B is the midpoint of ac. ab equals 4x-1 and bc equals 5x-5. what is the length of bc?

Answer:

24 messages a day

Step-by-step explanation:

Answer: 104 yards

Step-by-step explanation:

First and foremost, we need.to know that: 1 yard = 3 feet

Since she wants each balloon string to be 6 feet long and she wants to get 52 balloons. The total feet that is required for the balloon would be:

= 52 × 6

= 312 feet

Then we convert 312 feet to yard. This would be:

= 312 feet / 3 feet

= 104 yards

Answer:x=−3 2​/3

​​

Step-by-step explanation:

We can infer that young people drive more quickly than older people because the interval does not contain zero.

We need to construct the 90% confidence interval for the difference between the population means μ1 - μ2, in the case that the population standard deviations are not known. The following information has been provided about each of the samples;

Sample Mean 1 (X1) = 79

Sample Standard Deviation 1 (s1) = 2.2360

Sample Size 1 (N₁) = 9

Sample Mean 2 (X2) = 73

Sample Standard Deviation 2 (s2) = 1.732

Sample Size 2 (N₂) = 7

Based on the information provided, we assume that the population variances are equal, so then the number of degrees of freedom is,

df = n + n₂ - 2 = 9 + 7 - 2

   = 14

The critical value for a = 0.1 and df = 14 degrees of freedom is the = t1 - a/2n - 1 = 1.761.

The corresponding confidence interval is computed as shown below,

Since the population variances are assumed to be equal, we need to compute the pooled standard deviation, as follows:

Sp =\(\sqrt{\frac{(n1 - 1)s1^2+(n2 - 1)s2^2}{n1+n2-2} }\) = 2.035

Since we assume that the population variances are equal, the standard error is computed as follows:

se = Sp*\(\sqrt{\frac{1}{n1}+\frac{1}{n2} }\)

    = 1.026

Now, we finally compute the confidence interval;

CI = (X1-X2-te * se, X1 X2+te * se)

   = (79-73-1.761 x 1.026, 79-73 +1.761 x 1.026)

   = (4.193, 7.807)

Therefore, based on the data provided, the 90% confidence interval for the difference between the population means μ - μg is 4.193< μ - μg < 27.807, which indicates that we are 90% confident that the true difference between population means is contained by the interval (4.193, 7.807).

As the interval does not contain zero, we can say that young people drive faster than old people.

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The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store, with both stores having the same price.

The difference between the two terms is that "difference" refers to the way in which two or more things are not the same, whereas "difference" is more of a comparison between two or more things.

The difference between the lowest price in store 1 and the lowest price in store 2 is the difference between the first digit of each store's key. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1.

The difference between the highest prices in store 1 and store 2 is the difference between the last digit of each store's key. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0.

The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1. This difference is reflected in the lowest prices of each store, with store 1 having a lower price than store 2.

The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0. This difference is reflected in the highest prices of each store, with both stores having the same price.

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You can use the following formula to calculate the surface area of the right rectangular prism:

\(\sf SA=2(wl+lh+hw)\)

Where "w" is the width, "l" is the length, and "h" is the height.

Knowing that this right rectangular prism  has a length of 8 centimeters, a width of 3 centimeters and a height of 5 centimeters, you can substitute these values into the formula.

Then, the surface of the right rectangular prism is:

\(\sf SA=[(3 \ cm\times 8 \ cm)+( 8 \ cm\times 5 \ cm)+(5 \ cm\times3 \ cm)]\)

\(\Rightarrow\sf SA=158 \ cm^2\)

Gwen is incorrect in stating that the sum of -1 3/4 and 2 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4. The two expressions yield different results.

To evaluate the expressions, let's consider each one separately and calculate their values.

Expression 1: -1 3/4 + 2 1/2

-1 3/4 can be written as -7/4 in improper fraction form, and 2 1/2 can be written as 5/2 in improper fraction form. Adding these fractions, we get:

-7/4 + 5/2 = (-7*2 + 5*4)/(4*2) = (-14 + 20)/8 = 6/8 = 3/4.

Expression 2: (2 and 1/2) - (1 and 3/4)

2 and 1/2 is equivalent to 5/2, and 1 and 3/4 is equivalent to 7/4. Subtracting these fractions, we get:

(5/2) - (7/4) = (10/4) - (7/4) = 3/4.

As we can see, the sum of -1 3/4 and 2 1/2 is 3/4, whereas the difference between 2 and 1/2 and 1 and 3/4 is also 3/4. Therefore, Gwen's statement is correct.

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The diameter of the tank is 25.8 feet.

We are given the volume of water tank. Also, we are provided the formula relating volume and density.

Rewriting the formula -

V = 1/6×π×d³, where d represents the diameter. Taking the value of π as 3.14

Rewriting the formula according to diameter -

d³ = 6V/π

Keep the values in formula to find the value of diameter of water tank

d³ = 6×9000/3.14

Performing multiplication and division to find the value of diameter

d³ = 54000/3.14

Performing division to find the value of diameter of water tank

d³ = 17197.45

d = ∛17197.45

Taking square root to find the value of diameter of water tank

d = 25.8 feet

Hence, the diameter of tank is 25.8 feet.

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We have to solve the following inequality:

Answer:

Graphs 1, 2, 3

Step-by-step explanation:

Graph 1 represents a linear function with a domain containing all real numbers, as any input substituted into the equation or function will produce a corresponding output. The arrows on the opposite ends of the line represents the infinite input values that have its corresponding output values.

Graph 2 represents a quadratic function with a domain containing all real numbers, as it does not have any constraints in terms of input values.  As it opens up, the graph of the parabola infinitely widens (horizontally).

Graph 3 represents an absolute value function with a domain containing all real numbers. Similar to the explanation for graph 2 on quadratic functions, the downward-facing graph of the given absolute value function widens infinitely horizontally, as it does not have any constraints on input values.

The series ∑=0infinity(3)2(2)! converges exactly to -9/2.

We can write the series using the Maclaurin series for cos(x) as follows:

∑=0infinity^n(3^(2n))/(2n)! = cos(3i)

The Maclaurin series for cos(x) is:

cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...

Substituting x = 3i, we get:

cos(3i) = 1 - (3i)^2/2! + (3i)^4/4! - (3i)^6/6! + ...

Simplifying the powers of i, we get:

cos(3i) = 1 - 9/2! - i(3)^3/3! + i(3)^5/5! - ...

The imaginary part of cos(3i) is:

Im(cos(3i)) = -3^3/3! + 3^5/5! - ...

The series for the imaginary part is an alternating series with decreasing absolute values, so it converges by the Alternating Series Test. Therefore, the exact value of the series is the real part of cos(3i), which is:

Re(cos(3i)) = cosh(3) = (e^3 + e^-3)/2

Using a calculator or a computer program, we can evaluate cosh(3) and simplify to get:

cosh(3) = (e^3 + e^-3)/2 = (1/2)(e^6 + 1)/(e^3)

Therefore, the series ∑=0infinity(3)2(2)! converges exactly to -9/2.

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Answer:

500 pennies

Step-by-step explanation:

Given that

Carmen saved 592 pennies.

Her sister saved 128 pennies.

Together, they put 250 pennies in wrappers and took them to the bank

We need to find out the total number of pennies Carmen and her sister have left

So,

= 592 pennies + 128 pennies  - 250 pennies

= 470 pennies

= 500 pennies

Hey there! I'm happy to help!

The factors are the numbers you multiply to get 47. And they can't be fractions or numbers with fractions. They have to be integers (numbers without fractions).

So far, we see that we can multiply 1 and 47 to get 47. To see if there are any more, we see what numbers 1-10 we can divide by.

We cannot divide by 2 because 47 is odd.

We cannot divide by 3 because it gives us 15.6666...

We can't divide by 4 because 47 is odd.

We can't divide by 5 because 47 does not have a 5 or 0 in the ones place.

We can't divide by 6 because 47 is odd.

We can't divide by 7 because it gives us 6.714285....

We can't divide by 8 because 47 is odd.

We can't divide by 9 because it gives us 5.2222

And we obviously can't divide it by 10.

Therefore, the factors of 47 are 1 and 47. A number whose only factors are 1 and itself is called a prime number.

I hope that this helps! Have a wonderful day! :D

Answer: 47 is a prime number

The exponent of prime number 47 is 1 . Adding 1 to that exponent we get (1+1)=2

Factor of 47: 1, 47

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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If an employee has already measured out 59 pounds of wild rice. The  number of pounds of long grain brown rice should she add to make the blend is: 88.5 pounds of long grain.

Let x represent number of pounds of long grain

6.45×59+3.95x=(59+x)×4.95

380.55+3.95x =292.05+4.95x

380.55–x =292.05

-x=292.05-380.55

-x = -88.5

x = 88.5 pounds of long grain

OR

6.45×59+3.95x=(59+x)×4.95

x=(6.45-4.95)×59

x=1.5×59

x=88.5 pounds of long grain

Therefore If an employee has already measured out 59 pounds of wild rice. The  number of pounds of long grain brown rice should she add to make the blend is: 88.5 pounds of long grain.

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The value of angle HZG in the given diagram by using properties of angles is 142 degrees.

It is given to us in the question that HZJ = 38 degrees.

Angles that are vertically opposite to each other in nature have equal value. We can observe in the diagram that HZJ and GZF are vertically opposite angles, and hence they are equal.

So if HZJ = 38 degrees

Then GZF = 38 degrees.

AZJ and HZJ are complementary angles because their sum is equal to 90 degrees as can be observed from the diagram.

Therefore, AZJ + HZJ = 90 degrees

AZJ + 38 = 90

AZJ = 52 degrees

AZF = 90 degrees (Given in the diagram already).

Now, if we carefully observe the diagram, we will notice that HZG and GZF are supplementary angles as they together lie in a straight line formation, which means their sum must be 180 degrees.

Therefore,

GZF + HZG = 180 degrees

38 + HZG = 180

HZG = 180 - 38

HZG = 142 degrees

Therefore, the value of angle HZG in the given diagram is 142 degrees.

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The required polar form is as follows: `z=√2(cos(7π/4)+isin(7π/4))`

Let's first find the modulus `r` of the complex number `z=-1+1j`.

Modulus `r` of the complex number is given by the formula,|z|=√(x²+y²)

where `z=x+yj`

r=|z|=√((-1)²+1²)

=√(1+1)

=√2

`z=-1+1j=r(cosθ+isinθ)`

Now, we have the value of `r` which is `√2`.

To find the value of θ, we will use the formula,

θ=tan⁻¹(y/x)

θ=tan⁻¹(1/-1)

θ=-π/4

`z=-1+1j=r(cosθ+isinθ)`

  =√2(cos(-π/4)+isin(-π/4))

  =√2(cos(7π/4)+isin(7π/4))

The polar form of the complex number `z=-1+1j` is `z=√2(cos(7π/4)+isin(7π/4))`.

Thus, the polar form of the complex number `z=-1+1j` is `z=√2(cos(7π/4)+isin(7π/4))`.

The polar form that is necessary is as follows: `z=√2(cos(7π/4)+isin(7π/4))`.

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Answer:

Step-by-step explanation:

25, i think

Radiation from the sun heats the Earth's surface by means of rays that are trapped in the atmosphere and allow the Earth to have constant heat.

The surface of the Earth heats up due to the sun's rays that hit it and when they enter the atmosphere they are reflected on the surface being trapped between the atmosphere and the surface.

Another important aspect to keep in mind is that the rays strike at different angles throughout the Earth, for example:

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Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).

Then substituting u = ln(x) and du = dx/x gives

\(\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}\)

Sin 7° is equal to sin(0.1221) = 0.1218693.

We must multiply the supplied value by \(\pi\)/180 to convert the angle's degree value to its counterpart in radians.

According to the given information

The angle 7°, or sin 7 degrees, is located between 0° and 90°. (First Quadrant).

Sin 7° value = 0.1218693 because the sine function is positive in the first quadrant.

Sin 7 degrees has a numeric value of 0.121869343.

Another way to define sin 7 degrees is to use the radian equivalent of the angle (7 degrees) (0.12217 . . .).

Using the degree to radian conversion, we can see that 7 degrees equals 7° (\(\pi\)/180°) in radians. rad = 0.1221 . . .

Sin 7° is equal to sin(0.1221) = 0.1218693.

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the solutions to the quadratic formula x² + 10x - 25 = 0 are x = -5 + √50 and x = -5 - √50.

We can set up a proportion using the given information to estimate the number of LMC students who have a family, job, and go to school. Let's represent the number of LMC students who have a family, job, and go to school as "x".

Based on the sample of 67 LMC students, we have the proportion:

49 (number of students with family, job, and school) / 67 (sample size) = x (number of students with family, job, and school) / 7560 (total number of LMC students).

We can solve this proportion by cross-multiplying and then solving for "x":

49 * 7560 = 67 * x

x = (49 × 7560) / 67 ≈ 5652

Therefore, using the proportion, we estimate that approximately 5652 out of the total 7560 LMC students have a family, job, and go to school.

Bonus: To solve the equation x² + 10x - 25 = 0 using the quadratic formula, we can identify the coefficients a, b, and c. In this case, a = 1, b = 10, and c = -25.

Applying the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), we substitute the values and solve:

x = (-(10) ± √((10)² - 4(1)(-25))) / (2(1))

x = (-10 ± √(100 + 100)) / 2

x = (-10 ± √200) / 2

x = (-10 ± 2√50) / 2

x = -5 ± √50

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According to Weber's law, two items must differ in weight by "5 percent"of weight in order to detect a difference.

We are given that Weber's law

For weight discrimination, Weber’s law states that the JND is proportional to the weight of the stimulus.

The JND is defined as the smallest difference between two weights that can be detected by an observer.

The proportionality constant is known as Weber’s fraction and varies depending on the type of stimulus and the sensory modality involved.

For weight discrimination, Weber’s fraction is typically around 2-3%.

This means that two items must differ in weight by approximately 2-3% of their weight in order to detect a difference.

The difference of weight in percent is 5%, the correct option is A.

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Find the values at which the rational function is undefined before you can graph it.Any values that would result in a denominator of zero for a function are undefined.

f(x) Equals x in Example 1. (x - 3).

The graph of the function.

From the given graph , the vertical asymptote is at x=2

Lets find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator =0

f(x) = 1/2x

2x = 0

x= 0

The second function has vertical asymptote at x=2

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Step-by-step explanation:

Using the equation \(a^{2} + b^{2} = c^{2}\)

so \(a^{2} = 35\) and \(b^{2} =50\)

\(a^{2} + b^{2} = 85^{2}\)

Answer:

85 units²

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

The hypotenuse is the side opposite the right angle ( third side ) , then

area = 35 + 50 = 85 units²

Answer:

s is not inversely proportional to t

Step-by-step explanation:

s is not inversely proportional to t.  I had responded that they were, based on the fact that as s went up, t went down.  But the question was not simply is there an inverse relationship, but are they inversely proportional.

The term proportional means that the relationship between s and t is a constant.  That is:

                                        t = s*(1/x)

Let's rewrite that to y*x = k and then check the numbers.  See the attached spreadsheet.  If the relationship were inversel proportioanl, thaen the product of t*s would be a contant for the series.  The third set is different from the first two.  The data has an is inverse relationship, but it is NOT proportional.

The required table, which represents the relationship between the total time y and the number of rides x,
x         y[min]
1          3
2         6
3         9

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
Let,
Total time of ride a roller is directly proportional to the number of rides, x
y = kx
where k is the rate constant,
put y = 12 and x = 4
12 = 4k
k = 3
Now,
y = 3k
From the above expression, a table can be deduced.

Thus, the solution is given in the table as.
x         y[min]
1          3
2         6
3         9

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