Calculate the number of vertices in a full 5-ary tree with 35 internal vertices.
Also, find out the number of leaves

Answer:

$24.00=$21.50+r*$.50

Step-by-step explanation:

total cost= entrance fee + r (number of rides) * $0.50 (cost of rides)

$24.00=$21.50+r*$.50

2.50=r*.50

2.5/.5=r

r=5

Given:

Number of color pens Tracy have = 63

Number of color pens Jacob have = 46

To find:

How many more colors pens does Tracy have than Jacob​?

Solution:

We need to find the difference between the number of color pens Tracy have and the number of color pens Jacob have.

[tex]Difference=63-46[/tex]

[tex]Difference=17[/tex]

Therefore, Tracy have 17 more color pens than Jacob.

Answer: Read it to him again, and explain all the steps to him nice and slowly.

Answer:

61%

Step-by-step explanation:

We can see that out of all the people that were surveyed, 54% were 10th graders. Since 33% out of all the ones surveyed were 10th graders that chose robotics, the fraction would be 33/54 which is 0.611.

This is 61% approx.

Answer:

61%

Step-by-step explanation:

A P E X

Answer:

1 hour 56 minutes

Step-by-step explanation:

Given :

Time taken by Lucy = 3 hours 15 minutes = 3.25 hours

Time taken by brother = 4 hours 45 minutes = 4.75 hours

Rate = 1 / time taken

Lucy's rate = 1 / 3.25

Brother's rate = 1 / 4.75

Combined rate = Lucy's rate + brother's rate

Combined rate = 1/3.25 + 1/4.75

Combined rate = 0.5182186

Time taken if they work together = 1/ combined rate

= 1 / 0.5182186

= 1.9296 hours

= 1 hour (0.9296 * 60) minutes

= 1 hour 56 minutes (approximately)

Answer:

grade-point average (GPA).

Step-by-step explanation:

The Independent variable may be explained as the variable which is used to manipulate the variable to be predicted. The Independent variable also called the predictor variable takes up several input values in other to observe how the predicted variable changes due to this independent variable. In the scenario described above, the independent variable is the Grade - point average, as it is used to make prediction or manipulate the value of the starting salary earned by a graduate. The starting salary earned is the predicted variable or dependent variable in this scenario.

Answer:

a) A =   [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2

b) attached below ( Matrix dose not exist )

c) attached below  ( Matrix does not exist )

Step-by-step explanation:

a) Matrix

A =   [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2

From the matrix ; Column 1 and Column 2 Belong to COL(A)

while : (1,1)^T  =  ( 1,0 )^T +  ( 0,1 )^T  i.e. (1,1)^T  ∈  Row( A )

and (1, 2)^T. = ( 1,0 )^T + 2 ( 0,1 )^T   i.e. (1, 2)^T  ∈  Row( A )

Hence ; all requirements are fulfilled in Matrix A

b)  The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T

Matrix is Non-existent because condition is not met

attached below

c) Rank | A |

dimension of column space= 4 , dimension of Row space = 3

Given that ; column space ≠ Row space

Hence Matrix does not exist

Answer:

2.5

Step-by-step explanation:

5/8 ÷ 1/4

Division sign changes to multiplication and the reciprocal of the divisior is used to multiply instead :

5/8 * 4/1

= (5*4) / (8*1)

= 20 / 8

= 2.5

Answer:

Step-by-step explanation:

LA EDUCACION ES IMPIRTANTE YA QUE PROMUEVE UN MEJOR DESARROLLO DE LOS NIÑOS,NIÑAS Y ADOLESCENTES QUE LOS HACE FOMENTAR UN VINCULO MUY ESPECIAL CON SUS MAESTROS,COMPAÑEROS QUE LOS HACE SENTIR QUE SON PARTE DE SU FAMILIA ADEMAS ELLOS PASAN LA MAYORIA DE TIEMPO EN LA ESCUELA QUE LOS HACE SENTIRSE MÁS CÓMODOS COMO SI FUERA SU PROPIO HOGAR

Answer:

4 peaches

Step-by-step explanation:

$20/5 = 4 peaches

Answer:

The mean is [tex]\mu = 69.25[/tex]

Step-by-step explanation:

We are given the following distribution:

P(x = -500) = 0.076

P(x = -250) = 0.191

P(x = 0) = 0.265

P(x = 250) = 0.316

P(x = 500) = 0.152

Find the mean, µ for the probability distribution.

To find the mean, we multiply each outcome by its probability. So

[tex]\mu = -500*0.076 - 250*0.191 + 0*0.265 + 250*0.316 + 500*0.152 = 69.25[/tex]

The mean is [tex]\mu = 69.25[/tex]

If you folded the figure up, you would have a prism where the parallel bases are right triangles. Each lateral face is a rectangle.

It might help to imagine a room where the floor and ceiling are triangles (they are identical or congruent triangles). Each wall of this room is one of the rectangles shown.

Answer:

x = 2

Step-by-step explanation:

→ Work out the area of the first triangle

0.5 × 4 × 7 = 14

→ Set up an equation for the second base

0.5 × x × 14 = 14

→ Simplify

7x = 14

→ Divide both sides by 7

x = 2

Answer:

option B = 2cm

Step-by-step explanation:

[tex]Area \ of \ first \ triangle = \frac{1}{2} \times base_1 \times height_1 \ [ \where base_1 = 4\cm \ height_1 \ = 7cm \ ][/tex]

                                 [tex]=\frac{1}{2} \times 4 \times 7 \\\\= 14 \ cm^2[/tex]

Given area of second triangle is same as first.

[tex]Area \ of \ second \ triangle = \frac{1}{2} \times base_2 \times height_2 \ [ \ where \ height _ 2 = 14cm \ ][/tex]

                           [tex]14 = \frac{1}{2} \times base_2 \times 14\\\\14 = 7 \times base_2\\\\base_2 = 2 \ cm[/tex]

Answer:

B

Step-by-step explanation:

B

Answer:

(s/t)(100%)

Step-by-step explanation:

Represent salaries by s and total expenses by t.  Then the fraction of total expenses allocated to salary is

  s

------

  t

and so the percentage of total expenses which is allocated to salary is

(s/t)(100%)

Here,

we have to determine the percentage of total expenses which is allocated to salary.

Let,

The percentage of total expenses allocated to salary is,

Answer:

option B : 31.4 cm

Step-by-step explanation:

Given radius , r = 5cm

Circumference = [tex]2 \pi r[/tex]

                       = 2 x 3.14 x 5

                       =10 x 3.14

                       = 31.4 cm

Answer:

b. 31.4

Step-by-step explanation:

The radius of the circle can be plugged into C=(pi)2r. So 5x2= 10 and 10x(pi)= 31.4

Answer:

2b^2

Step-by-step explanation:

according to the question equation is

(a^2 + b^2 ) - (a^2 - b^2)

a^2 + b^2 - a^2 + b^2

plus a square and minus a square gets cancel

b^2 + b^2

since they are like terms they can be added

2b^2

Answer:

2b^2

Step-by-step explanation:

according to the question equation is

(a^2 + b^2 ) - (a^2 - b^2)

a^2 + b^2 - a^2 + b^2

= b^2 + b^2

like terms can be added

+2b^2

Answer:

Newton's law of cooling says that:

T(t) = Tₐ + (T₀ - Tₐ)*e^(k*t)

or:

[tex]\frac{dT}{dt} = -k*(T - T_a)[/tex]

in the differential form.

where:

T is the temperature as a function of time

Tₐ  is the ambient temperature, in this case, 70F

T₀ is the initial temperature of the object, in this case, 150F

k is a constant, and we want to find the value of k.

Then our equation is:

T = 70F + (150F - 70F)*e^(k*t)

Now we also know that after a minute, or 60 seconds, the temperature was 135F

then:

135F = 70F + (150F - 70F)*e^(k*60s)

We can solve this for k:

135F = 70F + 80F*e^(k*60s)

135F - 70F = 80F*e^(k*60s)

65F =  80F*e^(k*60s)

(65/80) = e^(k*60s)

Now we can apply the Ln(x) function to both sides to get:

Ln(65/80) = Ln(e^(k*60s))

Ln(65/80) = k*60s

Ln(65/80)/60s = k = -0.0035 s^-1

Then the differential equation is:

[tex]\frac{dT}{dt} = -0.0035 s^-1*(T - 70F)[/tex]

Answer:

A sample size of 3 is required.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.054.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours.

This means that [tex]\sigma = 3.6[/tex]

He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.

The sample size needed is of n, and n is found when M = 5. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5 = 2.054\frac{3.6}{\sqrt{n}}[/tex]

[tex]5\sqrt{n} = 2.054*3.6[/tex]

[tex]\sqrt{n} = \frac{2.054*3.6}{5}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.054*3.6}{5})^2[/tex]

[tex]n = 2.19[/tex]

Rounding up:

A sample size of 3 is required.

Answer:

C

Step-by-step explanation:  

Answer:

[tex]h(x) = \frac {3}{2}x + 1 \\ { \tt{let \: the \: inverse \: be \: { \bold{m}}}} \\ { \tt{m = \frac{1}{ \frac{3}{2}x + 1 } }} \\ \\ { \tt{m = \frac{2}{3x + 2} }} \\ \\ { \tt{m(3x + 2) = 2}} \\ \\ { \tt{3x + 2 = \frac{2}{m} }} \\ \\ { \tt{x = \frac{2 - 2m}{3m} }} \\ \\ { \tt{x = \frac{2}{3m}(1 - m) }} \\ \\ { \bf{h {}^{ - 1} (x) = \frac{2}{3x}(1 - x) }}[/tex]

Answer:

(6×10) + (0.7×10)

60+7=67

Answer:

TRUE

Step-by-step explanation:

Those lines around the -5 mean the absolute value of the number, basically the value of the number without any negative signs. SO the absolute value of -5 is just 5.

5 IS GREATER than 3, so this is true

ur welcome :)

Answer:

-5/16 or -0.3125

Step-by-step explanation:

Answer:

-11/12

Step-by-step explanation:

Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Answer:

-5 =x

Step-by-step explanation:

0 = In(x + 6)

Raise each side to base e

e^0 = e^ ln (x+6)

1 = x+6

Subtract 6 from each side

1-6 = x

-5 =x

Answer:

242 m³ of space is there in the fort.

Step-by-step explanation:

Given that,

The dimensions of first box is 4 meters long, 8 meters wide, and 8 meters high.

The dimensions of the second box is 2 meters long, 7 meters wide, and 1 meter high.

Space left = Volume of first box - volume of second box

= (4)(8)(8) - 2(7)(1)

= 242 m³

So, 242 m³ of space is there in the fort.

Answer:

One Apple.

Step-by-step explanation:

This is a basic subtraction and addition problem. She began with one apple and gave one to her friend. How many apples is Elysia holding now? 2-1= 1

One apple.

Elysia will have one apple, as one apple is being subtracted because she gave it to her friend.

In math, to subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less.

Given that, Elysia has 2 apples she gives 1 to her friend,

To find the number of apples Elysia left with, we will subtract the number of apples she gave to her friend to the number of apples she had,

Number of apples Elysia left with = 2-1 = 1

Hence, Elysia will have one apple.

Learn more about subtraction, click;

https://brainly.com/question/2346316

#SPJ2

Answer:

this probability is 0.68

Step-by-step explanation:

the probability she buys fruit but not a CD is

0.6 × (1 - 0.2) = 0.48

the probability she buys a CD by not fruit is

0.2 × (1 - 0.6) = 0.08

the probability that she buys both is

0.6 × 0.2 = 0.12

the probability that she buys fruit or a CD or both is adding all 3 probabilities :

0.48 + 0.08 + 0.12 = 0.68

Given:

The data values are:

164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171.

To find;

a. Lower quartile.

b. Upper quartile.

c. Interquartile range.

Solution:

We have,

164, 148, 137, 157, 173, 156, 177, 172, 169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, 171.

Arrange the data values in ascending order.

134, 137, 140, 145, 146, 148, 151, 152, 154, 156, 156, 157, 162, 163, 164, 165, 168, 168, 169, 171, 172, 173, 174, 174, 177.

Divide the data values in two equal parts.

(134, 137, 140, 145, 146, 148, 151, 152, 154, 156, 156, 157), 162, (163, 164, 165, 168, 168, 169, 171, 172, 173, 174, 174, 177)

Divide each parentheses in two equal parts.

(134, 137, 140, 145, 146, 148), (151, 152, 154, 156, 156, 157), 162, (163, 164, 165, 168, 168, 169), (171, 172, 173, 174, 174, 177)

a. Location of lower quartile is:

[tex]Q_1=\dfrac{1}{4}(n+1)\text{th term}[/tex]

[tex]Q_1=\dfrac{1}{4}(25+1)\text{th term}[/tex]

[tex]Q_1=\dfrac{26}{4}\text{th term}[/tex]

[tex]Q_1=6.5\text{th term}[/tex]

The lower quartile of the weights is:

[tex]Q_1=\dfrac{148+151}{2}[/tex]

[tex]Q_1=\dfrac{299}{2}[/tex]

[tex]Q_1=149.5[/tex]

Therefore, the location of the lower quartile of the weights is between 6th term and the 7th term. The value of the lower quartile is 149.5.

b. Location of upper quartile is:

[tex]Q_3=\dfrac{3}{4}(n+1)\text{th term}[/tex]

[tex]Q_3=\dfrac{3}{4}(25+1)\text{th term}[/tex]

[tex]Q_3=\dfrac{3\cdot 26}{4}\text{th term}[/tex]

[tex]Q_3=19.5\text{th term}[/tex]

The upper quartile of the weights is:

[tex]Q_3=\dfrac{169+171}{2}[/tex]

[tex]Q_3=\dfrac{340}{2}[/tex]

[tex]Q_3=170[/tex]

Therefore, the location of the upper quartile of the weights is between 19th term and the 20th term. The value of the upper quartile is 170.

c. The interquartile range of the given data set is:

[tex]IQR=Q_3-Q_1[/tex]

[tex]IQR=170-149.5[/tex]

[tex]IQR=20.5[/tex]

Therefore, the interquartile range of the weights is 20.5.

Answer:

Father's age = 64 years

Step-by-step explanation:

Given:

Mummy's age = Aliyah's age + 32

Father's age = Mummy's age + 8

Tota age = 144

Find:

Father's age

Computation:

Assume;

Aliyah's age = a

So,

Mummy's age = a + 32

Father's age = a + 32 + 8

Father's age = a + 40

Aliyah's age + Mummy's age + Father's age = Total age

a + a + 32 + a + 40 = 144

3a + 72 = 144

3a = 144 - 72

3a = 72

a = 24

Father's age = a + 40

Father's age = 24 + 40

Father's age = 64 years