a number increased by 15 is 114
​

The confidence interval indicates that we are 95% sure that the mean height is within 0.4 inches of the sample mean of 6 feet and 5 inches.

For a smaller sample size, the confidence interval would become larger.

With a higher level of confidence, the confidence interval would become larger.

The confidence interval is:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

The margin of error is given by:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which:

The interpretation of an interval is that we are x% sure that the population mean is in that interval, in which x% is the confidence interval. Hence, considering the margin of error and the sample mean for this problem, the confidence interval indicates that we are 95% sure that the mean height is within 0.4 inches of the sample mean of 6 feet and 5 inches.

The margin of error equation means that:

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The equidistant point of  the triangle is point O , which is shown below.

In the question ,

we have to find the equidistant point in the triangle ,

We know that the equidistant point from the vertices of the triangle is the circumcenter ,

let the circumcenter be point O .

The perpendicular bisectors of the given triangle ABC are AC and BC that intersect at point O .

We have to prove that point O lies on the perpendicular bisector of AB and it is equidistant from A , B and C .

So ,we draw OA ,OB and OC .

we know that any point on perpendicular bisector of a segment is equidistant from endpoints of the segment.

that means , OA = OC and OC = OB .

which means OA = OB .

we also know that any point that is equidistant from end points of a segment lies on its perpendicular bisector.

So, we can say that point O is on the perpendicular bisector of AB .

and

Since OA = OB = OC , the point O is equidistant from A , B and C .

Therefore , the equidistant point of the triangle is the circumcenter (point O) .

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Answer:5.5

Step-by-step explanation:

5.46

You rounded to the nearest tenths place. The 4 in the tenths place rounds up to 5 because the digit to the right in the hundredths place is 6.

5.5

When the digit to the right is 5 or greater we round away from 0.

5.46 was rounded up and away from zero to 5.5

Answer:

Step-by-step explanation:

We know that the tenth of a decimal number is the first number after the decimal. In this case the tenth in 5.460 is the 4. 0.46 is all we need to round the number. Since 6 is greater than 5, 4 will round up. Hence the answer is 5.5.

According to the information provided, 4.5 litres of red paint and 1400 ml of blue paint are required to manufacture the paint mixture.

Red paint requires 3/4 x 6 = 9/2 = 4.5 litres.

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The equivalent resistance of the network shown is: \(R_{eq}=16.463\Ohm\)

So, first of all, we can start by determining what each of the resistances is equal to. In this case we can start by saying that \(R_{1}=11R_{11}\) This means that:

\(R_{1}=11(3\Ohm)\)

Therefore:

\(R_{1}=33\Ohm\)

We can now use this value to find the value of the other resistances. The given condition for the resistances can be represented with the following formula:

\(R_{n}=\frac{R_{1}}{n}\)

so:

\(R_{2}=\frac{R_{1}}{2}=\frac{33}{2}\Ohm\)

\(R_{3}=\frac{R_{1}}{3}=\frac{33}{3}\Ohm=11 \Ohm\)

\(R_{4}=\frac{R_{1}}{4}=\frac{33}{4}\Ohm\)

\(R_{5}=\frac{R_{1}}{5}=\frac{33}{5}\Ohm\)

\(R_{6}=\frac{R_{1}}{6}=\frac{33}{6}\Ohm=\frac{11}{2}\Ohm\)

\(R_{7}=\frac{R_{1}}{7}=\frac{33}{7}\Ohm\)

\(R_{8}=\frac{R_{1}}{8}=\frac{33}{8}\Ohm\)

\(R_{9}=\frac{R_{1}}{9}=\frac{33}{9}\Ohm=\frac{11}{3}\Ohm\)

\(R_{10}=\frac{R_{1}}{10}=\frac{33}{10}\Ohm\)

\(R_{11}=3\Ohm\)

So now that we know what each resistance is equal to, we can go ahead and analyze the circuit.

In this case we can see that \(R_{10}\) and \(R_{11}\) are parallel, so we can calculate their equivalent resistance.

\(R_{1011}=\frac{R_{10}R_{11}}{R_{10}+R_{11}}\)

Which yields:

\(R_{1011}=\frac{(\frac{33}{10}\Ohm)(3\Ohm)}{\frac{33}{10}\Ohm+3\Ohm}\)

\(R_{1011}=\frac{11}{7}\Ohm\)

Now, \(R_{8}\), \(R_{9}\) and \(R_{1011}\) are connected in series, so we can calculate their equivalent resistance like this:

\(R_{891011}=R_{8}+R_{9}+R_{1011}\)

\(R_{891011}=\frac{33}{8}+\frac{11}{3}+\frac{11}{7}\)

\(R_{891011}=\frac{1573}{168}\Ohm\)

Now,  we can see that \(R_{7}\) and \(R_{891011}\) are parallel, so we can calculate their equivalent resistance.

\(R_{7891011}=\frac{R_{7}R_{891011}}{R_{7}+R_{891011}}\)

Which yields:

\(R_{7891011}=\frac{(\frac{33}{7}\Ohm)(\frac{1573}{168})}{\frac{33}{7}\Ohm+\frac{1573}{168}\Ohm}\)

\(R_{7891011}=\frac{4719}{1505}\Ohm\)

Now, \(R_{5}\), \(R_{6}\) and \(R_{7891011}\) are connected in series, so we can calculate their equivalent resistance like this:

\(R_{567891011}=R_{5}+R_{6}+R_{7891011}\)

\(R_{567891011}=\frac{33}{5}\Ohm+\frac{11}{2}\Ohm+\frac{4719}{1505}\Ohm\)

\(R_{567891011}=15.236\Ohm\)

Next,  we can see that \(R_{4}\) and \(R_{567891011}\) are parallel, so we can calculate their equivalent resistance.

\(R_{4567891011}=\frac{R_{4}R_{567891011}}{R_{4}+R_{567891011}}\)

Which yields:

\(R_{4567891011}=\frac{(\frac{33}{4}\Ohm)(15.236\Ohm)}{\frac{33}{4}\Ohm+15.236\Ohm}\)

\(R_{4567891011}=5.352\Ohm\)

Now, \(R_{2}\), \(R_{3}\) and \(R_{4567891011}\) are connected in series, so we can calculate their equivalent resistance like this:

\(R_{234567891011}=R_{2}+R_{3}+R_{4567891011}\)

\(R_{234567891011}=\frac{33}{2}\Ohm+11\Ohm+5.352\Ohm\)

\(R_{234567891011}=32.852\Ohm\)

Finally, we can see that \(R_{1}\) and \(R_{234567891011}\) are parallel, so we can calculate their equivalent resistance.

\(R_{eq}=\frac{R_{1}R_{234567891011}}{R_{1}+R_{234567891011}}\)

Which yields:

\(R_{eq}=\frac{(33\Ohm)(32.852\Ohm)}{33\Ohm+32.852\Ohm}\)

\(R_{eq}=16.463\Ohm\)

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Answer:

D.

Step-by-step explanation:

Order of operation states that in order for the addition to be done first, it must be in a set of parenthesis. Then, 4 multiplied by the sum would mean the addition has to be done first. so, yeah.

Don't know if that helps. I hope it does. Have a great day

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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Answer:

1/6 that's the answer

Step-by-step explanation:

so you do 43/6-7=43/6-42/6=1/6

Answer:

Actually the answer is -⅙

Step-by-step explanation:

43/6 written differently is 7 ⅙, because the fraction 42/6 is the same as 7 (42÷6=7). But since your number is 43/6 you get

7 1/6.

your original number is larger than 7 but the question was what number you have to "add" to get to 7. so they number has to be a negative number.

like this:

43/6 + (-1/6) = 42/6. which you rewrite now as

43/6 - 1/6 = 42/6. and I explained that 42/6 is the same as 7.

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Answer:

B. y=-0.5x + 1

Step-by-step explanation:

first look at the slope: slop = rise over run. for every 2 units right, the point goes 1 unit down. so the slope if -1/2 or -0.5

next look at the y-intercept. the y-intercept of this graph is 1

plug these into the equation y= mx + b to get y = -0.5x + 1

Answer:

A. y = -0.5x + 1

Step-by-step explanation:

Hello!

An equation of a line is written in slope-intercept form: \(y = mx + b\)

The y-intercept is found when x=0, or then the line crosses the y-axis.

Over here, we can see that the line crosses the y-axis at point (0,1), so the y-intercept is positive 1.

Slope is calculated by rise over run, or the ratio of how much the graph rises over how much the graph runs. Use points to determine how the graph changes. (For simple calculations, use integer points, such as (0,1) and (0,2)

Now that we have the slope and the y-intercept, we can plug those values to make our equation.

The correct answer is Option A. y = -0.5x + 1

Answer:

\(3 (t * b)\)

Step-by-step explanation:

Txbx3 expand-

3 (t * b)

*= times btw

Answer:

i have no idea.....

Step-by-step explanation:

Answer:

sin(5x)

Step-by-step explanation:

Recall that the half angle identity relates the sine of half an angle to the square root of one minus the cosine of the angle as shown below:

\(sin(\frac{\theta}{2} )=+/-\sqrt{\frac{1-cos(\theta)}{2} }\)

therefore, in our case:

\(sin(5\,x )=+/-\sqrt{\frac{1-cos(10\,x)}{2} }\)

so, make sure you type the expression : "sin(5x)" in the provided text-box.

This year, the number of raffle tickets sold for a school's extracurricular activities fundraiser is 848. It is estimated that the number of raffle tickets sold will increase by 5% each year.

The total number of raffle tickets sold at the end of 9 years is approximately 9,818.  

To find the total number of raffle tickets sold at the end of 9 years, we need to calculate the number of tickets sold each year and sum them up.

Starting with the initial number of tickets sold, which is 848, we will increase this number by 5% each year for a total of 9 years.

Year 1: 848 + (5% of 848) = 848 + 42.4 = 890.4

Year 2: 890.4 + (5% of 890.4) = 890.4 + 44.52 = 934.92

Year 3: 934.92 + (5% of 934.92) = 934.92 + 46.746 = 981.666

Year 9: Ticket sales at the end of 9 years = Number of tickets sold in Year 8 + (5% of Year 8 sales)

Year 9: Total = 1,399.585 + 69.97925 = 1,469.56425 ≈ 1,469.56

The total number of raffle tickets sold at the end of 9 years is approximately 1,469.56.

The correct option is 9,818.

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9514 1404 393

Answer:

  B, C

Step-by-step explanation:

Linearly dependent sets can be found using row-reduction techniques. If a row ends up zero, then the set is linearly dependent. Equivalently, the determinant of a 3×3 matrix can be computed. If it is zero, the set is dependent. The cross-product of two 3-D vectors can be computed. If it is zero, the vectors are dependent.

Any set of vectors that has more elements than each vector does must necessarily be dependent.

It is helpful to be able to use a calculator capable of performing these calculations (as opposed to doing it by hand). The first attachment shows the result of computing the reduced row-echelon form of the first set of 3 vectors. The set is found to be independent.

__

The second set of vectors is clearly dependent, as the second vector is 5 times the first.

__

The third set contains more vectors than there are elements to a vector. Hence at least one of them can be created using some combination of the others. This set is dependent.

__

The cross-product of the fourth set is non-zero, so it is independent. The second attachment shows the result of a row-reduction tool on these vectors.

Answer:

millilitres (ml)

.......

Answer:

A, B, E

Step-by-step explanation:

I hope this helps!!!

Step-by-step explanation:

\(2 ^{ \frac{1}{2} } = 2 ^{1 \times \frac{1}{2} } = \sqrt{2} \\ {2}^{ \frac{2}{3} } = 2 ^{2 \times \frac{1}{3} } = \sqrt[3]{2 ^{2} } \\ 3 ^{ \frac{3}{2} } = {3}^{3 \times \frac{1}{2} } = \sqrt[]{ {3}^{3} } \\ {3}^{ \frac{1}{3} } = 3 ^{1 \times \frac{1}{3} } = \sqrt[3]{3} \)

Step-by-step explanation:

\( \sf \: {2}^{ \frac{1}{2 } } = \sqrt{2} \)

\( \sf \: {2}^{ \frac{2}{3} } = \sqrt[3]{ {2}^{2} } \)

\( \sf \: {3}^{ \frac{3}{2} } = \sqrt{ {3}^{3} } \)

\( \sf \: {3}^{ \frac{1}{3} } = \sqrt[3]{3} \)

The results show that the most common response was access, with 27% of the respondents choosing it as the most urgent health problem.

Cost came in second place, with 20% of the respondents choosing it. Obesity and cancer followed closely behind, with 14% and 13% of the respondents choosing them, respectively. Government interference and the flu were the least common responses, with only 3% and less than 0.5% of the respondents choosing them, respectively.

The margin of sampling error for the poll is ±4 percentage points, which means that if the poll was conducted multiple times, 95% of the time, the results would be within 4 percentage points of the actual population values.

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Row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

row 1 of the given matrix are: 2, 0, and 3, multiplying row 1 with 1/4 gives;

1/4 × 2 = 1/2

1/4 × 0 = 0

1/4 × 3 = 3/4

Therefore, row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.

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Answer:

10 + $25.75x

Step-by-step explanation:

He has 10 dollars to start out with, then you put x to show that we don't know how many lawns he will mow, but that's how much he makes when he does.

Answer:

15/4

Step-by-step explanation:

sin60 =z/15

z=15sin60 =(15√3)/2

cos30 =b/z

b = zcos30 = (15√3)/2 * √3/2 = 45/4

a = 15-b = 15-45/4 = 15/4

The value of a is 15/4

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

According to the given figure,

Here is a right triangle

Let, The hypotenuse = 15

perpendicular = z and base = 15 = a + b

⇒ sin60 = perpendicular/hypotenuse = z/15

⇒ z = 15sin60 = (15√3)/2

⇒ cos30 = base/hypotenuse = b/z

⇒ b = zcos30 = (15√3)/2 * √3/2 = 45/4

⇒ a + b = 15

Substitute the value of b in the above equation,

⇒ a = 15-b = 15-45/4 = 15/4

Hence, the value of a is 15/4.

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Answer:

-2,1,6,13,22

Step-by-step explanation:

cn = n^2 -3

Let n=1

c1 = 1^2 -3 = 1-3 = -2

Let n=2

c2 = 2^2 -3 = 4-3 = 1

Let n=3

c3 = 3^2 -3 = 9-3 = 6

Let n=4

c4 = 4^2 -3 = 16-3 = 13

Let n=5

c5 = 5^2 -3 = 25-3 = 22

We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

Using the following property of logarithms:

\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)

Therefore,

\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)

So, \(log4 (0.5^(1/2)) =-0.0752\)

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Answer:

496 cm²

Step-by-step explanation:

Area of polygon :

A = 1/2(p * a)

P = perimeter

a = apothem

Perimeter = 5s (pentagon)

s = side length = 18

P = 5 * 18 = 80 cm

a = 12.4

A = 1/2(80 * 12.4)

A = 1/2(992)

A = 496 cm²

Answer:

More info

Step-by-step explanation:

I need more info than that please!`

1 feet = 12 inches  

3 feets= 36 inches

8 feets = 96 inches

hope this helps  

Assume the year that it would take to these trees have the same height is : x (years)

After x years, type A tree has heigth: 36 +23x (inches)

After x years, type B tree has heigth: 96 +17x (inches)

We have  36+23x = 96+17x

Solve the equation, we have x=10

Conclusion: It will take 10 years to these trees have the same height.

Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

Answer:

C. The first equation should be multiplied by 7 and the second equation by -6.

Step-by-step explanation:

have a great day peeps :)

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The correct option is C.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

In the two of the given equation, to eliminate x we need to make the coefficients of x in both the terms equal, therefore, if we take the LCM of the two terms then it will be 42.

Thus, to make the coefficient of x equal to 42, we need to multiply the first equation should be multiplied by 7 and the second equation by -6.

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