Four more than twenty-six time a number is equivalent to 12 times the same number less 15.
What is the number?

Answer:

Step-by-step explanation:

G is the incenter of ΔABC,

Incenter of a triangle is defined by the point where angle bisectors of the interior angles intersect.

10). m∠ABG = m∠CBG = 25°

11). m∠BCG = m∠ACG = 18°

  Therefore, m∠BCA = m∠BCG + m∠ACG = 2×18° = 36°

12). m∠ABC + m∠BAC + m∠ACB = 180°

  2(25)° + m∠BAC + 36° = 180°

    m∠BAC = 180° - 86° = 94°

13). m∠BAG = [tex]\frac{1}{2}[/tex](m∠BAC) = 47°

14). Since, incenter is equidistant from all sides of the triangle,

     Therefore, DG = GF = FE = 4 units

15). In right triangle BEG,

     tan(25)° = [tex]\frac{\text{GE}}{\text{BE}}[/tex]

     BE = [tex]\frac{\text{GE}}{\text{tan}25}[/tex]

           = [tex]\frac{4}{\text{tan}25}[/tex]

     BE = 8.6

16). In right triangle BEG,

     cos(25)° = [tex]\frac{\text{4}}{\text{BG}}[/tex]

     BG = [tex]\frac{4}{\text{cos}25}[/tex] = 4.4

17). In right triangle GEC,

    sin(18)° = [tex]\frac{\text{GE}}{\text{GC}}[/tex]

    GC =  [tex]\frac{\text{4}}{\text{sin}(18)}[/tex] = 12.9

Answer:

The answer is "0.0764"

Step-by-step explanation:

Please find the complete question in the attached file.

[tex]\to \mu = \$ \ 4064\\\\\to \sigma = \$ \ 460 \\\\\to \sigma \bar{x} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]

        [tex]= \frac{460}{\sqrt{21}}\\\\ = \frac{460}{4.58257569}\\\\=100.3802[/tex]

[tex]\to P(\bar{x}< \$ \ 3920) = \frac{P((\bar{x} - \mu \bar{x})}{\frac{\sigma \bar{x}<(3920 - 4064)}{100.3802)}}[/tex]

[tex]\to P(z < -1.43) = 0.0764 \\\\\to P(\bar{x}< \$ \ 3920) = 0.0764\\\\[/tex]

Answer: The notebook is worth 2.79

Step-by-step explanation: Let's start off with taking 50% off of 6, which is 3$. Now we need to do 7% of 3:

7 x 3 = 21

21 / 100 = 0.21

3 - 0.21 = 2.79

Hope this helps :)

Answer:

the answer is 1.06

Step-by-step explanation:

Answer:

2 1/3+5/6+1/6= 3 1/2

Step-by-step explanation:

Change your denominator to 6 and add then reduce if possible

Answer:

A. F

B. D

C. C

D. E

E. G

F. G

G. D

Step-by-step explanation:

Answer: A. 9/4

              C. -1.75

              D. 1.75

              E -2      

              F-1

              -2 1/2  

Step-by-step explanation:

Answer:

Let's calculate the "cups of sugar per dozen cookies" ratio:

2 cups

---------- = 0.8  (Rina)        

  2.5                                  

2.25 cups

------------- = 0.75 (Jonah)

     3

Rina uses more sugar for a dozen cookies.

Answer:

D. x = 3

Step-by-step explanation:

We would like to find out for what value of x does f(x) = g(x). This is essentially the same as asking us to find the x-value for which f(x) = k, where k is some number, and g(x) = k, as well.

Looking at the two tables provided, we notice that when x = 3, both f(x) and g(x) equal -2. So, the answer is D.

Answer:

B

Step-by-step explanation:

Answer:

The student solved the inequality correctly, but the graph incorrectly represents the solution calculated.

Step-by-step explanation:

Answer:

6 + 3 + 1.15 = 10.15 miles

Step-by-step explanation:

Answer:

0.0157

Step-by-step explanation:

From the information given:

The sample size  = 70

The expected no. of days of year that are birthday of exactly 4 people is:[tex]P = \bigg [ \dfrac{1}{365} \bigg]^4[/tex]

The expected number of days with 4 birthdays = [tex]\sum \limits ^{365}_{i=1} E(x_i)[/tex]

[tex]\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ ^{70}C_{4} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{70-4} \bigg][/tex]

[tex]\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ \dfrac{70!}{4!(70-4)!} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{66} \bigg][/tex]

[tex]\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ 916895 \times 5.6342 \times 10^{-11} \times 0.8343768898 \bigg][/tex]

= 0.0157

Therefore, the required probability = 0.0157

Answer:

3 cm on the map represents 31.5 km in reality.

3cm : 31.5 km

1cm :  31.5/3 km

1cm : 10.5km

So the scale on the map is 1cm represents 10.5 km.

Answer:

Step-by-step explanation:

710 + 640 = 1350m

Answer:

For the first 30 minutes, we will have a line with a given steepness, this will represent the 30 minutes riding at a fast pace.

Then he stops for 20 minutes, we will represent this with a constant line.

Then he again moves for another 30 minutes, but with a slower pace than in the first 30 minutes, then this line will be less steep than the first line.

A sketch of this situation can be seen below.

Answer:

constants

Step-by-step explanation:

That is, they're the terms without variables. We call them constants because their value never changes, since there are no variables in the term that can change its value.

The term or number with no variable attached is called a constant as in the polynomial or expression.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

A number consists of the expression with no variable.

As we know, the expression is a combination of numbers, variables, and operators.

If we take an example of the polynomial.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm p(x) = a_0+a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

Here a₀ is a constant because the term a₀ has no variables.

Thus, the term or number with no variable attached is called a constant as in the polynomial or expression and the constant value does not change.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ6

Answer:

n-6

Step-by-step explanation:

Answer: The answer should be A.

Step-by-step explanation: When solving the first and third equations, it becomes 0=0. I'm assuming that is one solution. Then 8x-10y=5 should be the other solution. In other words, there is 2 solutions.

The correct diagram represents the type of solution to this system of equations is shown in Option A.

We have to given that,

System of equations are,

7x - 12y + z = -1   .. (i)

8x - 10y = 5        .. (ii)

21x - 36y + 3z = -3  .. (iii)

Now, From equation (i);

Multiply by 3;

3( 7x - 12y + z)  = -1 × 3

21x - 36y + 3z = - 3

Which is same as equation (iii).

Hence, Equation (i) and (ii) are parallel to each other.

And, It's a triple relationship.

Thus, Only option A has parallel planes.

So, Option A is true.

Learn more about systems of equations at:

brainly.com/question/14323743

#SPJ2

Answer:

The answer is B, or the second one.

90 Adult tickets and 18 Children's tickets

Step-by-step explanation:

(90 x 15) + (18 x 9)

The number of fluid ounces of lemonade made by James and Eric is a

multiple of the number pitchers mixed.

The number of pitchers James and Eric mix = 6 pitchers each

Number of fluid ounces of lemonade James makes per pitcher = 26 fluid Ounces

Volume of lemonade Eric makes per pitcher = 32 fluid ounces

Volume of lemonade James makes = 26 fluid Ounce × 6 = 156 fluid Ounces

Volume of lemonade Eric makes = 32 fluid ounces × 6 = 192 fluid Ounces

Total volume of lemonade made by James and Eric = (156 + 192) fluid Ounces = 344 fluid ounces

Volume of lemonade per glass = 8 Ounces

Number of glasses filled = 344 fluid Ounces ÷ 8 Ounces/glass = 43 glasses

Therefore, given that the number of glasses of 8 ounces of lemonade that can be filled using the 344 fluid ounces is exactly 43 glasses, we have;

Learn more about division in arithmetic here:

https://brainly.com/question/3060423

https://brainly.com/question/10910164

Answer:

you need more than one point to find the slope of a line?

Step-by-step explanation:

Answer:

4 ( 3 + x )

Step-by-step explanation:

Pull out a four from both parts

4( 3 + x)

Answer:

x

Step-by-step explanation:

[tex]\huge \bigg( {x}^{ \frac{2}{3} } \bigg) ^{ \frac{3}{2} } \\\\

\huge= {x}^{ \frac{2}{3} \times \frac{3}{2} } \\\\

\huge= {x}^{ \frac{6}{6} } \\\\\huge= x \\ [/tex]

Answer:

m∠B = 105°

Step-by-step explanation:

Given

We know that the sum of angles in a triangle = 180°

A + B + C = 180°

x + 5 + 3x + x = 180°

5x + 5 = 180°

5x = 180° - 5

5x = 175

x = 175 / 5

x = 35

Thus, the measure of ∠B will be:

m∠B = 3x

         = 3(35)

         = 105°

m∠B = 105°

Answer:4=1/2x

X=8

Step-by-step explanation:

Answer:

The slope is -3

Step-by-step explanation:

the equation for finding the slope between two different points is:

M= (y2-y1)/(x2-x1)

Or in other words the change in y over the change in x.

M= (9+6)/(3-8) = 15/-5 = -3.

(sidenote: I added 9 and 6 for the change in y because you cannot subtract a negative number. Instead you have to add it.)

Answer:

1/6

Step-by-step explanation:

Answer: 1.6 in per hour

Answer:

hourly rate.

Step-by-step explanation:

As others have noted, it is a simple mathematical division problem (4/2.5) and the average is 1.6 inches per hour.

However, if this is for sizing civil works such as culverts or plumbing storm water drainage systems to mitigate flooding, the highest rate per hour must be known and usually the highest ten minutes rainfall rate expressed as an hourly rate.

For example, if 4.0 inches fell over that 2.5 hours, nothing says that a rain band did not dump 3 inches in the first hour, (3 inches per hour cumulative) or 0.75 inches in a ten minute period (4.5 inches per hour rate), with the remainder of the storm tapering off to lesser rates. So the average is correct, but the peak hour is much more important for practical purposes.