A metal shop is cutting a rectangular piece of sheet metal with a width of 60 inches and a length of 144 inches. The shaded parts of the diagram represent two rectangular sections, A and B, that will be cut and removed.

Part A :What are the dimensions of section B?​
Part B:What will be the area, in square inches, of the piece of sheet metal after both sections are cut and removed?
​

Answer:

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.

Answer:

the best answer is option d

Step-by-step explanation:

4/5 x -10 = -40/5 = -8

t x t = t^2

-8t^2

Answer:

\( \sf \: d) \: - 8 {t}^{2} \)

Step-by-step explanation:

Given expression,

\( \sf \rightarrow \: \frac{4}{5}t \: ( - 10t )\)

Let's simplify the expression,

\( \sf \rightarrow \: \frac{4}{5} t \: ( - 10t) \: \)

\( \sf \rightarrow \: ( \frac{4}{5} \times - 10)( {t} \times t)\)

\( \sf \rightarrow \: ( \frac{ - 40}{ \: 5} )( {t}^{2} )\)

\( \sf \rightarrow \: - 8{t}^{2} \)

Hence, the option (d) is correct.

Answer:

1. The cost increases $0.30 each time 1 goldfish is

added.

{ 1, 29}

Integers are both positive and negative whole numbers.

29 is a prime number, therefore, the Integer factors are only 1 and 29

Prime numbers are numbers that have only two factors which is 1 and itself

Answer:

27

Step-by-step explanation:

45/5=9

9*3=27

Answer: 27

Step-by-step explanation:

45/5=9

9x3=27

The given function is one-to-one and the inverse of f(x) is \(f^{-1}(x)=\sqrt[3]{x-8}+2\)

In the given question,

Given expression; \(f(x)=(x-2)^3+8\)

We have to show that this function is one-to-one algebraically.

We also have to find the inverse of f(x).

To find the function is one-to-one we firstly find the f(-x).

If f(x) ≠ f(-x) then the function is one-to-one.

To find f(-x) we have to put x = -x in the given function.

The given function is \(f(x)=(x-2)^3+8\).

Now putting x = -x

\(f(-x)=((-x)-2)^3+8\)

\(f(-x)=(-x-2)^3+8\)

Taking minus sign out. When we take minus sign out then there have power 3 on the minus sign. Since power is odd so the value of \((-)^3=-\)

So now the function is \(f(-x)=-(x+2)^3+8\)

Now we can see that f(x) ≠ f(-x) .

So the given function is one-to-one.

Now finding the inverse of f(x).

To find the inverse of f(x) let f(x)=y.

Now putting in place of f(x) y

\(y=(x-2)^3+8\)

Subtract 8 on both side

\(y-8=(x-2)^3+8-8\)

Simplifying

\(y-8=(x-2)^3\)

Taking cube root on both side

\(\sqrt[3]{y-8}=x-2\)

Add 2 on both side

\(\sqrt[3]{y-8}+2=x-2+2\)

Simplifying

\(\sqrt[3]{y-8}+2=x\)

Replace x and y to each other

\(\sqrt[3]{x-8}+2=y\)

\(y=\sqrt[3]{x-8}+2\)

Put \(y=f^{-1}(x)\)

\(f^{-1}(x)=\sqrt[3]{x-8}+2\)

Hence, the inverse of f(x) is \(f^{-1}(x)=\sqrt[3]{x-8}+2\).

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Kelly made at least $28 in 75% of the weeks she worked.

To determine the amount Kelly made in at least 75% of the weeks she worked, we need to first arrange the dollar amounts in ascending order:
16, 18, 21, 21, 28, 28, 32, 35
Next, we need to find the value that represents 75% of the weeks worked.

Since Kelly worked for 7 weeks, we can calculate 75% of 7 weeks as follows:
(75/100) x 7 = 5.25.
Since we cannot have a fraction of a week, we will round up to the nearest whole number, which is 6.

Therefore, we will consider the first 6 weeks of earnings.
Now, we will identify the amount earned in the 6th week:
16, 18, 21, 21, 28, 28, 32, 35.
The amount earned in the 6th week is $28.

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This means that when all 8 parts are arranged in a single row, probability there are 28 different conceivable configurations. Finley can have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces.

Finley features eight game pieces, each of which is entirely either all red or all black and simply differs in colour. This indicates that there are 28 distinct configurations that may be made using the 8 pieces arranged in a single row. Finley could have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces. This is due to the fact that the 8 pieces can be arranged in a variety of ways, and each arrangement will be deemed distinct as long as it contains at least one red and one black piece. For instance, the configuration could be as follows if there are 4 red and 4 black pieces: If there are four red pieces and four black pieces, for instance, the arrangement might be either black-red-black-red-black-red-red or red-black-red-black-red-black. No matter the configuration, there are a total of 28 arrangements.

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Answer:

The volume of the spherical grain is of 1.13*10^-7 cubic centimeters.

Step-by-step explanation:

The volume of a sphere with radius r is given by the following formula:

In this question:

The spherical grain has volume of 5*10^-3 centimeters = 0.005. So r = 0.005. Then

The volume of the spherical grain is of 1.13*10^-7 cubic centimeters.

Answer:

Step-by-step explanation:

Answer:

Hi there! The answer is C.

(3 {x}^{2} + 3 ) + (3 {x}^{2} + x+ 4) =(3x

2

+3)+(3x

2

+x+4)=

First we work out the parenthesis, which is easy, because we can just remove them.

3 {x}^{2} + 3 + 3 {x}^{2} + x + 4 =3x

2

+3+3x

2

+x+4=

Now rearrange our expression (in order to collect the terms later).

3 {x}^{2} + 3 {x}^{2} + x + 3 + 4 =3x

2

+3x

2

+x+3+4=

Now we can collect the terms.

6 {x}^{2} + x + 76x

2

+x+7

The answer is C.

~

Step-by-step explanation:

this is your correct answer

a) The initial number of infections refers to the time t = 0, not 1. At the start, there are

\(P(0) = \dfrac{700}{1 + 49e^{-0}} = \dfrac{700}2 = \boxed{350}\)

infected students.

b) Here you look for the time t such that P(t) = 600. We have

\(\dfrac{700}{1+49e^{-0.3t}} = 600\)

\(\dfrac{700}{600} = 1+49e^{-0.3t}\)

\(\dfrac76 = 1+49e^{-0.3t}\)

\(\dfrac16 = 49e^{-0.3t}\)

\(\dfrac1{294} = e^{-0.3t}\)

\(\ln\left(\dfrac1{294}\right) = \ln\left(e^{-0.3t}\right)\)

\(-\ln(294) = -0.3t \ln(e)\)

\(\ln(294) = \dfrac3{10}t\)

\(t = \dfrac{10}3 \ln(294) \approx 18.945\)

Rounding up, the school will close after around 19 days.

The expected number of defective toys when 2 toys are selected at random is 0.077 (rounded to three decimal places).

To find the expected number of defective toys when 2 toys are selected at random, we first need to find the probability of selecting a defective toy on each pick.

On the first pick, the probability of selecting a defective toy is 4/13 since there are 4 defective toys out of 13 total. On the second pick, the probability of selecting a defective toy depends on whether or not a defective toy was selected on the first pick.

If a defective toy was selected on the first pick, then there are only 3 defective toys left out of 12 total toys remaining. So the probability of selecting a defective toy on the second pick would be 3/12 or 1/4.

If a non-defective toy was selected on the first pick, then there are still 4 defective toys left out of 12 total toys remaining. So the probability of selecting a defective toy on the second pick would be 4/12 or 1/3.

To find the expected number of defective toys, we need to multiply the probabilities of each scenario and add them together:

Expected number of defective toys = (4/13 x 3/12) + ((9/13) x 4/12)

Simplifying this equation gives us:

Expected number of defective toys = 1/13

Therefore, the expected number of defective toys when 2 toys are selected at random is 0.077 (rounded to three decimal places).

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The rate of the reaction is 0.02 M/s

The rate of a chemical reaction is defined as the rate of change in concentration of a reactant or product divided by its coefficient from the balanced equation.

Given that, for reaction A + 2B → 3C, the rate of change of C is found to be 0.06 M/s, we need to find the rate of the reaction.

Rate of reaction =

-d[A] / dt = 1/2 d[B] / dt = 1/3 d[C] / dt

-d[A] / dt = 1/3 d[C] / dt = 0.02 M/s

1/2 d[B] / dt = 1/3 d[C] / dt = 3/2 × 0.06 = 0.09 M/s

Rate = 1/3 d[C] / dt

= 1/3 × 0.06 = 0.02 M/s

Hence, the rate of the reaction is 0.02 M/s

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Answer:

x²+y²+2xy

Step-by-step explanation:

Hope it helps! If it did, please thank, rate and mark brainliest!

Answer:

O x² + 2xy + y². The result of squaring a binomial is the sum of the square of the first term in the binomial, the product of twice the first term and the second term and the square of the second term: (x + y)² = x² + 2xy + y².

The website which is cheaper for Caroline to buy the spice mix is French website.

Given data ,

Let's calculate the total cost for Caroline from both websites and determine which one is cheaper.

British website:

Price for 100 g = (£0.90 / 25 g) * 100 g = £3.60

Since the British website offers free delivery, the total cost remains £3.60.

French website:

Price for 100 g = (€1.20 / 50 g) * 100 g = €2.40

Delivery cost = €0.80

On simplifying the equation , we get

To convert the price and delivery cost to pounds, we'll use the conversion rate: €1 = £0.85.

Price in pounds = €2.40 * £0.85 = £2.04

Delivery cost in pounds = €0.80 * £0.85 = £0.68

Total cost = Price in pounds + Delivery cost = £2.04 + £0.68 = £2.72

Comparing the total costs:

British website: £3.60

French website: £2.72

Hence , Caroline would pay £2.72 for the spice mix from the cheaper website, which is the French website.

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Step-by-step explanation:

The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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The domain and the range of the transformed graph are given as follows:

The definitions of the domain and of the range of a function are given as follows:

After the reflection over the y-axis, the domain of the function is of:

[-2,5].

(as the reflection over the y-axis changes the signal of the x-values of the function).

After the translation of 3 units right, the domain of the function is of:

[1,8].

As the translation adds 3 to each value of x of the function.

After the vertical stretch by a factor of 2, the range of the function is of:

[-6,12].

As the stretch means that all the output values of the function are multiplied by 2.

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Answer:

4 US liquid gallons = 16 US liquid quarts

( Multiply the volume value by 4 )

Have a wonderful day! :-)

Answer:

16 quarts in 4 gallons

Step-by-step explanation:

1 gallon equals 4 quarts

Answer:

.

Step-by-step explanation:

A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising

At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.

During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.

Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.

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Given :

David rented a truck for one day there was a base fee of $17.99 .

Charge per mile driven is, c = 98 cents = $0.98 .

He pay $137.55 at the end of the day.

To Find :

How many miles did he drive the truck.

Solution :

Let, number of miles he drive is n.

So,

\(n = \dfrac{137.55 - 17.99}{0.98}\\\\n = 122\ miles\)

Therefore, number of miles he drive the truck is 122 miles.

In order to find the value of x, you first take into account that the angle ∠AED is equal ∠DEC. Furthermore, angle x is equal to ∠AED.

Thus, you have:

∠AED = ∠DEC = x

Next, you take into account that the sum of the angles ∠DEC + ∠BEC is equal to 180°, that is:

∠DEC + ∠BEC = 180

But, angle ∠BEC is equal to 3x - 10

∠BEC = 3x - 10

Then, you sum the algebraic expressions given above, just as follow:

∠DEC + ∠BEC = 180

x + 3x - 10 = 180

You solve the previous equation for x:

x + 3x - 10 = 180

4x = 190

x = 190/4

x = 85/2

Hence, the value of x is 85/2 °

Answer:

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

Area is the product of two dimensions, so the ratio of areas of similar figures is equal to the square of the scale factor k.

Hence the scale factor is:

Therefore the ratio of corresponding parts is:

The rules AAS, ASA, SSS and SAS are congruence rule of triangle  and the each rules has been explained

The rules AAS, ASA, SSS and SAS are congruence rule of triangle

SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent

SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to  the two sides and one included angles between the sides of the other triangle, then both triangles are congruent

ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent

AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent

Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle

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Answer: b =27

Step-by-step explanation:

24 = b -3   Just add 3 to both sides

+3         +3

b = 27

Answer:

b=27

Step-by-step explanation:

Let's solve your equation step-by-step.

24=b−3

Step 1: Flip the equation.

b−3=24

Step 2: Add 3 to both sides.

b−3+3=24+3

b=27

Answer:

b=27

(a) The area to the left of Z = -1.11 is 0.1331.
(b) The area to the left of Z = -0.51 is 0.3050.
(c) The area to the left of Z = -0.35 is 0.3632.
(d) The area to the left of Z = -0.03 is 0.4918.

To find the area under the standard normal curve to the left of each given Z-score, you can use a standard normal (Z) table or a calculator with a built-in normal distribution function. Here are the steps:

1. Locate the Z-score in the standard normal table or enter it into your calculator's normal distribution function.
2. Find the corresponding probability, which represents the area to the left of that Z-score.

Using these steps, you can find the area to the left of each Z-score:

(a) Z = -1.11:
The area to the left of Z = -1.11 is 0.1335 (rounded to four decimal places).

(b) Z = -0.51:
The area to the left of Z = -0.51 is 0.3050 (rounded to four decimal places).

(c) Z = -0.35:
The area to the left of Z = -0.35 is 0.3632 (rounded to four decimal places).

(d) Z = -0.03:
The area to the left of Z = -0.03 is 0.4901 (rounded to four decimal places).

Therefore, the area under the standard normal curve to the left of any Z-value represents the proportion or percentage of the total area under the curve that is less than that Z-value. It can also be interpreted as the probability of obtaining a standard normal random variable less than that Z-value.

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Answer:

\(x=24\frac{3}{4}\\ y=24\frac{1}{4}\)

Step-by-step explanation:

Let the two numbers be x and y

So we have:

\(x +y = 49\\x-y=\frac{1}{2}\)

using the elimination method, add the two equations together:

\(2x=49\frac{1}{2} \\2x=\frac{99}{2}\)

solve for x:

\(x=\frac{99}{4}\\x=24\frac{3}{4}\)

substitute our value for x back into the first equation we made:

\(x+y=49\\(\frac{99}{4}) + y=49\\y=49-\frac{99}{4}\\y=\frac{97}{4} \\ y=24\frac{1}{4}\)

therefore,

\(x=24\frac{3}{4}\\ y=24\frac{1}{4}\)

The limit of {an} as n approaches infinity is infinity, the sequence {an} diverges.

To determine whether the sequence {an} converges or diverges, we can take the limit as n approaches infinity and see what happens.

lim(n→∞) an = lim(n→∞) (n⁴ / n³ - 4n)

To make things easier, we can divide both the top and bottom by the cube of n.

lim(n→∞) an = lim(n→∞) (n⁴/ n³ - 4n) = lim(n→∞) (n / (1 - 4/n²))

As the value of n keeps increasing, the denominator 1-4/n^2 gets closer to the value of 1, allowing for further simplification.

lim(n→∞) an = lim(n→∞) (n / (1 - 4/n²)) = lim(n→∞) (n / 1) = ∞

Since the limit of {an} as n approaches infinity is infinity, the sequence {an} diverges

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