add the time for jogging and walking: 15 minutes + 45 minutes = 60 minutes or 1 hour.

On her first day, Marwa spent a total of 1 hour and 30 minutes exercising. She jogged for 15 minutes and walked for 45 minutes. It's important for her to continue this routine of exercising for 30 minutes every day to maintain her fitness as advised by the dietitian.

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Answer:

D. -29.5

Step-by-step explanation:

−14.160÷−0.48

Expand -14.16 over -0.48 by multiplying both numerator and the denominator by 100.

-1416 / -48

and lastly reduce the fraction -1416 / -48 to lowest terms by extracting and canceling out -24 to get 592/2 and

59/2 = 29 1/2 = 29.5

Answer:

\(r=\frac{5}{2}\sqrt{2}\)

Step-by-step explanation:

Triangles And Circles

If a right triangle is inscribed in a circle (or the circle is circumscribed around the right triangle), then the hypotenuse of the triangle is the diameter of the circle.

The right triangle has both legs of known lengths, thus the hypotenuse (the diameter of the circle is):

\(d^2=5^2+5^2\)

\(d^2=25+25=50\)

\(d=\sqrt{50}\)

Since 50=2*25:

\(d=5\sqrt{2}\)

Thus the radius of the circle is:

\(r=\frac{d}{2}\)

\(r=\frac{5\sqrt{2}}{2}\)

\(\boxed{r=\frac{5}{2}\sqrt{2}}\)

Answer:

y=3x+1

Step-by-step explanation:

Explanation:

If we plugged in x = 0, then

y = 3x-1

y = 3*0-1

y = 0-1

y = -1

This means the input x = 0 leads to the output y = -1. Therefore, the ordered pair (0,-1) is on the function line.

Similarly, you should find that x = 2 leads to y = 5, meaning (2,5) is another point on this line. The same goes for the other points mentioned.

The graph is shown below.

These are the roots of the given expressions.

a. The root is \(\(-5 - 5i\).\)

b. The root is\(\(-24i\).\)

a. To find the root of \(\(5(-1 - i)\),\) we can simplify the expression:

\(\(5(-1 - i) = -5 - 5i\)\)

Thus, the root is \(\(-5 - 5i\).\)

b. To find the root of \(\(3(-8i)\),\) we simplify the expression:

\(\(3(-8i) = -24i\)\)

Therefore, the root is\(\(-24i\).\)

In both cases, we multiplied the given complex numbers by their respective coefficients. When we multiply a complex number by a scalar, such as 5 or 3, it scales both the real and imaginary parts of the complex number. In case (a), both the real part (-1) and the imaginary part \((-i) of \(-1 - i\)\) are multiplied by 5, resulting in\(\(-5 - 5i\).\) In case (b), the imaginary part (-8i) is multiplied by 3, yielding \(\(-24i\).\)

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Answer:

The pizza restaurant put 1/10 of the sauce on each pizza.

Step-by-step explanation:

Take the 3/5, and on a calculator divide the 3 by the 5:

0.6

Then, take the 0.6 and divide it by the 6 pizzas:

0.1, converted into a fraction equals 1/10.

The pizza restaurant put 1/10 of the sauce on each pizza.

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Answer:

C (-3)^2 = 9 not -9

Step-by-step explanation:

-3*-3 = 9  not -9

The square root of a negative number is imaginary not real

Answer:

C

Step-by-step explanation:

and you can also tell because the square roots of negative numbers will always be a non-real number so it will definitely not be -3

Answer:

y = 5A/r - 2

Step-by-step explanation:

It is a simple algebra. pkease see the above

Answer:

Step-by-step explanation:

The  product of prime polynomials which is equivalent to 30x3 – 5x2 – 60x is option C) 5x(2x – 3)(3x + 4).

We have 30x³ - 5x² - 60x

We take common value out so

5x(6x² - x - 12)

By following the factorization method we get,

6x² - x - 12

b²-4ac = -1² - 4x6x(-12)

= 289

x = -b ± √289/2a

= 1 ± 17/-2

x = 3/2 or x = -4/3

So,

6x² - x - 12

6(x-3/2)(x-(-4/3))

(2x-3) (3x+4)

Therefore,

30x³ - 5x² - 60x = 5x(6x² - x - 12)

= 5x (2x-3) (3x+4)

The  product of prime polynomials is equivalent to 30x3 – 5x2 – 60x is 5x(2x – 3)(3x + 4).

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Answer:

\(the \: equipment \: price \: is : 2,200.\)

Step-by-step explanation:

\(let \: the \: original \: price \: be \: x \\ then \: 17.5\% \: of \: x = 385 \\ \frac{17.5}{100} \times x = 385 \\ 17.5x = 100 \times 385 \\ x = \frac{38500}{17.5} \\ x = 2,200.\)

Answer: 6 divided by 2/3 = 9

Step-by-step explanation:

For division always take the first number in the word problem so in this question the answer would be 6 then you take the 2/3 and divide it by 6. So it would be 6 divided by 2/3. then you take the 9 from the word problem  and do 6 divided by 2/3 equals 9. So in this question the answer would be option 2 or could also be called option B. And if this is it that means the answer is, 6 divided by 2/3 = 9.

The division equation which representant this situation is 6 ÷ 2/3 = 9.

Division equations are mathematical equations with the division operator in them. Division equations are useful not only in math class, but in everyday life as well. For example, if we wanted to evenly distribute a bag of candies among our friends, we could use division to find our answer. Assume we have 100 candy bars and four friends. Divide 100 by 4 to find out how many candies each person gets. We discover that our answer is 25, which means that each of our friends receives 25 candies.

It's our job to figure out what the division equals. This can be represented by a variable, such as x. As a result, our total division equation will be: 100/4=x. On both sides of the equals sign, we have things.

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step 1

Calculate the average of the numbers

so

average=1,962.2/20

average=98.11

step 2

Subtract the mean from each number and Square each of the differences

so

(98.0-98.11)^2=0.0121

(98.4-98.11)^2=0.0841

(97.4-98.11)^2=0.5041

(97.0-98.11)^2=1.2321

(96.5-98.11)^2=2.5921

.

.

.

.step3

Add up all of the results from Step 2 to get the sum of squares

step 4

Divide the sum of squares, by the number of numbers minus one ( in this problem divided by 19)

step 5

Take the square root to get the result, this number s the sample standard deviation

The correct answer is OD. Although the word "then" appears in the statement, it is not used as a logical connective. So the statement is not compound.

The statement "If Laura sells her quota, then Marie will be happy" is a single declarative sentence. It consists of a conditional clause ("If Laura sells her quota") and a consequent clause ("then Marie will be happy"). However, these two clauses are not independent statements that can stand alone. Instead, they are connected in a cause-and-effect relationship. The word "then" in this context is not functioning as a logical connective, but rather as an indicator of the consequent clause.

A compound statement is formed by combining two or more independent statements using logical connectives such as "and," "or," or "if...then." In the given statement, there is no logical connective joining two independent statements.

Therefore, the statement is not compound.

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Answer:

y=-2

Step-by-step explanation:

\(\frac{-1-y}{10-6}=\frac{1}{4} \\4(-1-y)=1(10-6)\\-4-4y=4\\y=-\frac{8}{4} =-2\)

hope this helps

We have

First, we need to do the operation above

So we will do all the options and if the result is the same as the result above the expression is equal to the given.

A. (3.15) × (0.45)=1.41

B. (3.15) ÷ (0.45)=7

C. (3.15) × 1/0.45=7

D. (3.15) ÷ 45/100=7

E. (3.15) ÷ 100/45=1.41

F. 0.45/3.15​=0.14

As we can see the expressions that are equals are B,C,D

Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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For the value of L = 144.48, the probability of having L greater than the mean glucose level of Shelia is 0.02.

Here it is given that Sheila's glucose level follows a normal distribution with a mean of 128 mg/dl and a standard deviation of 8 mg/dl

L is the patient's blood test level.

It is given that the probability that the mean glucose level i.e 128 mg/dl is above L is 0.02.

We need to find L

We know

P(128>L) = 0.02

or, 1 - P(128 ≤ L) = 0.02

or, P(128 ≤ L) = 0.98

We know that for any Normal distribution we find the probability by converting it to standard form and then checking the p-value.

P(X < x) = Φ[(x - μ)/σ]

where,

μ = mean

σ = standard deviation

Therefore,

Φ[(L - 128)/8] = 0.98

we see that for a Z score of 2.06,

Therefore we get

(L - 128)/8 = 2.06

or, L - 128 = 16.48

or, L = 128 + 16.48

= 144.48

Therefore, the value of L would be 144.48

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Complete Question

Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with a mean of 128 mg/dl and a standard deviation of 8 mg/dl. Let L denote a patient's glucose level.

If measurements are made on four different days, find level L such that there is a probability of only 0.02 that the mean glucose level of four test results falls above L for Shelia's glucose level distribution. What is the value of L?

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Answer:

Quartic function

Step-by-step explanation:

Answer: Quartic function

Step-by-step explanation:

Answer:

The rule is "Subtract 9"

n = 11

Step-by-step explanation:

To find the rule you have to find what's common with all of them. This requires a little bit of testing.

THINK

Do I divide by 10? No because it doesn't work for all of them.

Do I divide by 4? No because it doesn't work for all of them.

Do I subtract by 9? Yes because it works for all of them.

Rules can be a lot of things. Subtraction, multipilcation, division, addition, or with variables.

Answer:

Step-by-step explanation:

To find the surface area of the solid square pyramid, we need to find the area of each of the five faces and then add them together.

Since the base of the pyramid is a square with side length of 2 inches, its area is 2^2 = 4 square inches.

Each of the four triangles is a right triangle with height 5 inches and base equal to a side of the square base. Therefore, the area of each triangle is:

(1/2) * base * height = (1/2) * 2 * 5 = 5 square inches

The total area of the four triangles is 4 times the area of one triangle, which is:

4 * 5 = 20 square inches

So, the total surface area of the solid square pyramid is the sum of the area of the base and the area of the four triangles:

4 + 20 = 24 square inches

Therefore, the answer is option (c) 24 square inches.

The probability that a randomly selected loan application takes longer than 13 days to process is 2/5 or 0.4.

Given that the time to process a loan application follows a uniform distribution over the range 7 to 17 days.

The standard uniform distribution is a special case of the beta distribution, with parameters (1,1).

We need to find the probability that a randomly selected loan application takes longer than 13 days to process.

Now, we need to calculate the probability using the formula of the uniform distribution:

P(X > 13) = (17 - 13) / (17 - 7) = 4/10 = 2/5

Therefore, the probability that a randomly selected loan application takes longer than 13 days to process is 2/5 or 0.4.

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Answer: 343p

Step-by-step explanation: did the test

To solve this problem, we can use conditional probability and the given information.

Let's define the following events:

A: Driver is above the legal alcohol limit

B: Breathalyser test reading is above the legal limit

Given information:

P(A) = 0.17 (probability that a driver is above the legal limit)

P(B|A') = 0.06 (probability of a false positive, i.e., driver not above the limit but test shows above the limit)

P(B'|A) = 0.10 (probability of a false negative, i.e., driver above the limit but test shows below the limit)

We can now calculate the probabilities:

a. P(B|A'): Probability of a false positive

P(B|A') = 0.06

b. P(B|A): Probability of a true positive

P(B|A) = 1 - P(B'|A) = 1 - 0.10 = 0.90

c. P(B): Probability of a breathalyser test reading being above the limit

Using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

P(B) = 0.90 * 0.17 + 0.06 * (1 - 0.17) = 0.1532 + 0.0502 = 0.2034

d. P(A|B'): Probability of being under the legal limit, given the breathalyser reading is below the limit

Using Bayes' theorem:

P(A|B') = (P(B'|A) * P(A)) / P(B')

P(A|B') = 0.10 * 0.17 / (1 - P(B))

P(A|B') = 0.10 * 0.17 / (1 - 0.2034) = 0.017 / 0.7966 = 0.0213

Therefore, the answers to the four decimal places are:

a. Probability of incorrect classification: 0.0600

b. Probability of correct classification: 0.9000

c. Probability of test reading above the limit: 0.2034

d. Probability of being under the limit given a below limit reading: 0.0213

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Answer:

y = 3, TU = 6

Step-by-step explanation:

SU is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is

\(\frac{SV}{ST}\) = \(\frac{VU}{TU}\) , substitute values

\(\frac{24}{4y-2}\) = \(\frac{14.4}{2y}\) ( cross- multiply )

14.4(4y - 2) = 48y

57.6y - 28.8 = 48y ( subtract 48y from both sides )

9.6y - 28.8 = 0 ( add 28.8 to both sides )

9.6y = 28.8 ( divide both sides by 9.6 )

y = 3

Then

TU = 2y = 2 × 3 = 6