The cost of a telephone call is made up of a fixed connection fee and an additional cost per minute, as shown on the graph below.
a) What is the cost of the connection fee?
b) What is the cost per minute?
If your answers are decimals, give them to 1 d.p.

The missing angles of the isosceles triangle are as follows:

An isosceles triangle is a triangle that has two sides equal to each other and two angles congruent to each other.

The base angles of an isosceles triangles are congruent and the two legs are also equal.

Therefore, ΔHIJ

where

HI ≅ IJ

m∠H  = 3x + 10

m∠I = 6x - 20

Therefore,

m∠H ≅ m∠J

m∠H  + m∠I+ m∠J = 180

3x + 10 + 6x - 20 + 3x + 10 = 180

12x  = 180

x = 180 / 12

x = 15

Hence,

m∠H  = 3(15) + 10 = 55 degrees

m∠I = 6(15) - 20 = 90 - 20  = 70 degrees

m∠J = 55 degrees.

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In linear equation, For 20 Months Dagogo requires to upload videos to get 90,000,000  views on his channel.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.        

                                   The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Dagogo uploads 3 videos on his channel each month.

Each video gets an average of 1500000 views.

  3 Video get Views  = 3 * 1500000

                                = 4,500,000 Views

Views per month  =   4,500,000 Views

      Total Views = 90,000,000 views

Number of months = Total Views/Views per month

Number of months  = 90,000,000/4,500,000

      Number of months  20 Months

For 20 Months Dagogo requires to upload videos to get 90,000,000  views on his channel.

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The complete question is -

Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets an average of 150,000 new views. The average ratio of likes-to-views of Dagogo videos is 1:5. Dagogo wants to reach a total of 9,000,000 views on his channel. Assuming these rates continue, for how many months does Dagogo need to upload videos to get to 9,000,000 views on his channel?

Answer:

2000 likes per minute

Step-by-step explanation:

If each video averages 15 minutes and he gets an average of 150000 new views, we can divide.

150000/15=10000

If the ratio of likes to views is 1:5, we can assume 10000 is the "5" and divide it by 5.

10000/5=2000

2000:10000 = 1:5

2000 likes per minute

(KHAN)

Answer:

The answer is x = -6 and y = -5.

Step-by-step explanation:

To solve this problem, we can use substitution. Let's first solve one of the equations in terms of the variable y, and then substitute this value into the other equation.

4x = 3y - 9

3y = 4x + 9

Since the term "3y" is present in the other equation given, we can substitute the right side of this equation (4x + 9) into the other equation for 3y. This is shown below.

6x - 3y = -21

6x - (4x + 9) = -21

6x - 4x - 9 = -21

We can simplify the left side of the equation and solve for x.

2x - 9 = -21

2x = -12

x = -6

Now, we can substitute this value for x into one of our equations to solve for y.

4x = 3y - 9

4(-6) = 3y - 9

-24 = 3y - 9

-15 = 3y

y = -5

Therefore, the correct answer is x = -6 and y = -5.

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Answer:

  368

Step-by-step explanation:

You want the 41st term of the arithmetic sequence that starts 8, 17, 26.

The n-th term of an arithmetic sequence is given by ...

  an = a1 +d(n -1)

for first term a1 and common difference d.

The difference between terms is ...

  d = 17 -8 = 9

The first term is a1 = 8, so the 41st term is ...

  a41 = a1 +d(41 -1) = 8 +9(41 -1) = 368

The 41st term of the sequence is 368.

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[tex]17 - \frac{9}{7} j[/tex]

[tex]14 - 4 - \frac{6}{7} j - \frac{3}{7} j[/tex]

[tex]17 - \frac{6}{7} - \frac{3}{7}j [/tex]

[tex]17 - \frac{9}{7} j[/tex]

The number of independent pieces of information used to calculate a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. I

Itbis determined by subtracting the number of restrictions from the sample size. Subtract the number of relations from the number of observations to determine degrees of freedom. You need to deduct one (1) from the total number of observations, n, in order to calculate the degrees of freedom for a sample mean or average.

The degrees of freedom for the chi-square are calculated as df = (r-1)(c-1) where

r = the number of rows

c = the number of columns.

If the observed chi-square test statistic is greater than the critical value, the null hypothesis can be rejected.

Note that an overview was given as the information you gave is incomplete.

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Answer:

.

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

i'm kind of sure it's -4.7

Answer:

D

Step-by-step explanation:

y-intercept is when the line hits the y-axis, or when the x=0 on a line.

Look at the test below the axis.

y-axis = heartrate (resting)

for

x-axis = hrs of exercise per week

When x = 0, (0 hours of exercise,)  y = 80, (average resting heart rate.)Telling us the average resting heartrate pf people who do not exercise.

Answer:

You are going send Christmas cards to 100 of your friends. Each box of Christmas cards contains 15 cards and the cost per box is $17.00. You are going to purchase enough Forever stamps from the post office to mail 100 cards. How much will it cost in total?

1box - 15 card - $17

100/15 = 6.67     (round off to 7 box since u cant buy 6.67 box)

7 * $17 = $119

Therefore, you will spend $119 to buy 7 box with a total of 105 cards.

Step-by-step explanation:

The ordered pair -2,2 makes the inequalities y < –x + 1 and y > x true. Therefore, option B is true.

Inequality is the absence of an equality link between two expressions or values. An ordered pair is made up of the x and y coordinates, with two values stated in a certain order inside parenthesis.

Substitute the values from the given ordered pair one by one to check whether the given inequalities are true.

Substituting (-2,2) in y < –x + 1 and y > x,

For,  y < –x + 1

2<2+1

2<3

For, y > x

2>-2

This ordered pair (-2,2) makes the given inequalities true.

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The factorization of y²+7y-8 is (y+8)(y-1).

y²+7y-8

=y²+8y-y-8

=y(y+8)-1.(y+8)

=(y+8)(y-1)

The factors are (y+8), (y-1).

The method we are following here is factorize by grouping.

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The correct question is-

Factor y²+7y-8.

Answer:

Step-by-step explanation:

There is a probability of 33.45% that the age of randomly selected CEO will be between 50 and 55 years old.

What does the math term "probability" mean?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.              

                     Statistics is the study of events that follow a probability distribution.

Given that:

Mean = 56, standard deviation = 4, For 50:

z = (50 - 56) / 4 = -1.5

For 44:

z = (55 - 56) / 4 = -0.25

P(50 < x < 55) = P(z < -0.25) - P(z < -1.5) = 0.4013 - 0.0668 = 33.45

There is a probability of 33.45% that the age of randomly selected CEO will be between 50 and 55 years old.

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The initial purchase price of the best fit function is; $2500

The equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The formula to find the slope between two coordinates is;

m = (y₂ - y₁)/(x₂ - x₁)

If we take the coordinates (4, 5000) and (12, 10000), we have;

Slope = (10000 - 5000)/(12 - 4)

Slope = 625

Thus, the equation will be;

5000 = 625(4) + c

5000 - 2500 = c

c = $2500

y-intercept represents the intital price which is when x = 0 years.

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The correct option is A: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.

The given function is;

f(x) = StartRoot x EndRoot , which is written as;

f(x) = √x  

Domain for the  x   = [ 0 , ∞ )

x     f(x)

-1   undefined

0     0

1      1

4     2

The reflection over x-axis.

f(x) ---->  - f(x)

x     f(x)

-1   undefined

0     0

1      -1

4     -2

Thus, the correct option is; A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.

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The complete question is-

Which represents the reflection of f(x) = StartRoot x EndRoot over the x-axis?

A: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries undefined, 0, negative 1, negative 2.

B: A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 4. The second column is labeled f (x) with entries 1, 0, undefined, undefined.

C: On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the left through (negative 4, negative 2).

D: On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the right through (2, negative 4).

Answer:

D

Step-by-step explanation:

Edge 2023

Answer:

98 yd²

Step-by-step explanation:

diagonal = 7 · 2 = 14 yd

side = x² + x² = 14²

2x² = 196

x² = 196/2

x² = 98

x = √98

area = √98² = 98 yd²

The perimeter of the whole diagram in cm is derived as 86.6158 cm using trigonometric ratios.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the angle P for right-angled triangle formed by extending the line PQ to the base of the trapezium, so that we have opposite side of 7 cm (22 cm - 15 cm)

so; sinP = 7/25.3

P = sin^(-1)(7/25.3)

P = 16.06

The isosceles triangle PQR have the angle;

Q = 180 - 2(16.06) {sum of interior angles of Isosceles triangle with two equal base angles}

Q = 147.88°

Considering the smaller right-angled triangle formed by the height of the trapezium and one side of the Isosceles triangle, we have its angle;

Q = 180° - 147.88° {sum of angles on a straight line}

Q = 32.12

also;

sin32.12 = 7/hypotenuse (one of the equal sides of the Isosceles triangle)

hypotenuse = 7/sin32.12

hypotenuse = 13.1655

The length TS is equal to the adjacent side of the smaller triangle, so;

cos32.12 = TS/13.1655

TS = 13.1655 × cos32.12

TS = 1.51503

Therefore, the perimeter of the whole diagram is;

25.3 cm + 22 cm + 15 cm + 13.1655 cm + 11.1503 cm = 86.6158 cm.

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If both bouquets have 6 tickseeds, the first bouquet ( roses + tickseeds) has more flowers.

The problem can be solved using ratio.

Bouquet 1 :

Every 2 tickseeds there are 7 roses

Hence, the ratio

Tickseed : rose = 2 : 7    

If there are 6 tickseeds, then

2 : 7 = 6 : rose

rose = (6/2) x 7 = 21

Number of flowers = 6 tickseeds + 21 roses = 27 flowers

Bouquet 2 :

Every 3 tickseeds there are 4 daisies

Hence, the ratio

Tickseed : daisy = 3 : 4

If there are 6 tickseeds, then

3 : 4 = 6 : daisy

daisy = (6/3) x 4 = 8

Number of flowers = 6 tickseeds + 4 daisies = 10 flowers

Hence, if there are 6 tickseeds in each bouquet, the first bouquet contains more flowers.

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x = random variable = number of successful trials = 4

n = number of trials = 6

P = likelihood of success = 0.55

Q = likelihood of failure = 0.45

nCx = number of combinations of n objects taken x at a time

.

Binomial Distribution

b(x; n, P) = nCx * P^x * Q^(n - x)

.

b(4; 6, 0.55) = 6C4 * (0.55)^4 * (0.45)^2 = (15)(0.09150625)(0.2025) = 0.2779502

[tex]$W(\mathbf{x})$[/tex]is a linear transformation. it is not onto .The given statement is false.

The objective is to determine whether the following statement is true or false.

"If [tex]$$T_1(\mathbf{x})$ and $T_2(\mathbf{x})$[/tex] are onto linear transformations from [tex]$\mathbf{R}^n$[/tex] to [tex]$\mathbf{R}^m$[/tex] then [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex] is an onto linear transformation."

To check whether [tex]$W(\mathbf{x})$[/tex] is a linear transformation or not:

For a, b ∈ R and for x, y ∈ [tex]$\mathbf{R}^n$[/tex],

[tex]$$\begin{aligned}W(a \mathbf{x}+b \mathbf{y})= & T_1(a \mathbf{x}+b \mathbf{y})+T_2(a \mathbf{x}+b \mathbf{y}) \quad\left(\text { Since } W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})\right) \\= & {\left[a T_1(\mathbf{x})+b T_1(\mathbf{y})\right]+\left[a T_2(\mathbf{x})+b T_2(\mathbf{y})\right] } \\& \quad\left(\text { Since } T_1(\mathbf{x}) \text { and } T_2(\mathbf{x}) \text { are onto linear transformations }\right) \\\end[/tex]

[tex]= & a\left[T_1(\mathbf{x})+T_2(\mathbf{x})\right]+b\left[T_1(\mathbf{y})+T_2(\mathbf{y})\right] \\\\= & a W(\mathbf{x})+b W(\mathbf{y})\end{aligned}$$[/tex]

Therefore, [tex]$W(\mathbf{x})$[/tex] is a linear transformation.

To check whether [tex]$W(\mathbf{x})$[/tex] is onto:

Define the linear transformations:

[tex]$$T_1: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_1(\mathbf{x})=\mathbf{x}$[/tex]

[tex]$$T_2: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_2(\mathbf{x})=-\mathbf{x}$[/tex]

Then, [tex]$T_2(\mathbf{x})=-\mathbf{x}=-T_1(\mathbf{x}) \Rightarrow T_2(\mathbf{x})=-T_1(\mathbf{x})$[/tex]

The range of both functions [tex]$T_1, T_2$ is $\mathbf{R}$[/tex] This is same as the co-domain of [tex]$T_1, T_2$[/tex]. So, they are onto functions.

If A and B are the two sets, if for every element of B, there is at least one or more element matching with set A, it is called the onto function.

Therefore, [tex]$T_1, T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex]are onto linear transformations.

And, [tex]$W=T_1+T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex] is a mapping.

Now, [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex]

[tex]$$\begin{aligned}& =T_1(\mathbf{x})-T_1(\mathbf{x}) \\& =0\end{aligned}$$[/tex]

So, the range of [tex]$$W(\mathbf{x})$ is $\{0\} \neq \mathbf{R}($[/tex] co-domain of [tex]$W(\mathbf{x}))$[/tex]

Then, is [tex]$W(\mathbf{x})$[/tex] not onto.

So, the given statement is false.

Hence, the correct answer is 5th option

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if the pile contains only 25 quarters and only 40 dimes but at least 50 of each other kind of coin, then 20,281 collections of 50 coins can be chosen.

what are quarters?

Given that:

25 quarters and only 40 dimes

No. of. Ways with at least 26 quarters and 41 dimes.

26 + 41 = 67 coins, but we have only 50 coins.

There are 0 ways to select at least 26 quarters and 41 dimes.

[tex]A_{1}[/tex] = at least 26 quarters

[tex]A_{2}[/tex] = at least 41 dimes

Using inclusion / exclusion rule for the two sets:

N([tex]A_{1} U A_{2}[/tex]) = N ( [tex]A_{1}[/tex]) + N ( [tex]A_{2}[/tex])- N ([tex]A_{1}[/tex] ∩ [tex]A_{2[/tex])

                = 2925 + 220 - 0

                = 3145

Therefore, no . of . ways with at most 25 quarters and at most 40 dimes are

= 23426 - 3145

= 20,281 ways

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The tower is 24 feet tall.

To solve this problem, we need to use the formula for the volume of a rectangular prism, which is V = l × w × h, where l and w are the length and width of the base and h is the height.

We are given that the side length of the base of the building is 100 feet less than the height of the building, so the height of the building is h = l + 100, where l is the side length of the base. We can substitute this expression for h into the formula for the volume of the building:

V = l × w × (l + 100) = 2 million cubic feet

Since the building is 25 times as tall as the tower, the height of the tower is h = (1/25) × h = (1/25) × (l + 100). Substituting this expression for h into the formula for the volume of the building, we get:

V = l × w × (1/25) × (l + 100) = 2 million cubic feet

Solving this equation for l, we find that l = 500 feet. This is the side length of the base of the building, so the height of the building is h = l + 100 = 500 + 100 = 600 feet. The tower is (1/25) × 600 = 24 feet tall.

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The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable).

It is denoted by r-squared and typically takes values between 0 and 1. A value of 0 indicates that the independent variable does not explain any of the variance in the dependent variable, while a value of 1 indicates that the independent variable explains all of the variance in the dependent variable. The coefficient of determination (also known as the R-squared) is a measure of the proportion of the variance in the dependent variable (the y-variable) that is explained by the independent variable (the x-variable). A higher R-squared value indicates a stronger regression relationship between the two variables.

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Answer:

To calculate the total interest that Lucy will have to pay, we need to use the formula for simple interest: I = P * R * T, where I is the interest, P is the principal (the amount borrowed), R is the interest rate (as a decimal), and T is the time in years. Using this formula, we can calculate the total interest that Lucy will have to pay as follows:

I = P * R * T

I = $4000 * 0.05 * 2

I = $400

Therefore, the total interest that Lucy will have to pay is $400.

________________________________________________________

To calculate the total repayment amount (including interest), we need to add the total interest to the original amount borrowed, which in this case is $4000. Therefore, the total repayment amount will be $4000 + $400 = $4400. This is the amount that Lucy will have to pay back to her parents at the end of the two-year period.

Step-by-step explanation:

Answer:

Total interest = $400

Total repayment (including interest) = $4,400

Step-by-step explanation:

Simple Interest Formula

[tex]\large\boxed{ \sf I = Prt}[/tex]

where:

Given:

To find the total interest, substitute the given values into the formula and solve for I:

[tex]\implies \sf I=4000 \cdot 0.05 \cdot 2[/tex]

[tex]\implies \sf I=200 \cdot 2[/tex]

[tex]\implies \sf I=400[/tex]

Therefore, the total interest Lucy has to pay is $400.

The total repayment amount is the sum of the principal and the interest:

[tex]\implies \sf A=P+I[/tex]

[tex]\implies \sf A=4000 +400[/tex]

[tex]\implies \sf A=4400[/tex]

Therefore, the total repayment (including interest) is $4,400.

Answer:

0

Step-by-step explanation:

The expanded equation of the function f(x) = (3x + 2)⁴ is f(x) = 81x + 216x³ + 216x² + 96x + 16

From the question, we have the following parameters that can be used in our computation:

f(x) = (3x + 2)⁴

Using the pascal triangle at n = 4, we have the coefficients to be

Coefficient = 1     4     6     4     1

So, when the function f(x) = (3x + 2)⁴ is expanded, we have

f(x) = 1 * (3x)⁴ + 4 * (3x)³ * 2 + 6 * (3x)² * 2² + 4 * (3x) * 2³ + 1 * 2⁴

Evaluate

f(x) = 81x + 216x³ + 216x² + 96x + 16

Hence, the solution is f(x) = 81x + 216x³ + 216x² + 96x + 16

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I would prefer leaving the answer as a radical number as √5 since it is a shorter form and exact form of the answer.

My reasons for leaving it as a radical form or a decimal approximation are;

1) If we are trying to find an exact answer, then we should leave it as √5. For example, if we are told a square has an area of 5 square units, then it means that the exact length of the side is √5 units.

2) If √5 is the length of an object that has to be made to that specific length, then we would require an approximation. For example, if you are asked to make a square out of cardboard whose area is 5 square feet, then we will definitely need an approximation of √5 ft = 2.24 ft, which would help us make each side of the cardboard square in the length of 2.24 ft.

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