(4xyy)(5xy) Expand And Simplify (2024)

Answer:

10

Step-by-step explanation:

I divided 570 by 15 to see how many miles she can travel per gallon of gas which came out to be 38.

After that i divided the 380 by the 38. 380÷38 is 10.

Answer:

Need:

10 gallons

Step-by-step explanation:

Proportions:

15 gallons ⇒ 570 miles

A gallons ⇒ 380 miles

A = 15gallons * 380miles / 570miles

A = 10 gallons

The probability of a successful batting is 0.341; we need to find the probability of at least 1 hit within the first 5 at-bats; thus,

[tex]P(Hit)=1-P(NoHit)[/tex]

Therefore, we need to calculate the probability of not hitting the ball within the first 5 at-bats.

The binomial distribution states that

[tex]\begin{gathered} P(X=k)=(nBinomialk)p^k(1-p)^{n-k} \\ n\rightarrow\text{ total number of trials} \\ k\rightarrow\text{ number of successful trials} \\ p\rightarrow\text{ probability of a successful trial} \end{gathered}[/tex]

Thus, in our case,

[tex]P(k=0)=(5Binomial0)(0.341)^0(0.659)^5=1*1*0.124287...[/tex]

Then,

[tex]P(Hit)=1-0.124287...\approx0.876[/tex]Therefore, the answer is 0.876

The equation that gives us the amount of gas left in her car, given the driven miles, is

[tex]f(x)=15-\frac{x}{25}[/tex]

Notice that when x=25, there will remain 14 gallons of gas in the tank.

The x-intercept is

[tex]\begin{gathered} f(x)=0 \\ \Rightarrow0=15-\frac{x}{25} \\ \Rightarrow x=15\cdot25=375 \end{gathered}[/tex]

(375,0). This is the maximum distance one can drive when the amount of gas in the tank reaches zero gallons.

On the other hand, the y-intercept is

[tex]\begin{gathered} x=0 \\ \Rightarrow f(x)=15 \end{gathered}[/tex]

(0,15). This is the number of gallons in the tank when we have driven 0 miles.

Let's make the table of the prime factors of 84:

then we have that 84=2x2x3x7, therefore, the prime factors are 2, 3 and 7

Given:

Lan is working two jobs:

1) $19 per hour life guarding

2) $9 per hour clearing tables

The total hours per week = 14

He must earn a minimum of $180

Let x represents the number of hours life guarding and y represents the number of hours clearing tables

So, we have the following inequalities

[tex]\begin{gathered} x+y\le14 \\ 19x+9y\ge180 \end{gathered}[/tex]

We need to solve the inequalities by graph

So, we will graph the lines: x + y = 14 and 19x + 9y = 180

The shaded area represents the solution of the system of inequalities

The following figure represents the solution of the system of inequalities

A tall man(138cm) casts a shadow of 145cm

A building nearby casts a shadow of 188m

Using the information you have to determine the height of the building.

First step is to convert the units of the height of the man and the length of his shadow from cm to meters:

100cm=1m

So 145cm=1.45m

And 138co=1.38m

Now that the measurements are expressed in the same units you can determine the height shadow ratio of the man and use it to calculate the height of the bulding.

[tex]\frac{\text{height}}{\text{shadow}}=\frac{1.38}{1.45}[/tex]

Compare this ratio with the ratio between the heigth/shadow ratio of the building to determine the heigth of the building.

Said height will be symbolized as "x"

[tex]\begin{gathered} \frac{1.38}{1.45}=\frac{x}{188} \\ x=(\frac{1.38}{1.45})188 \\ x=178.92m \end{gathered}[/tex]

The building is 178.92m

Answer:

[tex]3x + 5 = 2x - 7[/tex]

The function is solved below

What is a function?

The function is instantly given a name, such as a, in functional notation, and its description is supplied by what it does to the input x, using a formula in terms of x. Instead of sine, put sine x. (x). Leonhard Euler invented functional notation in 1734. Some commonly used functions are represented with a symbol made up of many letters (usually two or three, generally an abbreviation of their name). In this scenario, a roman font is typically used, such as "sine" for the sine function, rather than an italic font for single-letter symbols. A function is also known as a map or a mapping, however some writers distinguish between "map" and "function."

The function can be written as

3x+4y-7 = 0

or, y = (-3/4)x + 7/4

so, slope = -3/4

and other function is

kx+12y+3 = 0

or, y = (-k/12)x - 1/4

so, slope = -x/12

Given the lines are parallel, so slopes are equal

i.e., -3/4 = -k/12

or, k = (3/4)12 = 9

Hence, the value of k is 9.

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Given data:

The given time taken by Tin to type 720 words is t=15 min.

The given expression can be wriiten as,

720 word=15 min

720 words= 15(60 sec)

720 words= 900 sec

1 word = 900/720 sec

=1.25 sec

Multiplying the above equation with 864 on both sides .

864 words= 864(1.25) sec

= 1080 sec

=1080/60 min

= 18 min.

Thus, the time taken bby Tine to type 864 words is 18 min.

The x intercept is the value of x when y = 0

Given that x intercept = - 1, the coordinate is (- 1, - 0)

The y intercept is the value of y when x = 0

Given that y intercept = - 2, the coordinate is (0, - 2)

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

x1 = - 1, y1 = 0

x2 = 0, y2 = - 2

Slope = (- 2 - 0)/(0 - - 1)

slope = - 2/1

slope = - 2

Given the system of equations:

[tex]\begin{gathered} y=-2x-7\rightarrow(1) \\ x-y=-8\rightarrow(2) \end{gathered}[/tex]

we will find the solution to the system by graphing

To draw the lines, we need to know two points on each line

so, substitute with two values of x and calculate the corresponding value of y

For line (1): y = -2x - 7

[tex]\begin{gathered} x=0\rightarrow y=-2\cdot0-7=-7 \\ x=1\rightarrow y=-2\cdot1-7=-9 \end{gathered}[/tex]

so, line (1) passes through the points ( 0, -7) and ( 1, -9)

For line (2): x - y = -8

y = x + 8

[tex]\begin{gathered} x=0\rightarrow y=8 \\ x=1\rightarrow y=1+8=9 \end{gathered}[/tex]

So, line 2 passes through the points ( 0, 8) and ( 1, 9)

The graph of the line will be as shown in the following picture

As shown in the figure:

Line (1) is the blue line

Line (2) is the red line

The point of intersection = ( -5, 3)

So, the solution is point ( -5, 3)

Answer:

32.50x + 7.50 < 235

Step-by-step explanation:

All the cost have to be less than 325. x stands for the number of people buying tickets.

a) The probability of losing money when standard deviation is 5% is 2.27%

b) The probability of losing money when standard deviation is 10% is 15.87%

Given,

There is an investment whose return is normally distributed.

The mean of the distribution = 10%

The standard deviation of the distribution = 5%

a) We have to determine the probability of losing money:

Lets take,

x = -0.005%

Now,

P(z ≤ (-10.005 / 5) ) = P(z ≤ - 2.001) = 0.02275

Now,

0.02275 × 100 = 2.27

That is,

The probability of losing money is 2.27%

b) We have to find the probability of losing money when the standard deviation is 10%

Let x be 0.01%

Now,

P(z ≤ (-10.01/10)) = P(z ≤ -1.001) = 0.15866

Now,

0.15866 × 100 = 15.87

That is,

The probability of losing money is 15.87%

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Let:

A = Draw a black card

B = Draw and odd number

C = Draw a card with a letter

so:

[tex]\begin{gathered} P(A\cap B)=\frac{8}{52}=\frac{2}{13} \\ P(C)=\frac{16}{52}=\frac{4}{13} \end{gathered}[/tex]

Therefore:

[tex]P((A\cap B)\cup C)=\frac{2}{13}+\frac{4}{13}=\frac{2+4}{13}=\frac{6}{13}[/tex]

[tex]\begin{gathered} \text{For }Albert \\ For\text{ \$1,000} \\ t=10years=120\text{ months} \\ i=1.2\text{\%=0.012} \\ C=1,000(1+0.012)^{120} \\ C=1,000(1.012)^{120} \\ C=\text{\$}4,184.67 \\ \text{For \$}500 \\ \text{lost 2\%=0.02 over 10 years, hence} \\ C1=500(1-0.02) \\ C1=500(0.98) \\ C1=\text{ \$}490 \\ \text{For \$}500 \\ i=0.8\text{ \%=0.008} \\ t=10 \\ C2=500(1+0.008)^{10} \\ C2=500(1.008)^{10} \\ C2=\text{ \$}541.47 \\ \text{Total}=\text{\$}4,184.67+\text{ \$}490+\text{ \$}541.47 \\ \text{Total}=\text{ \$5,216.14} \\ After\text{ 10 year Albert has \$5,216.14} \\ \text{For Marie} \\ For\text{ \$1,500} \\ Quaterly \\ 1\text{ year has }3\text{ quaternions, hence in 10 years are 30 quaternions, t=30} \\ i=1.4\text{ \% monthly, hence } \\ \frac{1.4\text{ \% }}{3}=0.467\text{ \%=0.00467} \\ C=1,500(1+0.00467)^{30} \\ C=1,500(1.00467)^{30} \\ C=\text{ \$}1,725.02 \\ \text{For \$500} \\ C2=500(1+0.04) \\ C2=500(1.04) \\ C2=\text{ \$}520 \\ \text{Total}=\text{ \$}1,725.02+\text{ \$}520 \\ \text{Total}=\text{ \$}2,245.02 \\ After\text{ 10 year Marie has \$2,245.02} \\ \text{For }Hans \\ t=10 \\ i=0.9\text{ \%=0.009} \\ C=2,000(1+0.009)^{10} \\ C=2,000(1.009)^{10} \\ C=\text{\$}2,187.47 \\ After\text{ 10 year Hans has \$}2,187.47 \\ \text{For }Max \\ For\text{ 1,000} \\ t=10 \\ i=0.5\text{ \%=0.005} \\ C=1,000e^{(-0.005)(10)} \\ C=\text{\$}951.23 \\ \text{For 1,000} \\ i=1.8\text{ \%=0.018} \\ t=20 \\ C1=1,000(1+0.018)^{20} \\ C1=1,000(1.018)^{20} \\ C1=\text{ \$1,428.75} \\ \text{Total =\$}951.23+\text{ \$1,428.75} \\ \text{Total}=\text{ \$2,379.98} \\ After\text{ 10 year Max has \$2,379.98} \\ \\ At\text{ the end of the competition is \$10,000 richer than his siblings} \end{gathered}[/tex]

The distance from Keith's house to Karen's house is

= 5/6 - 2/3

= 5/6 - 4/6

= 1/6 miles

Explanation

When the discriminant is negative, this implies that

[tex]b^2-4ac<0[/tex]

Answer: In this case, the equation has no real solutions;

First, lets calculate how much the expended in the perfume:

[tex]2\times(4.36)+5\times(2.15)_{}+4\times(2.27)=28.55[/tex]

So, for 11 ounces of perfume, they need $28.55, so the minimum that the perfume need to cost per ounce is:

[tex]\frac{28.55}{11}=2.5954\cong2.6[/tex]

So, about $2.6 per ounce of perfume.

Answer: [tex]y=-\frac{5}{2}x+16[/tex]

Step-by-step explanation:

The equation in point-slope form is [tex]y-1=-\frac{5}{2}(x+6)[/tex]. To find the equation in slope-intercept form, isolate [tex]y[/tex].

[tex]y-1=-\frac{5}{2}(x-6)\\\\y-1=-\frac{5}{2}x+15\\\\y=-\frac{5}{2}x+16[/tex]

We are given a problem that can be solved using a system of linear equations. Let A, be the number of adults, and S the number of students. Since there are in total 142 people and there were two days, this means that the sum of the number of adults and the number of students must be 284, which can be written mathematically as follows:

[tex]A+S=284,(1)[/tex]

This is our first equation. The second equation is found using the total sales of $1948. Since the ticket per adult is $8 and per student is $5, we have the following equations:

[tex]8A+5S=1948,(2)[/tex]

To solve this equation we will solve for A in equation (1), by subtracting S to both sides;

[tex]\begin{gathered} A+S-S=284-S \\ A=284-S \end{gathered}[/tex]

Now we will replace this value in equation (2):

[tex]8(284-S)+5S=1948[/tex]

Now we will apply the distributive property:

[tex]2272-8S+5S=1948[/tex]

Addins like terms:

[tex]2272-3S=1948[/tex]

Subtracting 2272 to both sides;

[tex]\begin{gathered} 2272-2272-3S=1948-2272 \\ -3S=-324 \end{gathered}[/tex]

Dividing both sides by -3:

[tex]S=-\frac{324}{-3}=108[/tex]

Now we replace this value in equation (1), where we have already solved for A:

[tex]\begin{gathered} A=248-108 \\ A=140 \end{gathered}[/tex]

Therefore, there were sold 108 student tickets and 140 adult tickets.

Since the rectangles are similar, that means their sides are proportional.

Since the bigger rectangle has a base of 24cm and the smaller one's base is 20cm, the proportion the sides hold is

[tex]\frac{24}{20}=1.2[/tex]

This means the sides of the larger rectangle are 1.2 times larger than those of the smaller one.

The area of the small rectangle is 80cm². Since

[tex]A=b\mathrm{}h[/tex]

where b is the lenght of the base and h is the lenght of the height, then

[tex]80=20\cdot h_1[/tex][tex]\frac{80}{20}=h_1=4[/tex]

So the height of the small rectangle will be 4cm. But as we previously deduced, the height of the larger rectangle will be 1.2 times larger than that of the smaller one, so it's height will be

[tex]h_2=4\cdot1.2=4.8[/tex]

And so, its are is

[tex]A_2=24\cdot4.8=115.2[/tex]

We can confirm this because

[tex]\frac{115.2}{80}=1.44=1.2^2[/tex]

which is the proportion the areas of the rectangles hold.

Coplanar lines are lines that lies in the same plane.

By definition, two distince lines that lies in the same plane and that do not intersect are said to be parallel

Hence the correct choice is A

Answer:

14980

Step-by-step explanation:

4 2 8
x
3 5
-----------
2 1 4 0 ---> 428 x 5
1 2 8 4 ---> 428 x 3 but since 3 is in the 10s place we shift by 1
--------------- to the left. You can think of that 1248 as 12480
1 4 9 8 0 --> add the two rows

Hope that helps. I tried my best to explain :)

Answer:

428

× 35

+ 2140

+ 1 284

= 1 4980

Step-by-step explanation:

[tex]\begin{gathered} f(x)=2x \\ g(x)=\frac{2}{3}x+7 \end{gathered}[/tex]

The vertical translation involves shifting the graph either up or down on the y axis. For example.

[tex]\begin{gathered} y=f(x) \\ \text{translated upward }it\text{ will be } \\ y=f(x)+k \end{gathered}[/tex]

When a graph is vertically compressed by a scale factor of 1/3, the graph is also compressed by that scale factor. This implies vertical compression occurs when the function is multiplied by the scale factor. Therefore,

[tex]\begin{gathered} f(x)=2x \\ \text{The vertical compression by a scale of }\frac{1}{3}\text{ will be} \\ g(x)=\frac{1}{3}(2x)=\frac{2}{3}x \end{gathered}[/tex]

Finally, the vertical translation up 7 units will be as follows

[tex]g(x)=\frac{2}{3}x+7[/tex]

The answer is a. There is a vertical compression by a factor of 1/3 . Then there is a vertical translation up 7 units.

We have the next system of equations

2x+3y=0 ...(1)

6x+9y=0 ...(2)

I order to solve this system by elimination we will multiply the first equation by -3

So we will have

-6x-9x=0

then we add the equation above with the second equation

-6x-9x=0

+6x+9y=0

As we can see we obtain 0=0 which means that we have infinity solutions

ANSWER

Infinity solutions

Input data

7h + 3

Procedure

A term is a single mathematical expression.

3 = is a single term.

It is simply a numerical term called a constant.

7h = is also a single term. , The coefficient of the first term is 7

The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3

The first point = (-5,6)

The second point = (-9,-6)

The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]

= -12/-4

= 3

Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3

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Answer:

A.it can't be endeavor.

The description for the table in word will be A. The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.

What is a proportional relationship?

Proportional connections are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

In this case, the table shows a proportional relationship between workout and calories burned. In 1 hour, 320 calories are burned.

In conclusion, the correct option is A.

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Solve;

[tex]\begin{gathered} f(x)=-2x-3 \\ f(-1)=-2(-1)-3 \\ f(-1)=2-3 \\ f(-1)=-1 \end{gathered}[/tex]

The answer is -1

That is f(-1) = -1