Karen needs to take her pet kitten, Scooter, to the vet for a checkup. It's hard to get Scooter into his carrying case for the trip to the vet. He never wants to go! Scooter's carrying case has a rectangular front that is 11 inches wide and 9 inches tall. The case is 16 inches long. What is the volume of Scooter's carrying case?

Answer:

\(18.83\)

Step-by-step explanation:

For right triangles only, the tangent of an angle is equal to its opposite side divided by its adjacent side.

Therefore, we have the equation:

\(\tan 33^{\circ}=\frac{x}{29},\\x=29\tan 33^{\circ}\approx \boxed{18.83}\)

Answer:

7.20

Step-by-step explanation:

Answer:

7.20 or 6.90

Step-by-step explanation: most likely 7.20 because 3 pounds of apples is 6.90 so adding a half to that would be 7.20

Answer:

x=-5

Explanation:

Given the equation

First, we open the brackets

Next, we collect like terms and simplify

Finally, divide both sides by 5.

Option D:

32 ÷ (–16) is equivalent to –18 ÷ (9).

Given expression:

–18 ÷ (9)

Let us first solve this expression.

                = -2  (negative by positive is negative)

To find which expression has the same value for the given expression:

Option A: –18 ÷ 2

            = –9 (negative by positive is negative)

This is not equivalent expression.

Option B: –12 ÷ (–3)

                = 4  (negative by negative is positive)

This is not equivalent expression.

Option C: –10 ÷ 5

            = –2 (negative by positive is negative)

This is not equivalent expression.

Option D: 32 ÷ (–16)

                = -2  (positive by negative is negative)

This is the equivalent expression to the given expression.

Hence ,32 ÷ (–16) is equivalent to –18 ÷ (9).

Option D is the correct answer.

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The answer choice which is a function among the given answer choices is; Choice B as they are all correct.

From conventional mathematics, a function from a set x to a set y assigns to each element of X exactly one element of Y.

The set of values x is called the domain of the function and the set of values y is called the codomain/range of the function.

Functions basically represents the idealization of how a varying quantity depends on another quantity.

It therefore follows from the paragraph above that all of the answer choices are functions.

Therefore, the answer choice which is a function among the given answer choices is; Choice B as they are all correct.

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Answer:

Input work is the work done on a machine as the input force acts through the input distance. This is in contrast to output work which is a force that is applied by the body or system to something else. Output work is the work done by a machine as the output force acts through the output distance.Jan 15, 2020 hwgsvsd d jxvsd

dvsud sgsgs hsysvdudbd dvyd dhsgtsjd vsytwgsud gsyfwuyebdbhys. dusgcejd b

Answer:

send the whole statement

#a

\(\\ \sf{:}\dashrightarrow 4^3=(2\times 2)^3=2^6\)

#b

\(\\ \sf{:}\dashrightarrow 3^2.3^3=3^5\)

#c

\(\\ \sf{:}\dashrightarrow (2^3)^4=2^{12}\)

#d

\(\\ \sf{:}\dashrightarrow x^3y^4\checkmark\)

#e

\(\\ \sf{:}\dashrightarrow 8x^2y^5=2^3x^2y^5\)

#f

\(\\ \sf{:}\dashrightarrow( 9x^2)^2=(3^2x^2)^2=3^4x^4\)

Answer:Since 2/5 is basically a part of a whole, you would have to divide 60 by 20. You would get thirty. Thirty times five is 150.

Step-by-step explanation:

Answer: 40 years old.

Step-by-step explanation:

Let man's age = a

Let son's age = b

Since a man is 4 times as old as his son, therefore

a= 4b

In 5 years, he will only be 3 times as old as his son, therefore

a+5=3(b+5)

Apply substitution method :

4b+5=3b+15

b=10

a=40

Answer:

96*48=4608

Step-by-step explanation:

4*24=96

6*8=48

am I right to think that this is multiplication

if not then use the 2 numbers and their sign whatever it may be.

Answer:

9%

Step-by-step explanation:

To find the increased amount, subtract this month sales from the last month sales.      

Increased amount = 196200 - 180000

                              = £ 16,200

Now, find the increased percentage using the formula,        

\(\boxed{\bf Increased \ percentage = \dfrac{Increased \ amount}{Original \ amount}*100}\\\\\)

                                        \(= \dfrac{16200}{180000}*100\\\\= 9\%\)

Answer: 2

Therefore , the solution of the given problem of expressions comes out to be  potential energy at 550 metres of altitude is roughly 2,798.46 Joules.

Instead of producing estimates at random, it is preferable to use expanding, decreasing, & blocking moving numbers. They were only able to assist one another by exchanging resources, knowledge, or answers to problems. In addition to arithmetic operations like addition, negation, synthesis, and combination, a truth statement may also contain formulas, components, and notations. It is feasible to evaluate and analyse both sentences as words.

Here,

The gravitational potential energy of the bird at a height of 550m can be determined using the following formula, assuming you meant to say "0.52 kg bird" instead of "0.52k bird":

Mass times gravity times height equals gravitational potential energy.

where mass is measured in kilogrammes, gravity is the force of gravity, which accelerates objects near the Earth's surface at a rate of around 9.81 m/s2, and height is measured in metres.

Inputting the values provided yields:

The gravitational potential energy is equal to

=> 0.52 kg * 9.81 m/s2 *550 m,

=> 2,798.46 joules.

Hence, the bird's gravitational potential energy at 550 metres of altitude is roughly 2,798.46 Joules.

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As the p-value of the test, of 0.0002, is less than the significance level of 0.05, the information provide strong evidence for concluding that the company is not filling its bottles as advertised.

At the null hypothesis, it is tested if the tablets are filled as advertised, that is, the mean is of 5 grains, hence:

\(H_0: \mu = 5\)

At the alternative hypothesis, it is tested if the tablets are not filled as advertised, that is, if the mean is less than 5 grains, hence:

\(H_1: \mu < 5\)

The equation for the test statistic is defined as follows:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

In which the parameters are given as follows:

The values of these parameters for this problem are given as follows:

\(\overline{x} = 4.87, \mu = 5, s = 0.35, n = 100\)

Hence the test statistic is of:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{4.87 - 5}{\frac{0.35}{\sqrt{100}}}\)

t = -3.71.

Using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with 100 - 1 = 99 df, the p-value of the test is of:

0.0002.

Hence the information provide strong evidence for concluding that the company is not filling its bottles as advertised.

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Answer:

23

Step-by-step explanation:

The sale price of the item when displayed on sales costs $8.75 based on the stated original price and percentage discount offered.

The formula to calculate sale price of the item according to discount and original price will be -

Sale price = 25% × original price

Keep the value of original price in the formula to find the sale price

Sale price = 25% × 35

Performing multiplication and division by solving the percentage on Right Hand Side of the equation to find the value of sale price of the item

Sale price = 8.75

Hence, the item on sale costs $8.75.

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The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.

Congruency Requirements:

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side) 

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Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

We have,

To calculate the amount of barbed wire needed to fence the circular piece of land, we need to find the circumference of the circle.

Given:

Radius (r) = 25 cm

The formula for the circumference (C) of a circle is:

C = 2πr

Substituting the given radius into the formula, we have:

C = 2π x 25 cm

Now, we can calculate the circumference in centimeters.

C = 2 x 3.14 x 25 cm

C ≈ 157 cm

Now,

To convert centimeters to meters, we divide the circumference by 100.

C (in meters) = 157 cm / 100

C (in meters) ≈ 1.57 meters

Therefore,

Approximately 1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

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The complete question.

A circular piece of land with a radius of 25 cm is going to be fenced. How many meters of barbed wire are needed?

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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Given: The equation x² = 5x + 4

We have to draw the the graph for the given equation.

Consider the given equation,

x^2 - 5x - 4 = 0  

The vertex of the parabola of the form f(x) = ax^2 + bx + c   is given by x = -b/2a

Here,

a= 1

b= -5

c= -4

vertex = x = 5/2= 2.5

Also, the y coordinate at x = 2.5 is,

y = (2.5)^2 -5(2.5)-4

y = -10.25

Thus the vertex of parabola is (2.5 , -10.25)

y - intercept is the point where x = 0

put x = 0 in given equation

f(x) = 0 - 0 -4

f(x) = -4

hence y intercept is at (0, -4).

Now, we calculate x- intercept

x- intercept is where y is equal to 0.

Put f(x) = 0

We have,

x^2 - 5x - 4 = 0

by using quadratic formula,

x = -b ±√b² - 4ac/2a

x=5 ±√-5² - 4 (1)(-4)/2

x= 5±√41/2.

Hence with the obtained values the graph of the equation is obtained.

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The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

3/20.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of at bats in this problem is given as follows:

80.

In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

12/80 = 3/20.

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Answer:

696

Step-by-step explanation:

58/125 = 46.4%

0.464 x 1500 = 696 people