Layna can paint a 350-square foot room in 4 hours. It takes Bebe 7 hours to paint the same room. Which equation can be used to find the time in hours, t, it takes Layna and Bebe to paint the room together?


Rate
(Rooms per Hour)
Time
(Hours)
Fraction Completed
Layna
One-fourth

Bebe
One-seventh

One-fourth t + one-seventh t = 1
One-fourth t times one-seventh t = 1
4 t + 7 t = 1
4 t minus 7 t = 1

Answer:

X= 82⁰

z= 82⁰

Step-by-step explanation:

for X:

we can use co-interior angles sum up to make 180 so,

x+ 98= 180

x= 180-90= 82⁰

for z, we can use either angles on a straight line or corresponding angles

98 + z= 180

z= 180-98= 82⁰

corresponding angles are always equal and can be found in the F shape diagram when lines are parallel

therefore X and z are corresponding angles and since we found x= 82⁰ then z= 82⁰

sin A = 4/12 = 1/3

sin inv 1/3 = 19.47⁰

Answer:

option 4, 19.47°

Step-by-step explanation:

From angle A, the given side length are opposite and hypotenuse

SOH CAH TOA is

sinx = opposite / hypotenuse

cosx = adjacent / hypotenuse

tanx = opposite / adjacent

visual representation below

the given length fits the characteristic to use sin

sinA = opposite / hypotenuse

sinA = 4 / 12

common facto is 4 it becomes sinA = 1 / 3

Apply trig inverse property,

x = arcsin(1/3)

x = 19.47122°

Answer:

6-2w(w+2)

Step-by-step explanation:

6-2w²+4w

6-2w(w+2)

Answer:

3.678 Kilograms

Answer:

3678/1000

=3.678kg

the answer is 3.678kg

Answer:

[tex]\dfrac{\sqrt[12]{55296} }{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}=\dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}}[/tex]

Multiply the numerator and denominator by [tex]2^{\frac{2}{3}}[/tex] :

[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}[/tex]

[tex]\textsf{Apply exponent rule to the denominator} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2^{\frac{1}{3}+\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}[/tex]

Rewrite 1/4 as 3/12 and 2/3 as 8/12 :

[tex]\implies \dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}=\dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^c \cdot b^c=(a \cdot b)^c:[/tex]

[tex]\implies \dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}=\dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}[/tex]

Simplify the operation in the parentheses:

[tex]\implies \dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}=\dfrac{(216\cdot 256)^\frac{1}{12}}{2}=\dfrac{(55296)^\frac{1}{12}}{2}[/tex]

[tex]\textsf{Finally, apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]\implies \dfrac{(55296)^\frac{1}{12}}{2}=\dfrac{\sqrt[12]{55296} }{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2^{\dfrac{1}{4}}3^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]

[tex]\\ \rm\Rrightarrow 2^{\dfrac{1}{4}-\dfrac{1}{3}}3^{\dfrac{1}{4}}[/tex]

[tex]\\ \rm\Rrightarrow 2^{\dfrac{-1}{12}}3^{\dfrac{1}{4}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{1}{4}}}{2^{\dfrac{1}{12}}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{3}{12}}}{2^{\dfrac{1}{12}}}[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{3^3}{2}\right)^{\dfrac{1}{12}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3}{2}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3\times 2^82^3}{22^82^3}}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{27(256)(8)}{2^12}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{6912(8)}}{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{55296}}{2}[/tex]

The scale factor of the dilation of line segment BA is 1/5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in the size of a figure.

From the diagram:

scale factor of BA = AC / CA' = 4 / (4 + 16) = 1/5

The scale factor of the dilation of line segment BA is 1/5.

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Answer:

B

Step-by-step explanation:

I do believe

The distance travelled by boat after 1 hour will be 10km.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

The distance will be calculated as:-

a²+b²=c²

9² + 3 ²=  c ²

81+9 = c²

100 = c²

c = 10 km / hour

The distance travelled after one hour will be calculated as:-

Distance = Speed x Time

Distance = 10 x 1 = 10 Km

Therefore the distance travelled by boat after 1 hour will be 10km.

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The probability that a randomly selected pigeon gets an incorrect result is; 0.0103

We are told that;

1.5% pigeons are infected.

Inaccuracy of the test = 1 - 97% = 3%

1.5% of the pigeons are infected. Thus;

1 - 1.5% = 98.5% pigeons are un-infected.

Inaccuracy of test is 1 - 99% = 1% .

Thus;

0.03 and 0.01 are the probability of an error being made in infected and un-infected respectively.

Meanwhile, probability of infected and un-infected are 0.015 and 0.985 respectively.

Thus, the probability of a randomly chosen person gets an incorrect result = (0.03*0.015) + (0.985*0.01) =  0.0103

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Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The number of years for which James took the loan is 5.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

Amount after T years = P + SI

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

James paid off the loan on his motorboat in the year 2006. He originally borrowed $6500 to buy the boat, but with simple annual interest, he discovered that he paid a total of $8775 over the life of the loan. Also, the annual interest rate is 7%. Therefore,

A = P + (PRT)

8775 = 6500 + (6500×0.07×T)

2275 = 6500×0.07×T

T = 5

Hence, the number of years for which James took the loan is 5.

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Answer:  2001

Step-by-step explanation:

Answer:

47.5 games

Step-by-step explanation:

Finding A :

⇒ Games by A : Games by B = 3 : 1

⇒ Games by A : 10 = 3 : 1

⇒ Games by A = 30

==============================================================

Finding C :

⇒ Games by B / Games by C × Games by A / Games by B = 3 × 4/3

⇒ Games by A / Games by C = 4

⇒ Games by C = 30/4

⇒ Games by C = 7.5

==============================================================

Total games won :

⇒ Games by A + Games by B + Games by C

⇒ 30 + 10 + 7.5

⇒ 47.5 games

The solution of the given radical expression√20 using factorization is [tex]2 \sqrt{5}[/tex]. Therefore, the correct option for the  radical expression√20 is option A, i.e  [tex]2 \sqrt{5}[/tex].

A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression.

Example = 4y, 3x+4.

An expression containing the values in the form of square root, cube root is called a radical expression.

The breaking of a number into its own factors, so that they multiply to give the same number again, is called factorization.

Given expression, √20

The solution of the expression can be obtained by the factors of 20.

[tex]\sqrt{20} = \sqrt{2\times2\times5}[/tex]

[tex]\sqrt{20}[/tex] = [tex]2 \sqrt{5}[/tex]

Here, 2 and 5 are factors of 20.

Thus, the value of the radical expression [tex]\sqrt{20}[/tex]  is [tex]2 \sqrt{5}[/tex].

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34

Step-by-step explanation:

=5x-4y+2z

=5×8-4×3+2×3

=40-12+6

=46-12

=34

Answer:

[tex]0.0166[/tex]

Step-by-step explanation:

Let the sample proportion be [tex]\hat{p}=0.14[/tex] and the sample size be [tex]n=439[/tex]:

[tex]\displaystyle \text{Margin of Error}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\text{Margin of Error}=\sqrt{\frac{0.14(1-0.14)}{439}}\\\\\text{Margin of Error}=\pm0.0166[/tex]

Answer:

Step-by-step explanation:

The original price of the car before 4 years will be $23,032.

Consider the function:

y = P (1 ± r) ˣ

Where x is the number of times this growth/decay occurs, P = original amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %

A Naomi's car exponentially depreciates at a rate of 8% per year.

If Nina bought the car when it was 4 years old for $16,500.

Then the original price will be

16500 = P(0.92)⁴

16500 = 0.716P

       P = $ 23,032

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The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]

The given parameters are:

The foci of a hyperbola are represented as:

Foci = (k ± c, h)

The center is:

Center = (h,k)

And the directrix is:

Directrix, x = h ± a²/c

By comparison, we have:

k ± c = ±5

h = 0

h ± a²/c = ±2

Substitute h = 0 in h ± a²/c = ±2

0 ± a²/c = ±2

This gives

a²/c = 2

Multiply both sides by c

a² = 2c

k ± c = ±5 means that:

k ± c = 0 ± 5

By comparison, we have:

k = 0 and c = 5

Substitute c = 5 in a² = 2c

a² = 2 * 5

a² = 10

Next, we calculate b using:

b² = c² - a²

This gives

b² = 5² - 10

Evaluate

b² = 15

The hyperbola is represented as:

[tex]\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1[/tex]

So, we have:

[tex]\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1[/tex]

Evaluate

[tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]

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The probability that a student who does not have a dog has a cat is 7/10.

Probability determines the chances that a random event would happen. The odds that the random event would happen lies between 0 and 1.

The probability that a student who does not have a dog has a cat = number of students that do not have a dog but has a cat / total number of students that do not own a dog

=  7/10.

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Surface area is all the area of all sides while volume is the amount of space (a substance) occupies in a solid.

For example:

A cube has a length,breadth and height of 5cm,find:

a) surface area of the cube;

b) and the volume of the cube.

a) area of one side of the cube = 5 x 5

                                                    = 25cm²

Total surface area = 25cm x 6 (a cube has 6 sides)

                               = 150cm²

b) volume of cube = length x breadth x height

                              = 5 x 5 x 5

                              = 125cm³

Hope this helps you :]

p.s. can you mark me as the brainliest? <3

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

As we know, all sides of a Rhombus are equal to each other ~ so we can conclude that :

[tex]\qquad \sf  \dashrightarrow \:4x - 16 = 2x + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:4x - 2x = 6 + 16[/tex]

[tex]\qquad \sf  \dashrightarrow \:2x = 22[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 22 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 11[/tex]

Now, plug in the value of x in any equation to get the side length of rhombus ~

[tex]\qquad \sf  \dashrightarrow \:2x + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:2(11) + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:22 + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:28 \: \: units[/tex]

Side PS = Side QR = 28 units

Step-by-step explanation:

73° starting temperature.

every hour -2° for 4 hours.

that means -2×4 = -8° during 4 hours.

so, the resulting temperature is

73 - 8 = 65°

Answer:

By using the pythsgorean theorem! simple

Answer:[tex]\sqrt{155}[/tex]

Step-by-step explanation:

Oh god pythagorean triples got thrown out the window for this one. This will be a bit ugly.

First, we find the other side length of the rectangle using the pythagorean theorem.

Then, we use that side length in ANOTHER pythagorean theorem to get our answer.

Well, we know that the side length is [tex]\sqrt{5^{2}+9^{2} }[/tex]

We'll use whatever that number is, let's call it x for now, in our other expression:

[tex]\sqrt{x^{2}+7^{2}}[/tex]

So we can do this in one clean equation by substituting our first equation as x in the second one.

Or do them separately. Your choice.

Anyways, try to solve this one now that you know what to do. If you need more help then message.

Answer:

4/7 or 57 percent rounded up

Step-by-step explanation:

initially, you put 8/14 as a fraction then divide both the top and bottom by 2 to get 4/7 as that's the lowest you can get the number reduced.

Answer:

62.8ft

Step-by-step explanation:

20/2=10 so 10*2=20 so 20*3.14=62.8

62.8

Answer:

314

Step-by-step explanation:

20/2 = 10

10 * 10 = 100

3.14 * 100 = 314

Answer:

864

Step-by-step explanation:

First, you multiply 2 and 6, so it's 12, and multiply it by 144, so it's 1728, and divide it by 2. Therefore, it's 864!

Answer:

The Archimedes Principle

Step-by-step explanation: He took the 5 kg crown and dipped it in a vessel full of water. He calculated the displaced water.

Then he took 5 kg pure gold bricks and dipped it in a vessel full of water. He then calculated the displaced water and he found that the vessel with pure gold bricks displaced more water than the vessel with the crown. This is the Archimedes principle which states that the body at rest in a fluid is acted upon by a force pushing upward called the buoyant force, which is equal to the weight of the fluid that the body displaces.

Hope it helps you:))))

Have a good day

Answer:

Archimedes Principle

Step-by-step explanation:

Archimedes used the principle of buoyancy, which states that an object immersed in a fluid experiences an upward force equal to the weight of the fluid it displaces. By applying this principle, Archimedes was able to determine the density of an object and distinguish between real gold and fake gold objects.

To solve his problem, Archimedes first measured the weight of the suspect gold object on a scale. He then filled a container with water and recorded the amount of water displaced when the object was submerged. According to the principle of buoyancy, the weight of the water displaced by the object is equal to the weight of the object itself.

Next, Archimedes compared the weight of the object to the weight of an equivalent volume of pure gold. Since the density of gold is known, he could calculate the expected weight of a genuine gold object with the same volume as the suspect object. If the weight of the suspect object matched the expected weight, it was likely made of real gold. However, if the weight was significantly different, it indicated that the object was made of a less dense material, such as a gold alloy or another metal.

By using the principle of buoyancy and comparing the weight of objects to the weight of the water they displaced, Archimedes devised a method to identify fake gold objects and ensure the integrity of the king's treasure. This principle is known as Archimedes' principle and has since become a fundamental concept in physics.

Answer:

$986.28

Step-by-step explanation:

$124.21 + $211.94 = $336.15

700 - 336.15 = 363.85

622.43 + 363.85 = 986.28

Answer:

It is isosceles by the base angles theorem. It states that when the base angles are equal, the triangle is isosceles.

Step-by-step explanation:

unknown measure : 50°

Answer:

It would be about 1/4

Step-by-step explanation: