Model with math Katrina and Becca exchanged 270 text messages in 45 minutes. An equal number of texts was sent each minute. The girls can send 90 more text messages before they are charged additional fees. Complete the double-number line diagram . At this rate for how many more minutes can the girls exchange texts before they are charged extra

Step-by-step explanation:

10 + x = 30

or, x = 30 - 10

x = 20

Answer:

  B.) 4x^2 - 15x - 54

Step-by-step explanation:

You want the product f(x)·g(x) when f(x) = 4x+9 and g(x) = x-6.

The distributive property can be used to find the product. Each term of one binomial is multiplied by every term of the other, and like terms are combined.

  f(x)·g(x) = (4x +9)·(x -6)

  = 4x(x -6) +9(x -6)

  = 4x² -24x +9x -54 = 4x² +(-24 +9)x -54

  f(x)·g(x) = 4x² -15x -54 . . . . . . . . . . matches choice B

__

Additional comment

The product of two binomials is sometimes described using the mnemonic FOIL, for First, Outer, Inner, Last. These refer to the locations of the terms involved in the four products

These products are the same as the ones we show above.

The FOIL mnemonic is only helpful for two binomials. Any polynomials can be multiplied using the distributive property.

Answer:

x= 2.7,-11.7 (sorry if im wrong) :'C

Answer:

Step-by-step explanation:

define function fg(x) :

Fg(x)  = f(g(x))

         = [tex]\frac{5}{x}[/tex] (4-2x)-1

         = [tex]\frac{20}{x}[/tex] - [tex]\frac{10x}{x}[/tex] - 1

         = 20 - 10x -1

         = 20 - 1 - 10x

         = 19 - 10x

Answer:

3 feet

Step-by-step explanation:

All 4 sides are equal so 12/4=3

As per given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.

As given in the  question,

Number of copies of 26 pages article print by printing center is equal to 1,233 copies

Number of copies of 12 page article print by printing center is equal to 658 copies

Total number of pages print by printing center during this one week is equal to

= ( 1233 × 26 ) + ( 658 × 12 )

= 32,058 + 7896

=39,954 pages

Therefore, for the given data of printing, the total number of pages print by printing center during the week is equal to 39,954 pages.

Learn more about total number here

brainly.com/question/14993202

#SPJ4

Answer:

27

Step-by-step explanation:

I broke the figure up into 3 rectangles.

5x2 = 10

2x3 = 6

4x5 = 20

This adds to 36.  Then subtract out the green square of 9

36 - 9 = 27

Drake needs 144 ft² (squared feet) of fabric to make the 8 ft long and 18 ft tall sail.

The area (square units) of two lengths is the product of the multiplication of the two lengths.

The area refers to the space occupied by a two-dimensional object or structure.

Areas are stated in square feet to show the squared units occupied by such objects.

The length of a sail = 8 feet

The height of the sail = 18 feet

The square area = 144 ft² (8 x 18)

Thus, Drakes requires a fabric measuring 144 ft² (squared feet) to make the sail.

Learn more about the squared area at https://brainly.com/question/25292087

#SPJ1

Answer:

$47.76

Step-by-step explanation:

77 : 100 = x : 207.65

x = (207.65 * 77)/100

x = 159.8905

final price = 207.65 - 159.8905 = 47.7595= $47.76

Answer:

Subtract 3 3/4 from 10 1/2.  Note that the LCD is 4, so 10 1/2 = 10 2/4.

What is    10 2/4

              -  3 3/4

-------------------------

                    ?

Since 2/4 is smaller than 3/4, you must borrow 1 from that 10.

Now your problem looks like   9 6/4

                                              -3 3/4

                                            ----------

                                                6 3/4   (answer)

The remnant of the board is 6 3/4 feet long.

Step-by-step explanation:

A population has a standard deviation of 10 and a mean of 75.

The sample mean has a standard deviation of 5 and an expectation of 100.The empirical rule states that there is a 68% probability of being between 95 and 105 (within one standard deviation of its expected value) if it is approximately normal.

What is meant by a standard deviation?

A measure of how dispersed the data are in relation to the mean is called the standard deviation (or ).Data with a low standard deviation are grouped around the mean, while data with a high standard deviation are more dispersed.

How can I determine the standard deviation?

Step 1: Locate the mean. Step 2: Find the square of the distance from the mean for each data point. Step 3: Sum the results of Step 2's values. Step 4: Divide by how many data points there are.

Learn more about standard deviation here:

https://brainly.com/question/475676

#SPJ4

Answer:

-4

Step-by-step explanation:

The line intercepts at the y axis on exactly -4.

Answer:

The y-intercept is (0,-4).

Step-by-step explanation:

You can see that for the y-axis, that is the first point the line passes through. Hope this helps! Good luck! I am up doing math too. -_- Don't mark me brainliest, I just like to help.

The Fourier series representation of the output y(t) is;

(a) y(t) = 0.097 cos(3πt - 67)

(b) y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

Given;

A causal continuous-time LTI system whose input x(t) and output y(t) are related by the following differential equation;

[tex]\frac{d}{dt}y(t) + 4y(t) = x(t)[/tex]

By taking Laplace's Transform;

sY(s) + 4Y(s) = X(s)

Y(s)/X(s) = H(s) = 1/(s + 4)

(a) When input x(t) = cos3πt

∵ ω = 3π

H(jω) = 1/(jω + 4)

H(jω₁) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.097

∠H(jω) = -tan⁻¹(ω/4) = -67° = Ф₁

y(t) = H(jω₁)*cos(3πt + Ф₁)

→ y(t) = 0.097 cos(3πt - 67)

(b) When input x(t) = sin3πt + cos(6πt + π/4)

∵ ω = 6π

H(jω) = 1/(jω + 4)

H(jω₂) = 1/[tex]\sqrt{w^2+4^2}[/tex] = 0.051

∠H(jω) = -tan⁻¹(ω/4) = -78° = Ф₂

y(t) = H(jω₁) * sin(3πt + Ф₁) +  H(jω₂) * cos(6πt + π/4 + Ф₂)

→  y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

The Fourier series representation of the output y(t) is;

y(t) = 0.097 cos(3πt - 67)

y(t) = 0.097 sin(3πt - 67) + 0.051 cos(6πt + π/4 -78)

To learn more about the continuous-time LTI system click here:

brainly.com/question/15694303

#SPJ4

Answer:

slope = 10

Step-by-step explanation:

Solve the equation for "y". In other words, isolate "y":

y + 7 = 10(x - 4)

y = 10(x - 4) - 7

y = 10x - 40 - 7

y = 10x - 47

Above is a linear expression in slope-intercept form "y = mx + b", where "m=slope" and "b=y-intercept". "m=10", so 10 is the slope

Answer:

1/2

Step-by-step explanation:

Because the y is going up by 0.5 which in a fraction form is 1/2 and it isn't negative 1/2 because the number is growing and is not decreasing.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

1) Find the difference between  and y

2) Find the pattern between the numbers

As we can see there is a pattern of subtract [tex]\frac{1}{2}[/tex] between every number

To find this just subtract each number by the other

As 0.5 is equal to [tex]\frac{1}{2}[/tex] the answer to the solution would be [tex]\frac{1}{2}[/tex]

Hope this helps, have a great day!!

Answer:

Bottom left

Step-by-step explanation:

Let's look at it as (1/3)^x first. This function would have a y-intercept of (0,1) (because (1/3)^0 is 1), and would then become (1/3) times smaller for every 1 unit increment of x. This would look like the top left graph in these options. However, we are given (1/3)^-x, which means, in terms of transformations, that the graph is flipped across the y-axis. Algebraically, this looks like (1/3)^(-x) which equals to  [tex]\frac{1}{(1/3)^x}[/tex], which simplifies down to 3^x, which would look like the bottom left graph.

1. The number of sides of the polygon is of: 12 sides.

2. The missing exterior angles are of: α = 48.5º.

3. The size of the exterior angle is of 20º, hence the polygon has 18 sides.

A regular polygon is a polygon in which all the sides have the same length.

The relation between the measure of the exterior angles of a regular polygon and the number of sides is given as follows:

Measure of each angle = 360º/number of sides.

For item a, the measure of each angle is of 24º, hence the number of sides is obtained as follows:

24º = 360º/number of sides.

24n = 360

n = 360/24

n = 12 sides.

The sum of the measures of the external angles of a polygon is always of 360º.

Hence, for item 2, the missing angles are obtained as follows:

2α + 90 + 55 + 40 + 78 = 360

2α + 263 = 360

2α = 97

α = 97/2

α = 48.5º.

An interior angle and it's exterior angle are supplementary, hence, for item 13, the measure of the exterior angle is of:

Exterior angle = 180º - 160º = 20º.

Then the number of sides of  the polygon is obtained as follows:

20n = 360

n = 360/20

n = 18 sides.

A similar problem, also featuring polygons, is presented at brainly.com/question/224658

#SPJ1

Standard deviation for the given set of data { 6,7,8,9,10} is equal to √2.

As given in the question,

Given set of data is equal to :

{ 6,7,8,9,10}

[tex]x_{i}[/tex] = { 6,7,8,9,10}

Here total number of observation 'N' is equal to 5.

Mean [tex]\bar{x}[/tex] = ∑x / n

            = ( 6+ 7+ 8 + 9 + 10 ) / 5

            = 40 /5

            = 8

[tex]\sum (x_{i} -\bar{x})^{2}[/tex] = ( 6- 8)² + (7-8)² + (8 - 8)²+ ( 9 -8)² + (10 - 8)²

                 = 4 + 1+ 0 + 1+ 4

                 = 10

Standard deviation = [tex]\sqrt{ \frac{\sum (x_{i} -\bar{x})^{2}}{N}[/tex]

                                = √10/5

                                = √2

Therefore, standard deviation for the given set of data { 6,7,8,9,10} is equal to √2.

Learn more about standard deviation here

brainly.com/question/14747159

#SPJ4

Answer:Here's the basic equation

m(d) = 10d + 20(d - 2)  (the money total is the 10 dollar bills plus the 20 dollar bills (which are two less than the 10 dollars))

Step-by-step explanation:

To simplify it, start by distributing the 20:

m(d) = 10d + 20d - 40

add like terms

m(d) = 30d - 40

The probability that a dart hits one of the shaded areas is 1/6 when a dart is thrown at a regular hexagon dartboard with the design shown.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions.

Here,

angle of hexagon=360/6=60°

using trigonometric ratios,

area of triangle=bh/2

=(h*h√3/2)/2

=h²√3/4

area of hexagon=6*area of triangle

=6*(h²√3/4)

=3√3*h²/2

area of rectangle=bh

=h*h√3

=h²√3

area of shaded region,

=3√3*h²/2-h²√3

=h²√3/2

area of 1 shaded region=(h²√3/2)/2

=h²√3/4

Probability of hitting one shaded area,

=(h²√3/4)/(h²3√3/2)

=1/6

When a dart is thrown at a standard hexagonal dartboard with the pattern shown, the likelihood that it will land in one of the shaded areas is 1/6.

To know more about probability,

https://brainly.com/question/11234923?referrer=searchResults

#SPJ1

The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.

Given that,

p = $2,000, r = 3%, and t = 2 yr.

We have to find the i when i=prt.

Here,

i is interest amount.

p is principal amount.

r is rate of interest per year.

t is time period.

So,

Formula for finding interest amount is

i=prt

So,

i=2000(3/100)(2)

i=20×3×2

i=120

Therefore, The interest amount is $120 when given principal amount $2000, rate of interest per year is 3% and time period is 2 years.

To learn more about interest visit: https://brainly.com/question/19291527

#SPJ1

Answer:

Step-by-step explanation:

The question is asking how many times does 50 go into 425?

or 450/50 = ?

my calculator says it's 9 .  What does your calculator say?

since we now know it's 9 times,   we can just multiply 9 * 10 minutes

by observation of 9*10,  I get the answer,  what answer do you get?

Option c, d, f are true about the chi-square goodness of fit test.

Explanation:

a. It is common to use one-sided alternative hypotheses when performing the chi-square goodness of fit test.

FALSE, there is no such thing as one sided in chi-square goodness of fit test.

b. The chi-square test statistic follows a Poisson null distribution.

FALSE, chi square is a distribution of its own more like normal distribution.

c. It compares an observed frequency distribution with an expected frequency distribution.

TRUE, because this is what is done in chi-square test.

d. The null hypothesis is that there is no difference between the observed and expected values.

TRUE

e. The degrees of freedom are k - 1, where k is the number of classes.

FALSE, because k is the number of parameters and not the number of classes.

f. The nature of the expected frequency distribution depends on the probability model on which it is based.

TRUE, this is a fact line because the model whose hypothesis testing we are following we will follow expected frequency of that model only.

To know more about chi-square check below link:

https://brainly.com/question/4543358

#SPJ4

Answer:

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Answer:

B

Step-by-step explanation:

1.20x + 3.60 < 9.60

1.20x < 9.60 - 3.60

1.20x < 6

x < 6 ÷ 1.20

x < 5

The ratio of green apples to all apples in the basket is 5:14 and the ratio of red apples to all apples in the basket is 9:14.

According to the question,

We have the following information:

There are five green apples and nine red apples in a basket.

Now, total apples in the basket are (5+9) which is 14.

Now, the ratio of green apples to all apples in the basket:

Number of green apples : total apples in the basket

5:14

Now, the ratio of red apples to all apples in the basket:

Number of red apples : total apples in the basket

9:14

Hence, the ratio of green apples to all apples in the basket is 5:14 and the ratio of red apples to all apples in the basket is 9:14.

To know more about ratio here

https://brainly.com/question/13419413

#SPJ1

Answer:

Slope = - 2

Explanation step by step:

Answer:

$5

Step-by-step explanation:

Since $10 for 6 avocados and 3 = half of 6,

You would half $10 too = $5

Answer:

$5

Step-by-step explanation:

divide both numbers by 2 and there is your answer