what is the volume of the rectangular prism? ​

Answer:

Step-by-step explanation:

Whatever you do to the left you must do to the right, he multiplied 12 but forgot to multiply the -4 on the left and the + 1 on the right by the number 12

Answer:

4.5 miles per hour is her rate in miles per hour

Step-by-step explanation:

We want to convert 20 ft per second to miles per hour

If she jogs 20 ft in 3 seconds , then in one second , she will jog 20/3 ft

So convert 20/3 ft/second to miles per hour

Mathematically;

1 mile = 5280 feet

So one feet = 1/5280 mile

1 hour = 3600 seconds

1 second = 1/3600 hour

So, to go from miles/hour to ft/second ; we shall multiply by 1/5280 and divide by 1/3600

Hence; we have;

(20/3 * 1/5280)/1/3600

= 20/3 * 1/5280 * 3600/1

= 4.4545 which is 4.5 miles per hour

The smallest number of the data set is -2

The range of a data set is the difference between the largest number and smallest number in the data set. It is a simple measure of variability that gives an idea of how spread out the data is.

Range = largest number - smallest number

32 = 30 - smallest number

smallest number = 30 - 32 = -2

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Complete Question

The range of a data set is 32. If the largest number in the set is 30. what is the smallest number?

Answer:

-67

Step-by-step explanation:

To determine if a high school's claim of having unusually high math SAT scores is justified, we can compare the sample mean with the population mean using a z-score.

The average math SAT score is given as 514 with a standard deviation of 113. A random sample of 60 students from the high school yielded a sample mean of 531. By calculating the z-score and comparing it to the range of usual events, we can assess the validity of the high school's claim. To determine if the high school's claim is justified, we calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n))

Where:
x is the sample mean (531),
μ is the population mean (514),
σ is the population standard deviation (113),
and n is the sample size (60).

Substituting the values into the formula: z = (531 - 514) / (113 / sqrt(60))
Calculating the z-score gives us a value. By comparing the z-score to the range of usual events, we can determine if the high school's claim is justified. The range of usual events is typically within ±2 standard deviations from the mean. If the z-score falls within this range, it suggests that the sample mean is not significantly different from the population mean, and the claim of unusually high scores may not be justified.

Please note that the provided explanation assumes a normal distribution and the use of a one-sample z-test.

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Answer:

3.64m

Step-by-step explanation:

the square root of 41.73m/3.14

Answer:

The answe is b

Step-by-step explanation:

Because when u calculat,you’ll only get 1 answer.

pls mark BRAINLIEST

Answer:ur mom

Step-by-step explanation:is gae

The lines L1 and L2 do not intersect as their direction vectors are parallel, and there is no common point of intersection between them.

To determine whether the lines L1 and L2 intersect, we can compare their direction vectors. The direction vector of L1 is [2, -3, 5], obtained from the coefficients of the parameter t. The direction vector of L2 is [1, -3, -2], obtained from the coefficients of the parameter s.

If two lines in R3 are to intersect, their direction vectors must not be parallel. In this case, the direction vectors [2, -3, 5] and [1, -3, -2] are not parallel, so we proceed to check if the lines are skew or intersecting.

To determine if the lines are skew or intersecting, we need to compare their position vectors (the vectors obtained by setting the parameters t and s to zero). The position vector of L1 is [5, 7, -2], and the position vector of L2 is [8, -13, -9].

Since the position vectors are different, the lines L1 and L2 are not parallel and do not intersect at any point. Therefore, there is no common point of intersection between L1 and L2.

In summary, the lines L1 and L2 do not intersect since their direction vectors are parallel. Therefore, there is no common point of intersection between L1 and L2.

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

The circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.

We are given that:

Length of the shorter arc forming an angle of 45° with the center = 22 cm

AB = 22 cm

C is the center of the circle.

We know that the length of the arc is calculated as:

Length of an Arc = θ × (π / 180) × r

22 = 45 × (3.14 / 180) × r

22 = 0.785 r

r = 22 / 0.785

r = 28.0255

Circumference = 2 π r

Circumference = 2(3.14) (28.0255)

C = 176 cm

Therefore, we get that, the circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.

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Answer:

53 1/3 km/h

Step-by-step explanation:

average speed = (total distance)/(total time)

average speed = distance/time

time * average speed = distance

time = distance/(average speed)

250 km at 75 km/h

distance = 250 km

time = (250 km)/(75 km/h) = 3.33333... hours

350 km at 70 km/h

distance = 350 km

time = (350 km)/(70 km/h) = 5 hours

200 km at 30 km/h

distance = 200 km

time = (200 km)/(30 km/h) = 6.6666...  hour

total distance = 250 km + 350 km + 200 km = 800 km

total time = 3.33333... hours + 5 hours + 6.66666... hours = 15 hours

average speed = (total distance)/(total time)

average speed = (800 km)/(15 hours)

average speed = 53 1/3 km/h

The average speed of whole journey of the train is 45 km/hr

Average speed is the ratio of total distance travelled to total time taken. It is given by:

Average speed = total distance / total time

Given that a train travels 250 km with a average speed of 75 km/hr, hence:

75 = 250/time

time = 3.33 hours

It the travel 200 km with average speed of 30km/hr, hence:

30 = 200/time

time = 6.67 hours

The total distance = 200 km + 250 km = 450 km

The total time = 3.33 hr + 6.67 hr = 10 hours

Average speed = total distance/total time = 450 km/10 hours = 45 km/hr

The average speed of whole journey of the train is 45 km/hr

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The probability of rolling a sum less than 0.6366 is therefore 3/36, or 1/12, which is approximately 0.0833.

The numerical value of the area of a circle is given by the formula A = πr^2, where r is the radius of the circle. The numerical value of the circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

If the sum of the numbers rolled on the pair of standard dice is s, then the diameter of the circle is s. Therefore, the radius of the circle is s/2.

The inequality A < C can be rewritten as πr^2 < 2πr. Substituting r = s/2, we get:

(π/2) s^2 < πs

Dividing both sides by πs and simplifying, we get:

s < 2/π ≈ 0.6366

Therefore, the sum of the numbers rolled on the dice must be less than 0.6366 for the area of the circle to be less than the circumference of the circle.

To find the probability of this event, we need to find the probability that the sum of the numbers rolled on the dice is less than 0.6366.

There are 36 possible outcomes when rolling two standard dice, each with a value between 1 and 6. To find the probability of rolling a sum less than 0.6366, we need to count the number of outcomes that satisfy this condition.

The only possible sums less than 0.6366 are 2 and 3. There is only one way to roll a sum of 2 (rolling a 1 on both dice) and two ways to roll a sum of 3 (rolling a 1 and a 2, or a 2 and a 1). Therefore, there are three possible outcomes that satisfy the condition.

The probability of rolling a sum less than 0.6366 is therefore 3/36, or 1/12, which is approximately 0.0833.

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Hope you could understand.

If you have any query, feel free to ask.

With an annual dividend of $5.99 expected to grow at a constant rate of 3.5% and a market requirement of a 10.0% return, the stock is worth approximately $91.27.

The dividend discount model is a valuation method that estimates the intrinsic value of a stock by considering the present value of its future dividends. In this case, we can use the DDM formula to calculate the stock's worth:

Stock Price = Dividend / (Required Return - Dividend Growth Rate)

Given that Kraft Heinz pays an annual dividend of $5.99 and the expected growth rate is 3.5%, and the market requires a 10.0% return, we can substitute these values into the formula:

Stock Price = $5.99 / (0.10 - 0.035) = $5.99 / 0.065 ≈ $92.15

Therefore, based on the dividend discount model and the given assumptions, the stock price of Kraft Heinz is approximately $92.15.

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One bagel costs 155 cents.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let x = cost of one bagel

y = cost of one toast

z = cost of one muffin

If two pieces of toast and a bagel costs $3.15, then 2y + x = 3.15.

2y + x = 3.15   ⇒   x = 3.15 - 2y     (equation 1)

If a bagel and a muffin costs $3.30, then x + z = 3.30.

x + z = 3.30     (equation 2)

Substitute equation 1 to equation 2.

x + z = 3.30     (equation 2)

3.15 - 2y + z = 3.30   ⇒   z = 0.15 + 2y      (equation 3)

If a piece of toast, two bagels, and three muffins costs $9.15, then

y + 2x + 3z = 9.15     (equation 4)

Substitute equations 1 and 3 to equation 4.

y + 2x + 3z = 9.15     (equation 4)

y + 2(3.15 - 2y) + 3(0.15 + 2y) = 9.15

y + 6.30 - 4y + 0.45 + 6y = 9.15

3y = 2.4

y = 0.8

Substitute the value of y to equation 1.

x = 3.15 - 2y     (equation 1)

x = 3.15 - 2(0.8)

x = 1.55

Hence, the cost of one bagel is $1.55 or 155 cents.

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Answer:

x=9

Step-by-step explanation:

First, distribute the negative sign, changing (2x+9) to -2x-9

next, distribute. 10x+−2x+−9=(−3)(15)+(−3)(−4x)

then, combine like the like terms  (10x+−2x)+(−9)=12x−45

then you get  8x+−9=12x−45, and you will subtract 12x from both sides, resulting in −4x−9=−45. To get -4x by itself, add 9 to both sides

lastly, divide both sides by -4

x=9

Answer:

x = 9

Step-by-step explanation:

Distribute

10x - (2x + 9) = -3 (15 - 4x)

10 − 2 − 9 = − 3 (15 − 4)

Combine like terms

8 − 9 = − 3 (15 − 4 )

Rearrange terms

8 − 9 = − 3 (− 4 + 15)

Distribute

8 − 9 = 12 − 45

Add 9 to both sides of the equation

8 − 9 + 9 = 12 − 45 + 9

Answer:

1, 1

(x is equal to 1 and y is equal to 1)

Step-by-step explanation:

System:

{ -9x + 2y= -7

{ -12x + 3y= -9​

Getting a single x value:

[Given] -9x + 2y= -7

[Add 9x + 7 to both sides & then flip the equation] 9x = 2y + 7

[Divide both sides of the equation by 9] x = \(\frac{2}{9}\)y + \(\frac{7}{9}\)

Solving for y by plugging-in our x:

[Equation] -12x + 3y= -9​

[Plug-in] -12(\(\frac{2}{9}\)y + \(\frac{7}{9}\)) + 3(\(\frac{2}{9}\)y + \(\frac{7}{9}\)) = -9​

[Distribute -12 and 3]  \(\frac{-24y}{9}\) + \(\frac{-84}{9}\) + \(\frac{6y}{9}\) + \(\frac{21}{9}\) = -9​

[Multiply both sides of the equation by 9] -24y -84 + 6y + 21 = -81

[Combine like terms & add 63 to both sides] -18y = -18

[Divide both sides by -18] y = 1

Solve for x by plugging-in y,

[Given] -9x + 2y= -7

[Plug-in] -9x + 2(1) = -7

[Multiply] -9x + 2 = -7

[Subtract 2 from both sides] -9x = -9

[Divide both sides by -9] x = 1

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

two plus 5 times p or two more than the product of 5 and p.

Step-by-step explanation:

Answer:

-3/2

Step-by-step explanation:

rate of change is slope

Thus, a decision to not reject the null hypothesis should be interpreted with caution and further investigation may be needed to fully understand the underlying factors affecting student study habits at the university.

The null hypothesis in this scenario would be that the mean number of hours students study at the university (per day) is equal to or greater than 4.4 hours.

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Therefore, the volume of the tissue box is 8208 cubic inches.

To calculate the volume of the tissue box, we can use the formula:

Volume = Base Area * Height

Given that the base area is 16 square inches and the height is 513 inches, we can substitute these values into the formula:

Volume = 16 * 513

Volume = 8208 cubic inches

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Answer:

A = 76.3 degrees after 3 hours

Step-by-step explanation:

An exponential function is needed here:

A = P(1 - 0.05)^3, where this (1 - 0.95) reflects a DECREASE of 5%/hour.

Then:  A = (89 degrees)(0.95)^3, or

           A = 76.3 degrees after 3 hours

we have (6/7c)^2 = (6^2)/(7c)^2 = 36/49c^2

so the answer is D

ok done. Thank to me :>

The Cartesian equation will be;

⇒ x² + y² - 4x - 5y = 0

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The polar equation will be;

⇒ r = 4 sin(θ) + 5 cos(θ)

Now,

Substitute r = √x² + y² , r sin θ = x, r cos θ = y in above equation, we get;

The polar equation will be;

⇒ r = 4 sin(θ) + 5 cos(θ)

⇒ r² = 4 r sin(θ) + 5 r cos(θ)

⇒ x² + y² = 4x + 5y

⇒ x² + y² - 4x - 5y = 0

Thus, The Cartesian equation will be;

⇒ x² + y² - 4x - 5y = 0

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Answer:

problem 2

Step-by-step explanation:

The feeding time constraint for cats can be written symbolically as:

12 minutes/day * number of cats <= 8 hours/day

The feeding time constraint for dogs can be written symbolically as:

20 minutes/day * number of dogs <= 8 hours/day

The pampering time constraint for cats can be written symbolically as:

16 minutes/day * number of cats <= 8 hours/day

The pampering time constraint for dogs can be written symbolically as:

20 minutes/day * number of dogs <= 8 hours/day