A die is rolled 3 times. What is the probability of getting 1's on each roll?

Answer:

\(x=0.04m\)

Step-by-step explanation:

From the question we are told that:

Diameter \(d=24cm\)

Radius \(r=24/2=>12cm\)

Igniter distance \(d_g=9cm\)

Generally the equation for depth  is mathematically given by

 \(r^2=4d_gx\)

Therefore

 \(x=\frac{r^2}{4d_g}\)

 \(x=\frac{12^2}{4*9}\)

 \(x=4cm\)

 \(x=0.04m\)

Answer:

5

Step-by-step explanation:

One is given that the scale factor to get from triangle (ABC) to triangle (DEF) is (\(\frac{1}{2}\)). This essentially means that one has to multiply the sides of (ABC) by (\(\frac{1}{2}\)) to get the corresponding side in the triangle (DEF).

As one can see, side (AB) corresponds to side (DE), therefore, multiply the length of (AB) by (\(\frac{1}{2}\)) to get the side of (DE).

AB * \(\frac{1}{2}\) = DE

Substitute,

\(10*\frac{1}{2}=DE\)

Simplify,

\(5=DE\)

(\(ED\)) is another way of naming segment (\(DE\)) this is explicitly clear from the diagram of the tirnagles.

The measure of angle mKLM is 31.5°.

The angle mKLM can be found using the property of inscribed angle. An inscribed angle is an angle formed by two chords that intersect inside of a circle. The measure of an inscribed angle is half of the measure of its intercepted arc. In this case, the measure of the intercepted arc is the angle mKNM, which is 63°. Therefore, the measure of the inscribed angle mKLM is half of 63°, which is 31.5°.

Formula:

mKLM = 1/2 (mKNM)

mKLM = 1/2 (63°)

= 31.5°

mKLM = 31.5°

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Answer:

Step-by-step explanation:

there is no solution:

6-2(3-2x) = -4(3-x)

6-6+4x= -12+4x

4x= -12+4x

0=-12

Answer:

There are no solutions.

Step-by-step explanation:

6-2(3-2x)=-4(3-x)

6 + -6 + 4x = -12 + 4x

4x = 4x - 12

-4     -4

0 = -12

The weekly gross pay is 1040. The solution is obtained using arithmetic operations.

What are arithmetic operations?

There are four basic operations which are listed as follows:

•Addition(‘+’): This operation deals with finding the sum.

•Subtraction(‘-’): This operation deals with finding the difference.

•Multiplication(‘×’): This operation deals with finding the product.

•Division(‘÷’): This operation deals with finding the quotient.

Assumption: Weekly working hours are 40.

Since, the hourly rate is 20 per hour and working hours per week are 40

So, the weekly pay comes out to be 40*20= 800

The overtime rate is time and a half which comes out to be

20*1.5= 30 per hour

The overtime hours are 48-40=8 hours

So, the weekly overtime pay comes out to be 8*30= 240

The total pay= 800+240= 1040

Hence, the weekly gross pay is 1040.

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Answer:

hi kermit

Step-by-step explanation:

the answer is 4 to 10 its a 50 50 chance of wrong or right

Answer:

b

Step-by-step explanation:

I'm going with my gut along with what the image shows me.

The solution of the absolute function is  

t < -4

 t > 22/5

In interval notation it will be    (-∞,-4) ;(22/5,+∞).

What is absolute function?

An absolute value function is a function in algebra which consists of the variable in the absolute value bars. In general form of the absolute value function is f(x) = a |x - h| + k  where h, k are constants and the most commonly used form of this function is f(x) = |x|. Here a = 1 and h = k = 0.

The Absolute Value term is |5t-1|

For the Negative case it will be -(5t-1)

For the Positive case it will be  (5t-1)

at first we will solve for negative case:

-(5t-1) > 21

    Multiplying by the minus sign we get,

     -5t+1 > 21

    Rearranging and Adding up we get,

     -5t > 20

    Dividing both sides by 5

     -t > 4

    Multiplying both sides by (-1) we get,

     t < -4

 Now we will solve for positive case:

(5t-1) > 21

    Rearranging and Adding  up we get,

     5t > 22

    Dividing both sides by 5 we get,

     t > (22/5)

Hence the solution of the absolute function is  

t < -4

 t > 22/5

In interval notation it will be    (-∞,-4) ;(22/5,+∞).

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The succession time should be atleast t=9 to get a final copy that is less than 15% of the original size.

Lyndie is making reduced copies of a photo 25 centimeters in height. She sets the copy machine to an 80% size reduction.

Part a

Let the size of the page be q, when it is reduced to 80%, its size becomes

= 80%*q

= 0.80(q)

= 0.80q

When you want to return it into its original size q, you need to multiply the page by x

such that

x(0.80q) = q

\(x = \frac{q}{(0.80q)}\)

\(x = \frac{1}{0.80}\)

x = 1.25

x = 125%

Hence, the enlargement needed to be done is 25%.

Part b

The size of the page after t number of copying done is given by

\(C(t) = C_{0}(0.80)^{t}\)

where \(C_{0}\) is the original size of the page.

We want to find a value for t ∈ Ζ such that

\(\frac{C(t)}{C_{0} } = (0.80)^{t}\)

\(0.15 \leq (0.80)^{t}\)

To solve this equation, we can apply natural logarithm.

≅ \(In(0.15) \leq In(0.80)^{t} \\\\In(0.15) \leq tIn(0.80)\\\\\frac{In(0.15)}{In(0.80)} \leq t\\ \\0.80 \leq t\)

Hence the answer is the succession time should be atleast t = 9 to get a final copy that is less than 15% of the original size.

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Answer:

x = 2.3

Step-by-step explanation:

you divide both sides of the equation by 10

Answer:

still a square units.

Step-by-step explanation:

the answer x=2 hope it helps :D

Answer:

600 whiskers

Step-by-step explanation:

If you multiply 24 by 25 you get 600

Answer:

Step-by-step explanation:

3x+8y=-5

-2x+2y=18

Ok, so you want to get either x or y to cancel out so lets multiply the first equation by 2 and the second equation by 3.

6x+16y=-10

-6x+6y=54

Now x can cancel out. The new equation is:

22y=44

y=2

Now you input 2 into one of the original problems.

-2x+2(2)=18

-2x+4=18

Now subtract 4 from both sides.

-2x=14

Divide

x=-7

Now check your answer.

-2(-7)+2(2)=18

14+4=18

El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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Step-by-step explanation:

The measure of CED is p degree.

In triangle ABC and EDC,(Given)(Vertical opposite angles)

By AA rule of similarity,

Corresponding angles of similar triangles are same.

Therefore the measure of CED is p degree.

pls give brainest

4 hours ---> 6 kilowatts

1 hour -----> x kilowatts

answer:

1.5 kilowatts per hour

we have that

total coins=162

nickels=162*(2/9)=36

dimes=162*(2/9)=36

quarters=162-(36+36)=90

therefore

the ratio of Riley's nickels to dimes to quarters is

36:36:90

simplify

12:12:30

6:6:15

2:2:5

\({ \boxed{ \red{ \bold{3072}}}}\)

Step-by-step explanation:

Given,

\({ \green{ \sf{ {ar}^{2} = 24}}} \: { \to} \: { \tt{ {eq}^{n} (1)}}\)

\({ \green{ \sf{ {ar}^{5} = 192}}} \: { \to} \: { \tt{ {eq}^{n} (2)}}\)

From Eqⁿ (2),

\({ \green{ \sf{ {ar}^{2}. {r}^{3} = 192}}}\)

\({ \green{ \sf{24. {r}^{3} = 192}}}\)

\({ \green{ \sf{ {r}^{3} = \frac{192}{24}}}} \)

\({ \green{ \sf{ {r}^{3} = 8}}}\)

\({ \green{ \sf{ {r}^{3} = {2}^{3}}}} \)

\({ \boxed{ \purple{ \sf{r = 2}}}}\)

From Eqⁿ (1)

\({ \blue{ \sf{ {ar}^{2} = 24}}}\)

\({ \blue{ \sf{a {(2)}^{2} = 24}}}\)

\({ \blue{ \sf{4a = 24}}}\)

\({ \blue{ \sf{a = \frac{24}{4}}}} \)

\({ \boxed{ \purple{ \sf{a = 6}}}}\)

10th term is,

\({ \orange{ \sf{ {ar}^{9} }}}\)

\({ \orange{ \sf{6 {(2)}^{9}}}} \)

\({ \orange{ \sf{6(512)}}}\)

\({ \bold{ = }}{ \boxed{ \red{ \bold{3072}}}}\)

Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6

The parameters are given as:

Number - 4

Fraction - 3/6

The following steps can be used to determine the product as the product of a whole number and a unit fraction:

Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.

Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.

Step 3 - Write the given expression.

4 * 3/6

Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.

4 * 3 * 1/6

Step 5 - Simplify the above expression.

12 * 1/6

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Answer:

(4)

Step-by-step explanation:

element =4

frequency=1

cumulative frequency-=1

relative frequency=1

cumulative relative frequency=1

The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

a. The missing values of the logarithm expression is log₃(40).

b. The missing values of the logarithm expression is log₅(8).

c. The missing values of the logarithm expression is  log₂(1/25).

The missing values of the logarithm expression is calculated as follows;

(a). log₃5 + log₃8, the expression is simplified as follows;

log₃5 + log₃8 = log₃(5 x 8) = log₃(40)

(b). The log expression is simplified as;

log₅3 - log₅X = log₅3/8

log₅X = log₅8

X = 8

(c).  The log expression is simplified as;

-2log₂5 = log₂Y

log₂5⁻² = log₂Y

5⁻² = Y

1/25 = Y

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Answer:

the answer is below

Step-by-step explanation:

The z score is used to calculate by how many standard deviations the raw score is above or below the mean. The z score is given as:

\(z=\frac{x-\mu}{\sigma}\\\\\mu=mean,\sigma=standard\ deviation\)

1) For x = 3

\(z=\frac{x-\mu}{\sigma}=\frac{3-4}{2}=-0.5\)

For x = 6

\(z=\frac{x-\mu}{\sigma}=\frac{6-4}{2}=1\)

P(3 ≤ x ≤ 6) = P(-0.5 ≤ z ≤ 1) = P(z < 1) - P(z < -0.5) = 0.8413 - 0.3085 = 0.5328

2) For x = 50

\(z=\frac{x-\mu}{\sigma}=\frac{50-40}{15}=0.67\)

For x = 70

\(z=\frac{x-\mu}{\sigma}=\frac{70-40}{15}=2\)

P(50 ≤ x ≤ 70) = P(0.67 ≤ z ≤ 2) = P(z < 2) - P(z < 0.67) = 0.9772 - 0.7486 = 0.2286

3) For x = 8

\(z=\frac{x-\mu}{\sigma}=\frac{8-15}{3.2}=-2.19\)

For x = 12

\(z=\frac{x-\mu}{\sigma}=\frac{12-15}{3.2}=-0.94\)

P(8 ≤ x ≤ 12) = P(-2.19 ≤ z ≤ -0.94) = P(z < -0.94) - P(z < -2.19) = 0.1736 - 0.0143 = 0.1593

4) For x = 30

\(z=\frac{x-\mu}{\sigma}=\frac{30-20}{3.4}=2.94\)

P(x ≥ 30) = P(z ≥ 2.94) = 1 - P(z < 2.94) = 1 - 0.9984 = 0.0016

5)  x = 90

\(z=\frac{x-\mu}{\sigma}=\frac{90-100}{15}=-0.67\)

P(x ≥ 90) = P(z ≥ -0.67) = 1 - P(z < -0.67) = 1 - 0.2514 = 0.7486

6)  For x = 10

\(z=\frac{x-\mu}{\sigma}=\frac{10-15}{4}=-1.25\)

For x = 20

\(z=\frac{x-\mu}{\sigma}=\frac{20-15}{4}=1.25\)

P(10 ≤ x ≤ 20) = P(-1.25 ≤ z ≤ 1.25) = P(z < 1.25) - P(z < -1.25) = 0.8944 - 0.1056 = 0.7888

7)  For x = 7

\(z=\frac{x-\mu}{\sigma}=\frac{7-5}{1.2}=1.67\)

For x = 9

\(z=\frac{x-\mu}{\sigma}=\frac{9-5}{1.2}=3.33\)

P(7 ≤ x ≤ 9) = P(1.67 ≤ z ≤ 3.33) = P(z < 3.33) - P(z < 1.67) = 0.9996 - 0.9525 = 0.0471

8)  For x = 40

\(z=\frac{x-\mu}{\sigma}=\frac{40-50}{15}=-0.67\)

For x = 47

\(z=\frac{x-\mu}{\sigma}=\frac{47-50}{15}=-0.2\)

P(40 ≤ x ≤ 47) = P(-0.67 ≤ z ≤ -0.2) = P(z < -0.2) - P(z < -0.67) = 0.4207 - 0.2514 = 0.1693

9)  x = 120

\(z=\frac{x-\mu}{\sigma}=\frac{120-10}{15}=7.33\)

P(x ≥ 120) = P(z ≥ 7.33) = 1 - P(z < 7.33) = 1 - 0.9999 = 0.001

10) x = 2

\(z=\frac{x-\mu}{\sigma}=\frac{2-3}{0.25}=-4\)

P(x ≥ 2) = P(z ≥ -4) = 1 - P(z < -4) = 1 - 0.0001 = 0.999

From the given linear function, it is found that:

The density of the substance is of 1.5 grams per milliliter.

The slope-intercept representation of a linear function is given by the rule presented as follows:

y = mx + b

The coefficient m is the relevant coefficient of the linear function in this problem, which is the slope, representing by how much the output (in this case the mass) changes when the input (in this case the volume), increases by 1.

The density is given by the mass divided by volume, that is:

Density = mass/volume.

This graph is a proportional relationship, which is a special case of a linear function(intercept of 0), hence the density is calculated applying the division of the mass by the volume at any point of the graph.

Choosing point (2,3), the density is given as follows:

Density = 3/2 = 1.5 grams per milliliter.

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Answer:

Buffalo

Thats the answer because temp is decreasing back so 10 is higher plus lower than all

Answer:

12 cm is your answer right answer

1) To translate into a mathematical expression, " The product of -26 and the difference of x and y" we can write out as product this way:

2) Hence, -26x +26y it's a simplified version of -26(x-y)

Answer:

5√2, 5

Step-by-step explanation:

in a 90 45 45 triangle, each leg is the same legnth

the hypotenuse of a 90 45 45 triangle is x√2

x being the measure of the leg