A mixture calls for 1 cup of lemonade and 3 cups of iced tea how many total cups does the mixture have

➷ It would be [tex]-2\sqrt{6}[/tex]

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Answer:

Step-by-step explanation:

5^2(72-45)/5

25(27)/5

675/5

135

Final answer:

The evaluated expression of 5 to the second power (72 - 45) divided by 5 is 135. This is found by subtracting inside the parentheses, squaring the number 5, multiplying these results, and finally dividing by 5.

Explanation:

Evaluating the Expression

To evaluate the expression 5 to the second power (72 - 45) divided by 5, we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, we calculate the value within the parentheses:

72 - 45 = 27

Next, we raise 5 to the second power (also known as squaring a number):

52 = 5 × 5 = 25

Now, we multiply this result by the value we found within the parentheses:

25 × 27 = 675

Last, we divide by 5:

675 ÷ 5 = 135

Therefore, the evaluated expression is 135.

Answer:

Step-by-step explanation:

House?

Number of hours left to work(x) = 15 hours - (3 hours/day)x

Note how this Number of hours decreases steadily from its initial value (15 hours) at the rate of 3 hours/day.  The domain of x is [0,5].

By slope intercept form, the number of days that the Rebecca should volunteer exists 5 days.

The "equation of the straight line exists y = mx + c this form exists named slope intercept form".

Rebecca must complete 15 hours of volunteer work. She does 3 hours each day.

The linear equation exists in slope intercept form exists y = mx + c, where 'm' exists the slope straight line and 'c' exists y-intercept.

y = 15 hours - 3 hours/day x days

y = 15 - 3x ............(1)

To find y-intercept put x=0 in (1) we get,  

y = 15 - 3(0)

 = 15

y = 15

which exists the amount of volunteer hours.

Rebecca must complete at day 0.

0 = 15 - 3x

3x = 15

x = 5 [Number of days Rebecca would have to volunteer]

Therefore, utilizing slope intercept form, the number of days that the Rebecca should volunteer exists 5 days.

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Answer:

the answer is 3/4

Step-by-step explanation:

Answer:

The correct answer is 3/4

Step-by-step explanation:

1/2+1/4=3/4

Answer:   [tex]\bold{x^{\frac{1}{3}}}[/tex]

Step-by-step explanation:

[tex]\sqrt[6]{x^2} =x^{\frac{2}{6}}=x^{\frac{1}{3}}[/tex]

The slope is undefined because it is a vertical line

Answer:

Step-by-step explanation:

The vertical line equation has the form x = a (a - any real number).

The vertical line has an undefined slope.

We have x = -4. It's a vertical line. Therefore, the slope is undefined.

Answer: [tex](f\°g)(0)=3[/tex]

Step-by-step explanation:

- For the function g(x) you must find the value of y (output value) when [tex]x=0[/tex]. As you can see in the graph (observe the parabola), when [tex]x=0[/tex] (input value), then:

[tex]y=2[/tex] or [tex]g(0)=2[/tex]

- Now, 2 will be the input value of the function f(x). Then,  you must find the value of y (output value) when [tex]x=2[/tex]. As you can see in the graph of this function, when [tex]x=2[/tex], then:

[tex]y=3[/tex] or [tex]f(2)=3[/tex]

Therefore, you can conclude that:

[tex](f\°g)(0)=3[/tex]

Answer:

D

Step-by-step explanation:

The Answer is D, first you would multiply A by 2, then divide it by h. You would then subtract b2 giving you D.

The correct option is D

See the image

Answer:

3 ± i5

Step-by-step explanation:

Here we're given four sets of possible roots of the given polynomial.   Each set consists of two complex quantities and 1 real quantity.

First, we determine whether +4 is a root, then whether -4 is a root.  Let's use synthetic division to do that:

     -----------------------

4   /  1   -2    10   136

             4      8    72

    ---------------------------

        1     2    18    208     Since the remainder is not zero, 4 is not a root.

Eliminate the first two possible answer choices, and assume that -4 is a root.

Let's check this out to be certain:

     -----------------------

-4  /  1   -2    10   136

             -4   24  -136

    ---------------------------

        1     -6    34    0

Since the rem. is zero, -4 is a root, and the coefficients of the 2nd-degree quotient are 1, -6 and 34.

In other words, a = 1, b = -6 and c = 34.

Let's apply the quadratic rule to find the roots:

       6 ± √(36 - 4[1][34] )       6 ± √ (-100)

x = ------------------------------ = ----------------------- = 3 ± i5

                     2                                   2

So the correct answer is the last one of the four given possible answers:

3 ± i5

Answer:

[tex]3+5i, 3-5i,-4[/tex]

Step-by-step explanation:

Given is a cubic equation in x as

[tex]x^3-2x^2+10x+136=0[/tex]

We know by remainder theorem if f(a) =0 then x=a is a root

Constant term = 136 has factors as 1,2,4,8, 17, 34

We find that f(a) not 0 for a =1,2.

[tex]f(1) = 144\\f(2) = 156\\f(-1) = 123\\f(-4) = -64-2(16)+10(-4)+136 = 0[/tex]

Hence [tex]x=-4[/tex] is one zero.

We can divide by x+4 to make it as a quadratic equation

[tex]x^3-2x^2+10x+136=(x+4)(x^2-6x+34)[/tex]

Now using quadratic formula we can find other roots

[tex]x^2-6x+34=0[/tex] has roots as

[tex]x=\frac{6+/-\sqrt{36-136} }{2} \\=3+5i, 3-5i[/tex]

Thus roots are

[tex]3+5i, 3-5i,-4[/tex]

Check the picture below.

the volume of the prism will simply be the product of the triangular area and its length, it has a length of 8, thus

[tex]\bf \stackrel{\textit{area of a triangle}}{A=\cfrac{1}{2}bh}~~ \begin{cases} b=9\\ h=6 \end{cases}\implies A=\cfrac{1}{2}(9)(6)\implies A=27 \\\\\\ \stackrel{\textit{volume of the triangular prism}}{V=27\cdot 8}\implies V=216[/tex]

Answer: the trainer uses a stimulus, paired with a reward to ge the response they want.

Step-by-step explanation:

I'm pretty sure the answer is D

Answer:

The answer is D

Step-by-step explanation:

To find the slope you do y2-y1/x2-x1. This will leave you with 3/1 which is equivalent to 3.

Answer:

1/4 or 0.25

Step-by-step explanation:

Isn't latex a devil?

You want to know the probability of a blue marble.

Formula

P(blue) = #Blue / # Total

Givens

#Blue = 333

#Total = 333 + 444 + 555 = 1332

Solution

P(blue) = 333 / 1332      Divide by 111

P(blue) = 3/12

P(blue) = 1/4 or 0.25

Answer:

1/4 or 0.25

Step-by-step explanation:

Answer:

a is the _amplitude_(Length of the blades)_

The vertical shift, k, is the _Mill shaft height_

[tex]a = 15\ ft\\\\k = 40\ ft[/tex]

[tex]y = 15sin(\frac{\pi}{10}t) + 40[/tex]

Step-by-step explanation:

In this problem the amplitude of the sinusoidal function is given by the length of the blades.

[tex]a = 15\ ft[/tex]

The mill is 40 feet above the ground, therefore the function must be displaced 40 units up on the y axis. So:

[tex]k = 40\ ft[/tex]

We know that the blades have an angular velocity w = 3 rotations per minute.

One rotation = [tex]2\pi[/tex]

1 minute = 60 sec.

So:

[tex]w = \frac{3(2\pi)}{60}\ rad/s[/tex]

[tex]w = \frac{\pi}{10}\ rad/s[/tex]

Finally:

a is the _amplitude_(Length of the blades)_

The vertical shift, k, is the _Mill shaft height_

[tex]a = 15\ ft\\\\k = 40\ ft[/tex]

[tex]y = 15sin(\frac{\pi}{10}t) + 40[/tex]

Answer:

a is the length of the blade

the vertical shift , k, is the height of the windmill

a= 15 k= 40

the period is 20 seconds

b = pi/10

y=15sin(π/10t)+40

Step-by-step explanation:

Answer:

The pressure is [tex]20\ psi[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem we have

[tex]V*P=k[/tex]

where

V is the volume of a gas at a constant temperature

P is the pressure

we have

For [tex]V=100\ in^{3}[/tex],[tex]P=25\ psi[/tex]

step 1

Find the value of k

substitute the values of V and P

[tex]100*25=k[/tex]

[tex]k=2,500[/tex]

The equation is equal to  [tex]V*P=2,500[/tex]

step 2

Find the pressure when the volume is 125 cubic inches

For [tex]V=125\ in^{3}[/tex]

substitute in the equation and solve for P

[tex]125*P=2,500[/tex]

[tex]P=2,500/125=20\ psi[/tex]

Answer:

The y coordinate of point R is  [tex]-9[/tex]

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M(x,y)=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

In this problem

[tex]R(x2,y2)[/tex]

[tex]Q(-2,-6)=(\frac{-5+x2}{2},\frac{-3+y2}{2})[/tex]

so

[tex]-2=(-5+x2)/2[/tex] --->[tex]x2=-4+5=1[/tex]

[tex]-6=(-3+y2)/2[/tex] --->[tex]y2=-12+3=-9[/tex]

therefore

The y coordinate of point R is  [tex]-9[/tex]

[tex]\bold{Hey\ there!}[/tex]

[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

456.5

Step-by-step explanation:

The area of circle B is 4,500.81 inches².

The first step to take in order to determine the answer is to determine the value of the diameter of circle B.

Area of a circle = πr²

Where :

π = pi = 3.14

R = radius

500 = 3.14r²

r = √(500 / 3.14)

r = 12.62 inches

Diameter = 2 x radius

2 x 12.62 = 25.24 inches

The second step is to determine the diameter of circle B.

Dimeter of circle B = 3 x 25.24 inches = 75.72 inches

Radius of circle B = 75.72 inches / 2 = 37.86 inches

Determine tie area of circle B

Area of circle B = 3.14 x 37.86² = 4,500.81 inches²

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3^2 = 9

3^4= 81

9 x 81 = 729

Your answer is 729 . Good luck (:

Answer:

20

Step-by-step explanation:

Answer:

i got 15.5

Step-by-step explanation:

perpendicular means negative reciprocal so it would be -1/3

Answer:

slope = 0

Step-by-step explanation:

x = 3 is a vertical line parallel to the y- axis with undefined slope.

A line perpendicular to x = 3 is a horizontal line parallel to the x- axis with a slope of zero.

Answer:

$8.25

Step-by-step explanation:

We first need to find the amount of money we give the cashier

20+10 = 30

We give the cashier 30 dollars

Our bill was 21.75

30.00

-21.75

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

We need to borrow

2 10.00

-2 1  .75

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

We need to borrow

2 9. 10 0

-2 1  .7  5

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

We need to borrow

2 9. 9  10

-2 1  .7  5

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

  8 .2   5

We will get $8.25 back from the cashier

Answer:

Step-by-step explanation:

I gave total $20+$10= $30

$30-$21.75= $8.25

answer: D

explanation:

volume is equal to length * surface area.

surface of a tube base is a circle, so it' surface are can be calculated as:

[tex]\pi \: {r}^{2} [/tex]

where r is a radius

[tex] r \: = \frac{1}{2} diameter[/tex]

so you calculate volume V as:

[tex]v \: = \pi( {r}^{2} ) \times length \: = \pi \times \frac{1}{4} \times {diameter}^{2} \times length[/tex]

[tex]v = 3.14 \times \frac{1}{4} \times 4 \times 4 \times 24 = 301.44[/tex]

so the answer is D

The surface area of a rectangular prism is SA = 2wl + 2lh + 2hw

Answer:

There is no prism

Step-by-step explanation:

Answer:

The correct options are 1 and 2.

Step-by-step explanation:

The vertices of triangle are S(-4,4), T(-1,4), R(-1,1).

If triangle translated 2 units left,

[tex](x,y)\rightarrow (x-2,y)[/tex]

and then reflected over the y-axis,

[tex](x-2,y)\rightarrow (-x+2,y)[/tex]

The relation between image and preimage is

[tex](x,y)\rightarrow (-x+2,y)[/tex]                          ..... (1)

The vertices of image are

[tex]S(-4,4)\rightarrow S'(6,4)[/tex]

[tex]T(-1,4)\rightarrow T'(3,4)[/tex]

[tex]R(-1,1)\rightarrow R'(3,1)[/tex]

Therefore the vertices of image are S'(6,4),T'(3,4), R'(3,1).

1. A reflection over the y-axis and then a translation 2 units right is defined as

[tex](x,y)\rightarrow (-x+2,y)[/tex]

It is equivalent to relation 1, therefore option 1 is correct.

2. A 180 rotation about the origin, then a translation 2 units right, and then a reflection over the x-axis is defined as

[tex](x,y)\rightarrow (-x+2,y)[/tex]

It is equivalent to relation 1, therefore option 2 is correct.

3. A reflection over the y-axis and then a translation 2 units left is defined as

[tex](x,y)\rightarrow (-x-2,y)[/tex]

It is not equivalent to relation 1, therefore option 3 is incorrect.

4. A 180 rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis is defined as

[tex](x,y)\rightarrow (-x-2,y)[/tex]

It is not equivalent to relation 1, therefore option 4 is incorrect.

5. A reflection over the x-axis and then a translation 2 units right is defined as

[tex](x,y)\rightarrow (x+2,-y)[/tex]

It is not equivalent to relation 1, therefore option 5 is incorrect.

6. A reflection over the x-axis and then a translation 2 units left is defined as

[tex](x,y)\rightarrow (x+2,-y)[/tex]

It is not equivalent to relation 1, therefore option 6 is incorrect.

Therefore the correct options are 1 and 2.

Answer:

1 and 2 are the correct answers.

Step-by-step explanation:

Answer:

d). f(x)=-1/2x +6 (see attachment)

Step-by-step explanation:

Answer:

C. x = -5.6 and x = -1.4

Step-by-step explanation:

The quadratic formula is [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]. Here a=1, b=7, and c=8.

Substitute and you'll have:

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-7+/-\sqrt{7^2-4(1)(8)} }{2(1)}=\frac{-7+/-\sqrt{49-32} }{2)}[/tex]

[tex]\frac{-7+/-\sqrt{17} }{2}=\frac{-7+/-4.1 }{2}= -1.4, -5.6[/tex]

Answer: 3 classes

If we removed 5 students from each of the classrooms, we would be able to keep the 18 classes and give them exactly 30 students. However, we would also have the leftover students to put into classrooms.

If there are 18 classrooms with 5 extra students from each, we can use 18*5 to find how many total students we have.

18 * 5 = 90.

If each class size is 30, we need to divide 90 by 30 to find how many classes we need.

90 / 30 = 3 classes

Therefore, to reduce the class size to 30 students per class, 3 new classes must be formed.

To reduce the class size from 35 students to 30 students in a school with 18 classes, we need to calculate the total number of students and then determine how many new classes are needed.

1. **Total number of students:**

  [tex]\[ \text{Total students} = 18 \text{ classes} \times 35 \text{ students/class} = 630 \text{ students} \][/tex]

2. **Number of classes required with 30 students per class:**

 [tex]\[ \text{Required classes} = \frac{630 \text{ students}}{30 \text{ students/class}} = 21 \text{ classes} \][/tex]

3. **New classes to be formed:**

  [tex]\[ \text{New classes} = \text{Required classes} - \text{Current classes} = 21 - 18 = 3 \text{ classes} \][/tex]

63cm is smaller than 6 m

63 cm is less than 6 m. A centimeter is a small unit used to measure length. It is equal to one hundredth of a meter. The term "centi" is used in the International System of Units to represent 1/100 of something.

To look at the lengths of 63 cm and 6 m, one need to ensure that both values are in the same unit of measurement. Since 6 m is in meters, we should convert 63 cm to meters before making the comparison.

1 meter is equal to 100 centimeters, so one can convert 63 cm to meters by dividing it by 100:

63 cm = 63/100 m = 0.63 m

So,  both values are in meters, and one can compare them:

0.63 m < 6 m

Therefore,  one can say that 63 cm is less than 6 m.

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Answer:

If it is a cube, the answer would be 76.7 .

Step-by-step explanation: