sam can mow his yard in 5 hours. Lucy can mow the same yard in 3.5 hours. How long will it take them to mow the lawn together?

Answer:

[tex]x=\frac{3}{2}\\ y=\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]y=-x+2\\y=3x-4[/tex]

Let's solve one of them for x.

[tex]y=3x-4[/tex]

Add 4

[tex]y+4=3x[/tex]

Divide by 3.

[tex]x=\frac{y+4}{3}[/tex]

Now, plug the value of y in the formula, or you can plug the value of x in the other equation. I'll take this one.

[tex]x=\frac{y+4}{3}[/tex]

[tex]x=\frac{(-x+2)+4}{3}[/tex]

[tex]x=\frac{-x+2+4}{3}[/tex]

[tex]x=\frac{-x+6}{3}[/tex]

Multiply by 3 to get rid of the denominator.

[tex]3x=-x+6[/tex]

add x

[tex]3x+x=6[/tex]

Combine like terms;

[tex]4x=6[/tex]

Divide by 4.

[tex]x=\frac{6}{4}[/tex]

Simplify.

[tex]x=\frac{3}{2}[/tex]

Now that you found the value of x, replace it in any of the equations to find y.

[tex]y=-x+2\\y=-(\frac{3}{2})+2\\ y=-\frac{3}{2}+2[/tex]

[tex]y=\frac{-3+2*2}{2} \\y=\frac{-3+4}{2} \\y=\frac{1}{2}[/tex]

Proof:

[tex]y=3x-4\\\frac{1}{2}=3(\frac{3}{2})-4\\\frac{1}{2}=(\frac{9}{2})-4[/tex]

[tex]\frac{1}{2}=\frac{9-4*2}{2}[/tex]

[tex]\frac{1}{2}=\frac{9-8}{2}[/tex]

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

Answer:

719 = x

Step-by-step explanation:

877+100=_x_+258

Combine like terms

977 = x+258

Subtract 258

977 -258 = x+258-258

719 = x

Answer:

7 9/10

Step-by-step explanation:

Answer:

#3: x is approximately 0.37, -5.37, #4: x is approximately 4.19, -1.19

Step-by-step explanation:

You can solve using the quadratic equation or by solving with the perfect square

[tex]\frac{-b+/-\sqrt{b^{2}-4ac} }{2a}[/tex] = [tex]x^{2}+5x-2=0\\ \frac{-5+/-\sqrt{5^{2}-4(1)(-2) }}{2(1)}[/tex]

x is approximately 0.37, -5.37

Answer:

5040 different combinations

Step-by-step explanation:

0-9 = 10 numbers

1st digit can be 1 0f 10

2nd digit can be 1 of 9

3rd digit can be 1 of 8

4th digit can be 1 of 7

10×9×8×7=5040

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as the dimension of the polygon is not given.

However, I'll give a general explanation of how to calculate the area of a regular polygon.

If you follow these simple steps, you'll arrive at your answer.

The area of a polygon is calculated as thus;

A = ½(nbh)

Where A represent the area

n represents the number of sides

b represents the length of the base

h represent the height of the polygon

Take for instance, the polygon is a regular pentagon.

This means n = 5.

Also assume that the base and the height are 5cm and 7cm respectively.

This means that

Area = ½ * (5 * 5 * 7)

Area = ½ * 175

Area = 87.5cm²

Hence, the area of the polygon is 87.5cm²

Answer:

13p

Step-by-step explanation:

12p+p

Factor out the p

p(12+1)

p (13)

13p

Answer:

1472

Step-by-step explanation:

The sum of n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 9 and d = 19 - 14 = 5 , thus

[tex]S_{23}[/tex] = [tex]\frac{23}{2}[/tex] [ (2 × 9) + (22 × 5) ]

     = 11.5 (18 + 110) = 11.5 × 128 = 1472

Answer:

The length of the pool is [tex]L=24\:ft[/tex].

Step-by-step explanation:

The area of a rectangle is given by [tex]A=L\cdot W[/tex] where L is the length, W is the width.

If the length of the pool is 9 feet more than it’s width, this means that [tex]L=9+W[/tex]

We know that the area of a rectangular swimming pool is 360 [tex]\:ft^2[/tex]. So we simple insert the length ([tex]L=9+W[/tex]), width ( [tex]W[/tex]) and area (360) into the formula and  solve the resulting equation.

[tex]360=\left(9+W\right)W\\\\360=9W+W^2\\\\9W+W^2=360\\\\W^2+9W-360=0[/tex]

[tex]\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex][tex]\mathrm{For\:}\quad a=1,\:b=9,\:c=-360:\quad W_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\left(-360\right)}}{2\cdot \:1}\\\\W=\frac{-9+\sqrt{9^2-4\cdot \:1\left(-360\right)}}{2\cdot \:1}= 15[/tex]

[tex]W=\frac{-9-\sqrt{9^2-4\cdot \:1\left(-360\right)}}{2\cdot \:1}= -24[/tex]

A length cannot be negative. So [tex]W=15[/tex] and the length of the pool is [tex]L=9+15=24\:ft[/tex]

Answer:

It isn't 100

(0.5 is 1/2)

2/0.5=4

50x4=200

Hope this helps

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Suppose p = 6 and b = 8, so that tan x is 6/8

Then the hypotenuse is sq rt (6x6 + 8x8) = sq rt (36 + 64) = sq rt (100) = 10

So sin x = p / h = 6 / 10

And cos x = b / h = 8 / 10

So A is the answer

Answer:

A. sin x = 6/10 and cos x = 8/10.

Step-by-step explanation:

If tan x is 6/8 the  opposite side to x = 6 and the adjacent side = 8.

So the hypotenuse of the triangle = √(6^2 + 8^2)

= √100

= 10.

So sin x = 6/10 and cos x = 8/10.

Answer:

  2j -20 ≤ 46

Step-by-step explanation:

"20 less than double the number Jason [hit]" can be represented by 2j-20.

We are told that 46 is no fewer than this value, so it is greater than or equal to this value:

  46 ≥ 2j -20

  2j -20 ≤ 46 . . . . . swapping sides to match answer choices

Answer:

2j -20 ≤ 46

Step-by-step explanation:

Answer:

11,040 is the answer

Step-by-step explanation:

you just need to subtract

There are 36,960 people were supporting the home team.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

At the college football game there were 48,000 people.

If 77% of the people at the game were supporters for the home team then we need to find how many people were supporting the home team.

x/ 48000 = 77/ 100

here plugging in all our numbers gives us .

x =  (77/ 100)48000

x = 36,960

Therefore, There are 36,960 people were supporting the home team.

Learn more about percentages;

https://brainly.com/question/13450942

#SPJ2

Answer:

For the first city, the 95% confidence interval would be:

28,900 +/- 2300 x 3 = 28,900 +/-6900$

For the second city, the 95% confidence interval would be:

30,300 +/- 2100 x 3 = 30,300 +/- 6300$

la respuesta es 454 espero que te haya ayudado aunque sea un poquito :D

Answer:

  -12

Step-by-step explanation:

The value of f(-3) is found by finding the point on the solid blue graph where x = -3. That point has a y-value of -3, so f(-3) = -3.

The value of g(-7) is found by finding the point on the dashed purple graph where x = -7. That point has a value of 6, so g(-7) = 6.

Putting these numbers into your expression gives ...

  -6(-3) -5(6) = 18 -30 = -12

Answer:

a)  Null hypothesis : H₀ : μ = 5.5

 Alternative Hypothesis : H₁ : μ < 5.5

b) The test statistic

        |t| = |-3.33| = 3.33

c) P - value lies between in these intervals

0.001 < P < 0.005

Step-by-step explanation:

Step( i ):-

Given data the Population mean 'μ' = 5.5

The small sample size 'n' = 16

The sample mean (x⁻) = 5.25

Given the  percentage of SiO2 in a sample is normally distributed with a sigma of 0.3.

Null hypothesis : H₀ : μ = 5.5

 Alternative Hypothesis : H₁ : μ < 5.5

 Level of significance ∝ = 0.01

Step(ii):-

 The test statistic

                              [tex]t = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

                             [tex]t = \frac{5.25 -5.5}{\frac{0.3}{\sqrt{16} } }[/tex]

On calculation , we get

                            t = -3.33

                           |t| = |-3.33| = 3.33

Step(iii):-

P - value

The degrees of freedom γ = n-1 = 16-1 =15

The calculated value t = 3.33 (check t-table) lies between the 0.001 to 0.005

0.001 < P < 0.005

Condition(i)

P - value < ∝ then reject H₀

Condition(ii)

P - value > ∝ then Accept H₀

we observe that  0.001 < P < 0.005

P- value < 0.01

we rejected  H₀

(or)

The tabulated value  = 2.60 at 0.01 level of significance with '15' degrees of freedom

The calculated value t = 3.33 > 2.60 at 0.01 level of significance with '15' degrees of freedom

The null hypothesis is rejected

Conclusion:-

Accepted Alternative hypothesis H₁

The Claim that the true average is smaller than 5.5

Answer:

i) The bottles of iced tea filled in a plant is the Population

ii) The Average of Population μ = 20 is called Parameter

iii) The sample size 'n' = 50

iv) The mean of the sample 'x⁻ = 19.6 ounces

Step-by-step explanation:-

Population:-

The total number of observations which we are concerned , whether this number be finite or infinite is called Population.

In Given data

The bottles of iced tea filled in a plant is the Population

Parameter:-

The statistical constants of the Population namely mean and variance are usually refereed to as Parameters.

The Average of Population μ = 20 is called Parameter

Sample:-

A sample is a subset of population

given data sample size n=50 bottles at random from the days of production

Statistics

The sample mean x⁻ and variance S² is called statistics

Given data

These bottles contained an average of 19.6 ounces of iced tea

x⁻ = 19.6 ounces

Answer:

Step-by-step explanation:

4.5

Answer:

4.5

Step-by-step explanation:

i did the test

Answer:

it is one square

Step-by-step explanation:

in the middle is room for one but anywhere else isn't

Answer:

  [tex]a^5=3[/tex]

Step-by-step explanation:

When it comes to exponential expressions and logarithms, the following relationship applies:

  [tex]\log_b{(x)}=a\ \leftrightarrow\ b^a=x[/tex]

Here, it means ...

  [tex]\boxed{a^5=3}[/tex]

Answer:

[tex] \huge \purple { \boxed{{a}^{5} = 3}}[/tex]

Step-by-step explanation:

[tex] log_{a}(3) = 5 \\ 3 = {a}^{5} \\ \huge \red { \boxed{{a}^{5} = 3}}[/tex]

Answer:

The y-intercept is [tex]7[/tex]

Step-by-step explanation:

Think of y=mx+b

m is the slope

b is the y-intercept

since 7 is in the b, the y-intercept is 7.

Greetings, Brianna!

In this problem, we need to figure out how many grams of pepper Manuel has left after subtracting or taking away 0.7 grams from his original amount of 7.8 grams.

1. First of all, when subtracting decimals, the easiest thing to do is make sure your equations are lined up nicely. For example, if one number has a decimal point but the other doesn't we need to make it so the one that doesn't have a decimal point gets one. We can do this by adding .0, so we don't change the value, but rather make the subtraction process easier. Additionally, having a whole number and a decimal that is less than 1 can be tricky to subtract when lining up, so we could add a zero before the decimal. As you can see, there is no change we could make (similar to my examples), so the numbers are ready to subtract.

2. Because we know Manuel is taking the smaller number from the larger number, we will line it up as so:

7.8

-0.7

3. From there, it's quite simple: we subtract just as if it were a normal (vertical) subtraction problem, from right to left, top to bottom. Pretend the decimals aren't there (refer to text below with the matching asterisk)*.

[tex]8 - 7 = 1[/tex]

[tex]7 - 0 = 7[/tex]

7.8

-0.7

 71

4. Surely that's impossible; getting 71 grams as your answer. Heck, we never started anywhere close to that! But we're not done there!

Now we have to add our decimal point. Because you are subtracting, put it in the same place as the numbers before.  If you prefer just adding it as you go, refer to step #3. Place the decimal in the under the answer bar,  directly underneath the other points. Don't pay much attention to it.

*Important: This is different for other operations, but when it comes to adding and subtracting decimals, the decimal will be in the same place. That's why it is important we line up the numbers exactly!

 7.8

-0.7

 7.1

Therefore, our answer is 7.1 grams. Manuel has 7.1 grams of pepper left.

Please let me know if this helped! Tell me if you have any questions, and if you wouldn't mind, I'd be so grateful if you could rate me.

Answer:

-3 is not in the domain of f°g

Step-by-step explanation:

f°g=f(g(x))

f(x) = -4(√x-1)+8

*Remember that √x-1 has to be larger than 0

since √-3-1 = √-4, -3 is not in the domain of f°g

Answer:

Step-by-step explanation:

To find what a digit stands for, make all the other digits zero.

This is substantially what we do when we write the number in "expanded form."

  568,924,126

  = 500,000,000 +60,000,000 +8,000,000 +900,000 +20,000 +4,000 ...

     ... +100 +20 +6

The list of numbers in the sum is the list of numbers the digits stand for.

Answer:

-26

Step-by-step explanation:

One way to answer this question is to look at what's happening to the values of x and y.

x         y

24     -8

36       1

48      10

Go down the list of x values: they are increasing by 12 at each step

Go down the list of y values: they are increasing by 9 at each step.

The y-intercept of the line is the value of y when x = 0.

Think about reversing the steps (decrease x by 12 and decrease y by 10):

x         y

48     10

36       1

24      -8

12      -17

0      -26 <-----  the y intercept is -26.

Note: Your book or teacher may list y intercepts as points. If so, use (0, -26)

Answer:

( 5 x 9 ) - 14

Which equals 31

Answer:

31

Step-by-step explanation:

5 x 9- 14 is 31

Answer:

30 > x

Step-by-step explanation:

-13 > x-43

Add 43 to each side

-13+43 > x-43+43

30 > x