a right rectangular prism has a volume of 144 cubic centimeters and a height of 4 centimeters water a possible length and width in centimeters of the prism

Answer:

n = 10

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 12 and d = 5 and \(S_{n}\) = 345, thus

\(\frac{n}{2}\) [ (2 × 12) + 5(n - 1) ] = 345 ( multiply both sides by 2 )

n( 24 + 5n - 5) = 690 ← distribute and simplify left side

n(19 + 5n) = 690

19n + 5n² = 690 ( subtract 690 from both sides )

5n² + 19n - 690 = 0 ← in standard form

(5n + 69)(n - 10) = 0 ← in factored form

Equate each factor to zero and solve for n

5n + 69 = 0 ⇒ 5n = - 69 ⇒ n = - \(\frac{69}{5}\)

n - 10 = 0 ⇒ n = 10

However, n > 0 , thus n = 10

The measure of each inscribed angle at T and S is 72.5 degrees, and the sum of their measures is: 145 degrees

What is inscribed angle ?

An inscribed angle is an angle formed by two chords of a circle that have a common endpoint on the circle. The vertex of the inscribed angle is on the circle, and the sides of the angle intersect the circle at two distinct points.

There are some important properties of inscribed angles:

According to the question:
If the inscribed angles of T and S intercept the same arc, then they must be equal in measure. Let's call the measure of each angle x.

Since the sum of the measures of the angles in a triangle is 180 degrees, we can set up an equation to find the measure of the third angle in triangle TSY:

x + x + measure of angle YTS = 180 degrees

Simplifying the equation, we get:

2x + measure of angle YTS = 180 degrees

But we know that the measure of angle YTS is equal to half the measure of arc YZ, since it is an inscribed angle intercepting the same arc. So:

measure of angle YTS = 1/2 * measure of arc YZ = 1/2 * 70 degrees = 35 degrees

Substituting this value into our equation, we get:

2x + 35 degrees = 180 degrees

Solving for x, we get:

2x = 145 degrees

x = 72.5 degrees

Therefore, the measure of each inscribed angle at T and S is 72.5 degrees, and the sum of their measures is:

72.5 degrees + 72.5 degrees = 145 degrees

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The rule may be extended or generalized to products of three or more functions, to a rule for higher-order derivatives of a product, and to other contexts.

The simplified version of the expression would be 31-w

The numerical part of the expression given is :

Simplifying using Subtraction operation:

Adding the alphabetical part :

Therefore, the simplified form of the expression is 31-w.

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Answer:

Step-by-step explanation:

Solve for the equation equal to y

\(3x+4y=12\\4y=-3x+12\\y=\frac{-3}{4}+\frac{12}{4}\)

The slope here is -3/4. The slope of a line perpendicular to the original has a negated and inverted slope. Therefore the slope is 4/3

Answer:

1. (a)  [-1, ∞)

   (b)  (-∞, -1) ∪ (1, ∞)

2. (a)  (1, 3)

    (b)  (-∞, 1) ∪ (3, ∞)

3. (a)  9.6 m and 0.4 m

   (b)  03:08 and 15:42

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Part (a)

When x < 0, the function is f(x) = x².

Since the square of any non-zero real number is always positive, the range of the function f(x) for x < 0 is (0, ∞).

When x ≥ 0, the function is f(x) = sin(x).

The minimum value of the sine function is -1 and the maximum value of the sine function is 1.  As the sine function is periodic, the function oscillates between these values.  Therefore, the range of function f(x) for x ≥ 0 is [-1, 1].

The range of function f(x) is the union of the ranges of the two separate parts of the function.  Therefore, the range of f(x) is [-1, ∞).

Part (b)

The domain of the function g(x) = ln(x² - 1) is the set of all real numbers x for which (x² - 1) is positive, since the natural logarithm function (ln) is only defined for positive input values.

Find the values of x:

\(\implies x^2-1 > 0\)

\(\implies x^2 > 1\)

\(\implies x < -1, \;\;x > 1\)

Therefore, the domain of function g(x) is (-∞, -1) ∪ (1, ∞).

Part (a)

To determine the interval where f(x) < 0, we need to find the values of x for which the quadratic is less than zero.

First, set the function equal to zero and solve for x:

\(\begin{aligned} x^2-4x+3&=0\\x^2-3x-x+3&=0\\x(x-3)-1(x-3)&=0\\(x-1)(x-3)&=0\\ \implies x&=1,\;3\end{aligned}\)

Therefore, the function is equal to zero at x = 1 and x = 3 and so the parabola crosses the x-axis at x = 1 and x = 3.

As the leading coefficient of the quadratic is positive, the parabola opens upwards. Therefore, the values of x that make the function negative are between the zeros.  So the interval where f(x) < 0 is 1 < x < 3 = (1, 3).

Part (b)
Since the square root of a negative number cannot be taken, and dividing a number by zero is undefined, function f(x) has to be positive and not equal to zero:  f(x) > 0.

As the parabola opens upwards, the values of x that make the function positive are less than the zero at x = 1 and more than the zero at x = 3.

Therefore the domain of g(x) is (-∞, 1) ∪ (3, ∞).

Part (a)

The range of a sine function is [-1, 1]. Therefore, to calculate the maximal and minimal possible water depths of the bay, substitute the maximum and minimum values of sin(t/2) into the equation:

\(\textsf{Maximum}: \quad 5+4.6(1)=9.6\; \sf m\)

\(\textsf{Maximum}: \quad 5+4.6(-1)=0.4\; \sf m\)

Part (b)

To find the times when the depth is maximal, set sin(t/2) to 1 and solve for t:

\(\implies \sin \left(\dfrac{t}{2}\right)=1\)

\(\implies \dfrac{t}{2}=\dfrac{\pi}{2}+2\pi n\)

\(\implies t=\pi+4\pi n\)

Therefore, the values of t in the interval 0 ≤ t ≤ 24 are:

Convert these values to times:

Answer:

14 {final answer}

Step-by-step explanation:

Let's solve the problem,

→ (x² - 4y)/2

→ (4² - (4 × -3))/2

→ (16 + 12)/2

→ 28/2 = 14

Thus, the answer is 14.

Answer:

ture

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

The price of the cost per quart of laundry detergent is A = $ 3.47

Given data ,

Let the unit cost rate be A

Now , There are 4 quarts in a gallon, so a 2-gallon container contains 8 quarts.

To find the price per quart, we can divide the total cost by the number of quarts:

Price per quart = Total cost / Number of quarts

Price per quart = $27.76 / 8 = $3.47

Hence , the price per quart of laundry detergent is $ 3.47

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Combining similar terms:

Step-by-step explanation:

this is the answer in the picture

Answer:

They were 16 minutes late because 0.25 x 16 = 4 and 4 dollars were off of the delivery.

Step-by-step explanation:

Answer:

a. This probability is the p-value of Z when X = 60.

b. This probability is the p-value of Z when X = B subtracted by the p-value of Z when X = A.

c. The proportion is the p-value of Z when X is the length of the examination period. How many students is this proportion multiplied by the number of students.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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 p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean \(\mu\), standard deviation \(\sigma\).

a. What is the probability of completing the exam in one hour or less (to 4 decimals)?

This probability is the p-value of Z when X = 60.

b. What is the probability that a student will complete the exam in more than minutes A but less than B minutes (to 4 decimals)?

This probability is the p-value of Z when X = B subtracted by the p-value of Z when X = A.

c. Assume that the class has students and that the examination period is minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to nearest whole number)?

The proportion is the p-value of Z when X is the length of the examination period. How many students is this proportion multiplied by the number of students.

Answer:

Step-by-step explanation:

3x^2 = -12

x^2 = -4

x = ±√-4

this equation has no real solutions

Answer:

-------------------------------

56 would have a remainder of 2 using multiples of 3

56/3 = 18 remainder 2

56/6 = 9 remainder 2

56/9 = 6 remainder 2

56/18 = 3 remainder 2

56/27 = 2 remainder 2

Now divide 28 by the above numbers to see which ones have 1 as a remainder:

28/3 = 9 remainder 1

28/6 = 4 remainder 4

28/9 = 3 remainder 1

28/18 = 1 remainder 10

28/27 = 1 remainder 1

There are 3 numbers that will work.

Answer: c. 3

Answer:

96 in³

Step-by-step explanation:

Volume = 2(BHD) / 2

The 2s cancel out

Volume = 3(8)4

Volume = 96

Answer:

50 dozen total

Step-by-step explanation:

8/12 & 10/12.... average 9/12

11/12 - 9/12 =

2/12x = 100

2x = 1200

x = 600/12

50 dozen total

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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Answer:

x=42

Step-by-step explanation:

step 1: multiply 3 to both sides of the equation to isolate x

then you get x=14x3=42

x=42

Answer:

X=42

Step-by-step explanation:

14 * 3= 42

14 = x/3

14= 42/3

divide

14=14

Answer:

6 people

Step-by-step explanation:

To figure this out, let's set up an equation.

We know 30 people went last year to Universal, and that this is 5 times as many people as who went the year before

So to figure out how many went the year before, we divide 30 by 5

30/5 = 6

So 6 people went to Universal the year before.

I hope this helps :)

Answer:

23/72 or .3194

Step-by-step explanation:

Answer:

0.31944444444

Step-by-step explanation:

The probability distribution of the number of customers that enter the store on a given day is described as follows:

Poisson with a mean of 70 customers.

In a Poisson distribution, the mass function probability that X represents the number of successes of a random variable is given by the equation presented as follows:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

A combination of Poisson variables is a Poisson variable, hence the daily distribution is a Poisson variable with mean given by the sum of these following observations:

Hence the mean is of:

8 + 16 + 18 + 28 = 70 customers.

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The mean is 38.5. It tell us that the average distance a heavy ball was thrown is 38.5 feet.

A stem-and-leaf plot is table that displays a data set in ascending order.  used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. In this stem-and-leaf plot, the stem is the tens digit and the leaf is the units digit. For example, in the number 32, 3 is the stem 2 is the leaf.

The mean is a measure of the center of a dataset that is used to determine the average of a set of numbers

Mean = sum of numbers / total numbers in the data set

(20 + 21 + 24 + 31 + 32 + 36 + 41 + 43 + 47 + 51 + 51 + 65) / 12

462 / 12 = 38.5

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Answer:

$10.2925, Rounded up: 10.30

Step-by-step explanation:

First, you find what 15% is in a decimal. so you do 15 x 100 to get 0.15

Then you multiply that by 8.95 to get 1.3425

Finally, you add up the numbers and get 10.30 as a rounded answer :D

Answer:

A) 2 1/12

Step-by-step explanation:

I just added all the fractions and subtracted from 10 1/12 :)