An equilateral triangular plate with sides 6 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s^2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m^3.) rhog^3(3)^1/2 _______ dx = _______ N

Answer:

  5 feet

Step-by-step explanation:

"Twice as tall" means "2 times as tall".

  2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft

The child's mother is 5 feet tall.

Answer:

The mother is 5ft tall

Step-by-step explanation:

2 1/2 + 2 1/2 = 5ft

2ft+2ft = 4ft

1/2+1/2= 1ft

4ft+1ft = 5ft

Answer:

1/7

Step-by-step explanation:

There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7

Answer:

1/7

Step-by-step explanation:

The number from the list that is less than 2 is 1.

1 number out of a total of 7 numbers.

= 1/7

Answer:

7). y = 140

8). x = 9

Step-by-step explanation:

Question (7).

All-right pencil factory will produce the graphite pencils, table formed will represent a linear graph.

Three points on the graph are (12, 42) and (18, 63), (40, y)

Slope of the line passing through these points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{63-42}{18-12}[/tex] = [tex]\frac{y-42}{40-12}[/tex]

[tex]\frac{21}{6}[/tex] = [tex]\frac{y-42}{40-12}[/tex]

3.5 = [tex]\frac{y-42}{40-12}[/tex]

98 = y - 42

y = 140

Question (8),

If a bicyclist rides at a constant rate, table formed will represent a linear graph.

Slope of a line passing through three points (2, 25), (5, 62.5) and (x, 112.5) given in the table,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{62.5-25}{5-2}=\frac{112.5-62.5}{x-5}[/tex]

[tex]\frac{37.5}{3}=\frac{50}{x-5}[/tex]

37.5x - 187.5 = 150

37.5x = 337.5

x = 9

Answer:

The common difference is 1/2

Step-by-step explanation:

Data obtained from the question include:

3rd term (a3) = 0

Common difference (d) =.?

From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:

a7 – 2a4 = 1

Recall:

a7 = a + 6d

a4 = a + 3d

a3 = a + 2d

Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.

But, a3 = 0

a3 = a + 2d

0 = a + 2d

Rearrange

a = – 2d

Now:

a7 – 2a4 = 1

Substituting the value of a7 and a4, we have

a + 6d – 2(a + 3d) = 1

Sustitute the value of 'a' i.e –2d into the above equation, we have:

–2d + 6d – 2(–2d + 3d) = 1

4d –2(d) = 1

4d –2d = 1

2d = 1

Divide both side by 2

d = 1/2

Therefore, the common difference is 1/2

***Check:

d = 1/2

a = –2d = –2 x 1/2 = –1

a3 = 0

a3 = a + 2d

0 = –1 + 2(1/2)

0 = –1 + 1

0 = 0

a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2

a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2

= (–2 + 3)/2 = 1/2

a7 – 2a4 = 1

2 – 2(1/2 = 1

2 – 1 = 1

1 = 1

Answer:

7,273 Pesos

Step-by-step explanation:

1 Peso = $0.055

The formula below converts pesos to dollars:

1 Peso x 0.055 = $1

The formula below converts dollars to pesos:

$1/0.055= 1 Pesos

We use the second formula because we are coverting

from dollars to pesos.

$400/0.055=7,273 Pesos

Answer:

22

Step-by-step explanation:

If one Mexican peso is .055 U.S dollars that means it has a greater value than the dollar so we can make the following ratio 1:.055. But if the .055 is a 400 1:400 we just multiply to get 22.

Answer:

Ans) 42.7%

Step-by-step explanation:

For a continuous probability distribution, a curve known as probability density function contains information about these probabilities.

in the given range -

The probability that a continuous random variable = equal to the area under the probability density function curve

The probability that the value of a random variable is equal to 'something' is 1.

As per the diagram,

Weight of chocolate bar between 4 ounces and 7 ounces is highlighted in the blue part. That area is said to be 0.42739 and the total area under the curve is 1.

Hence required probability

=0.42739/1=0.42739

Ans) 42.7%

Round to nearest tenth of a percent

Answer:

-7

Step-by-step explanation:

4 + (−3 − 8)

PEMDAS

Parentheses first

4 + (-11)

Add and subtract next

-7

Answer:

first I'm using BODMAS

4+(-11)

= -7

hope it helps

Answer:

7

Step-by-step explanation:

This a special 90° 45° 45° triangle and is an Isosceles triangle at the same time

Of one of the equal side is 7 than the other one too must be 7

Answer:2/3

Step-by-step explanation:

Given that the length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. The domain of the function is (0, ∞).

The domain of a function is the set of all possible inputs for the function. In other words, domain is the set of all possible values of x. In this question, x is the width of the rectangle. Width of a rectangle existing in two dimensional space, cannot be negative or zero. Thus it is the set of all positive real numbers, or we say, (0, ∞).

Learn more about domain of a function here

https://brainly.com/question/13113489

#SPJ2

Answer:

She makes conclusion about a population that is not well represented by the sample.

Step-by-step explanation:

The conclusion she is making is about a population that is not well represented by her sample: the population is the homeowners in the nation, but the sample is made of homeowners or only her state.

The population about which she can make conclusions with this sample is the homeowners of her state, given that the sampling is done right.

Answer: The sample is biased

Step-by-step explanation:

yeah,when 15-7=8

the number is 8

Answer:

CI: {0.4085; 0.6647}

Step-by-step explanation:

The confidence interval for a proportion (p) is given by:

[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]

Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:

[tex]p=\frac{22}{41}=0.536585[/tex]

Thus the confidence interval is:

[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]

The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}

Answer:

(190-5a)°

Step-by-step explanation:

Sum of internal angles of a triangle equals to 180°

If the third angle is x, then we have:

The third angle is: (190-5a)°

Answer:

see below

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

4x - 3y = 12

Solve for y

Subtract 4x from each side

4x-4x - 3y =-4x+ 12

-3y = -4x+12

Divide by -3

-3y/-3 = -4x/-3 + 12/-3

y = 4/3x -4

The slope is 4/3 and the y intercept is -4

The slope is Positive

Answer:

11.70% probability that the mean height for the sample is greater than 64 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 63.5, \sigma = 2.96, n = 50, s = \frac{2.96}{\sqrt{50}} = 0.4186[/tex]

What is the probability that the mean height for the sample is greater than 64 inches?

This is 1 subtracted by the pvalue of Z when X = 64.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{64 - 63.5}{0.4186}[/tex]

[tex]Z = 1.19[/tex]

[tex]Z = 1.19[/tex] has a pvalue of 0.8830

1 - 0.8830 = 0.1170

11.70% probability that the mean height for the sample is greater than 64 inches

Answer:

The percentage of area is between Z =-2 and Z=2

P( -2 ≤Z ≤2) = 0.9544 or 95%

Step-by-step explanation:

Explanation:-

Given data Z = -2 and Z =2

The probability that

P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)

                   = 0.5 + A(2) - ( 0.5 - A(-2))

                  = A (2) + A(-2)

                 = 2 × A(2)     (∵ A(-2) = A(2)

                = 2×0.4772

              = 0.9544

The percentage of area is between Z =-2 and Z=2

P( -2 ≤Z ≤2) = 0.9544 or 95%

Answer:

Each table is $6 and each chair is $2.50

Step-by-step explanation:

Step-by-step explanation:

pnotgrt8rthan4 = 3 ÷ 7 × 100

= 42.8571428571 / 43%

Answer:

2/3

Step-by-step explanation:

There are 2 numbers out of 3 that fit the rule, 1 and 3. There is a 2/3 chance picking one of them.

Answer:

Step-by-step explanation:

This is the answer because one number that is select is one. A number greater than 2 is 3. SO it is 2/3.

Answer:

a) 16xy³

Step-by-step explanation:

For a binomial expansion (a + b)ⁿ, the r+1 term is:

nCr aⁿ⁻ʳ bʳ

Here, a = 4x, b = y, and n = 4.

For the fourth term, r = 3.

₄C₃ (4x)⁴⁻³ (y)³

4 (4x) (y)³

16xy³

Answer:

3/10ths of the money

Step-by-step explanation:

Add together the two numbers to get the total.

Josh gets 30 percent and Lucy gets 70 percent.

3/10

Answer:

3/10

Step-by-step explanation:

3+7=10  

Josh=3

Lucy=7

Answer:

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 13, \sigma = 0.2[/tex]

What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster

We have to find the pvalue of Z when X = 13.36.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13.36 - 13}{0.2}[/tex]

[tex]Z = 1.8[/tex]

[tex]Z = 1.8[/tex] has a pvalue of 0.9641

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Answer:

x = 3 or x = -5

Step-by-step explanation:

x² + 2x - 15 = 0

Factor left side of equation.

(x - 3)(x + 5) = 0

Set factors equal to 0

x - 3 = 0

x = 3

x + 5 = 0

x = -5

Answer:

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 0.03?

This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So

X = 0.08

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.08 - 0.05}{0.015}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 0.02

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.02 - 0.05}{0.015}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Answer:

[tex]153.86 \: {units}^{2} [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]

Answer:

153.86 [tex]units^{2}[/tex]

Step-by-step explanation:

Areaof a circle = πr^2

[tex]\pi = 3.14[/tex](in this case)

[tex]r^{2} =7[/tex]

A = πr^2

= 49(3.14)

= 153.86

Answers:

A ' = (-2, -3)

B ' = (0, -3)

C ' = (-1, 1)

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

Explanation:

To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.

Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]

Applying this rule to the three given points will mean....

The diagram is provided below.

Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.

Answer:

(-2,-3)...(0,-3)...(-1,1)

Step-by-step explanation:

Answer:

by using distance formula

d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

by putting the values of coordinates

[tex]d=\sqrt{(2-(-0.5))^2+(5-(-5))^2}[/tex]

[tex]d=\sqrt{(2+0.5)^2+(5+5)^2}[/tex]

[tex]d=\sqrt{(2.5)^2+(10)^2}[/tex]

[tex]d=\sqrt{6.25+100}[/tex]

[tex]d=\sqrt{106.25}[/tex]

[tex]d=10.3[/tex]

Step-by-step explanation:

i hope this will help you :)

Answer:

Do you have an image because I'm a bit confused with you just asking the measure of PSQ.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Given  

y

=

2

x

2

−

4

x

+

3

The y-intercept is the value of  

y

when  

x

=

0

XXX

y

=

2

(

0

)

2

−

4

(

0

)

+

3

=

3

For a quadratic in the general form:

XXX

y

=

a

x

2

+

b

x

+

c

the determinant  

Δ

=

b

2

−

4

a

c

indicates the number of zeros.

Δ

⎧

⎪

⎨

⎪

⎩

<

0

==⇒  

no solutions

=

0

==⇒  

one solution

>

0

==⇒  

two solutions

In this case

XXX

Δ

=

(

−

4

)

2

−

4

(

2

)

(

3

)

<

0

so there are no solutions (i.e. no values for which the expression is equal to zero).

This can also be seen from a graph of this equation:

graph{2x^2-4x+3 [-6.66, 13.34, -0.64, 9.36]}

Answer link

Vinícius Ferraz

Nov 13, 2015

(

0

,

3

)

Explanation:

x

=

0

⇒

y

=

0

−

0

+

3

y

=

0

⇒

x

=

−

b

±

√

b

2

−

4

a

c

2

a

a

=

2

,

b

=

−

4

,

c

=

3

But  

Δ

< 0, then there is no real root  

(

x

0

,

0

)

.

Answer:

it has 2

Step-by-step explanation:

I hope this helps!