If 30% of the students in Mrs.Rutherfords class like chocolate ice cream, then how many students are in Mrs. Rutherford’s class if six like chocolate ice cream

Answer:

both of them togther need to equal 180 so

10x-20+6x+8=180

16x-12=180

16x=192

192/16=12

x=12

Step-by-step explanation:

He would have 32 slices of butter.

The student will have 32 slices of butter if they cut 40 ounces into 1.25-ounce pieces by dividing the total amount by the size of each slice.

The student wants to know how many slices of butter they can get from 40 ounces if they are cutting it into 1.25 ounces each. To find out, they need to divide the total amount of butter by the size of each piece.

First, take the total amount of butter, which is 40 ounces.

Divide 40 ounces by the size of each slice, which is 1.25 ounces.

Calculate the division: 40 / 1.25 = 32 slices.

Therefore, the student will have 32 slices of butter if they cut 40 ounces into 1.25-ounce pieces.

He has read 46.66 %

Lets find the percentage

total pages are 300 and he has read 140

So

140/300 = 0.4666

Converting this into percentage again

We will multiply the decimal by 100

0.4666 x 100 = 46.66 %

Answer:

No 1 inch cubes will fit

28 one-half inch cubes will fit

Step-by-step explanation:

No cubes with a side length of 1 inch will fit because one dimension of the prism is only 1/2 inches, so we can't fit a 1 inch cube in anywhere.

Since one dimension is 1/2 inch, we can line up 1/2 inch cubes along the other 2 dimensions.  Let's say that the 1/2 inch dimension is the base, the 2 inch dimension is the height, and the 7/2 inch dimension is the length.

We can stack the cubes 4 high, (2 inches of height with 1/2 inch being the cube height, there are 4 halves in 2).

We can place 7 cubes along the length (7/2 inches = 3.5 inches.  There are 7 halves in 3.5).  

So we can have 4(7) = 28  one half inch cubes can fit in to the prism

Answer:

f(x)⁻¹ = 3x/(2 - x)

Step-by-step explanation:

Find the inverse of f(x) = 2x/(x+3)

The first step is to let f(x) = y

y = 2x/(x+3)

Then make x the subject of the formula

y = 2x/(x+3)

y(x + 3) = 2x

yx + 3y = 2x

yx - 2x = -3y

x(y - 2) = -3y

x = -3y/(y - 2)

∴ f(x)⁻¹ = -3x/(x - 2)

Dividing both numerator and denominator by -1;

f(x)⁻¹ = 3x/(2 - x)

Answer:   (x - 2)(7x + 13)  which is equivalent to 7x² - x - 26

Step-by-step explanation:

[tex].\qquad \dfrac{g(x)}{x^2+x-6}=7x+13\\\\\\\implies g(x)=(x^2+x-6)(7x+13)\\\\.\qquad \qquad =(x+3)(x-2)(7x+13)\\\\\\\text{What is g(x) divided by x+3?}\\\\\dfrac{g(x)}{3}=\dfrac{(x+3)(x-2)(7x+13)}{x+3}\\\\\\.\qquad =(x-2)(7x+13)\\\\\\.\qquad =7x^2+13x-14x-26\\\\\\.\qquad =\large \boxed{7x^2-x-26}[/tex]

Answer:

Step-by-step explanation:

Each factor corresponds to a zero of the function.

If (x+4) is set = to 0, the corresponding root is x = -4.

If (-7x - 60) is set = to 0, the corresponding root is x = -60/7.

The factors (-7x-60)(x+4) represent the roots or solutions of the original quadratic equation in its expanded form, which are obtained by setting each factor equal to zero and solving for x.

The factors (-7x-60)(x+4) in the factored form represents the roots of a quadratic equation. In a quadratic equation of the form ax² + bx + c = 0, the roots or solutions of the equation can be obtained by factoring the quadratic expression. In this case, the equation being factored must have been -7x² - 28x - 60x - 240 = 0. The roots are the values that make each factor equal to zero, so the roots of the original equation are obtained by solving -7x-60 = 0 and x+4 = 0, to get x = -60/(-7) = 8.57 and x=-4.

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Answer:

4 is the real part

2 is the imaginary part

Step-by-step explanation:

A complex number is written in the form a+bi

where a is the real part and b is the imaginary part

4 +2i

4 is the real part

2 is the imaginary part

Answer:

4 is real. 2 is imaginary

Step-by-step explanation:

Answer:

x = 5√3; y = 5

Step-by-step explanation:

Finding y:  The sine function links the 30° angle, the 10 unit hypotenuse and the side opposite the angle, y:

sin 30° = 1/2 = y/10

Solve the equation of ratios

1        y

-- = -----  using cross-multiplication first:  2y = 10 → y = 5

2     10

We can now find x either by using a similar approach and the cosine function or by using the Pythagorean Theorem:

x² + y² = 10² = 100  →  x² = 100 - y²  =  100 - 5²  = 75

If x² = 75, then x = ±√75 = ± (√25)·(√3)   →  ±5√3

Since lengths are always positive,   take x = 5√3 as the answer.

Answer:

2 2/3

Step-by-step explanation:

Make them into improper fractions first.

11/2 - 17-6

Then multiply 11/2 so that they have common denominators.

33/6 - 17/6

Then solve.

33/6 - 17/6 = 16/6

Then convert back into a mixed number.

2 4/6 or 2 2/3

Yeah the correct option is option D

Answer: 890.12 cm^3

Step-by-step explanation:

The formula for the volume of a cylinder is

[tex]V=\pi *r^2*h[/tex]

V=628.3185307 cm^3

or simply

V=628.32 cm^3

Since, you know the radius of the hemisphere on top, you also know the radius since the height of the hemisphere is the same as it is wide.

Next, the formula for the volume of a sphere is

[tex]V=\frac{4}{3} \pi *r^3[/tex]

so the volume of a hemisphere is half of that or:

[tex]V=\frac{2}{3} *\pi *r^3[/tex]

V= 261.7993878 cm^3

or simply

V=261.80 cm^3

Finally, you add both of the volumes together to get

V= 890.1179185 cm^3

or simply

V=890.12 cm^3

Answer:

2 is your answer. 36 divided by 6 is 6. 6 divided by 3 eaquls 2

Step-by-step explanation:

Answer:

(36÷6)÷3 = 2

Step-by-step explanation:

First, you would solve what is in the parentheses.

(36÷6)÷3 = (6)÷3           Now, find 6÷3

                = 6÷3 = 2

so,  (36÷6)÷3 = 2

I hope you find this helpful. :)

Alright, let's solve this problem! :)

First we need to subtract 5k from both sides.

3k−5k>12

Then we simplify 3k - 5k to -2k.

-2k > 12

Now we divide both sides by -2.

k < -12/2

Now we simplify 12/2 to 6.  

k < -6

✔️Done!

Have an amazing day!

Answer:

You'll need [tex]36\ ft^{2}[/tex] of outdoor carpet for this hole

Step-by-step explanation:

we know that

The area of the outdoor carpet is equal to the area of the triangle minus the area of the rectangle

step 1

Find the area of the rectangle

The area of rectangle is equal to

[tex]A=bh[/tex]

we have

[tex]b=3\ ft[/tex]

[tex]h=2\ ft[/tex]

Calculate the area

[tex]A=(3)(2)=6\ ft^{2}[/tex]

step 2

Find the area of the triangle

[tex]A=(1/2)bh[/tex]

we have

[tex]b=12\ ft[/tex]

[tex]h=7\ ft[/tex]

Calculate the area

[tex]A=(1/2)(12)(7)=42\ ft^{2}[/tex]

step 3

Find the difference

[tex]42\ ft^{2}-6\ ft^{2}=36\ ft^{2}[/tex]

Answer:

1/6 of a pound

Step-by-step explanation:

Multiply both the numerator and denominator for a common denominator.

2/3 * 2/2 = 4/6.

Then subtract to find out how much more she had yesterday.

5/6-4/6=1/6.

1/6 pound

Match the denominator

2/3 = 4/6

Subtract

5/6 - 4/6 = 1/6

Answer:

option D

D. x = 5, y = 2

Step-by-step explanation:

Given in the question two equation,

Equation 1

5.3x + y = 28.5

Equation 2

4.2x + 3.1y = 27.2

rearrange equation 1 in terms of y

y = 28.5 - 5.3x

Substitute the value of y in equation 2

4.2x + 88.35 - 16.43x = 27.2

4.2x - 16.43x = 27.2 - 88.35

-12.23x = -61.15

x = 61.15/12.23

x = 5

put value of x in any of the equation

y = 28.5 - 26.5

y = 2

Answer: 1/3

Hope This Helps ^_^

The correct answer is A.

Hope this helps.

Answer:

The answer is A.

Step-by-step explanation:

This is because it wants you to represent the answer in Slope-Intercept Form. Which is y = mx + b. B is the y intercept, which is where it starts. On a graph, the y-intercept starts at ZERO. The 3 is at the zero, so you know what the first number is. Then, you need to see the fluctuation (change) in the value of each number in the y as you increase in x. As the x increases by one, you can see that the y decreases by two. So now you know, the ROC or Rate of Change is two, which is your slope. Slope is m. So if m is two, that makes 2x.

Hopefully this helps!

Answer:

79.25 square inches

Step-by-step explanation:

To find the area of the figure, split it into two shapes - a rectangle and a semi-circle.

The area of a rectangle is A = b*h. Substitute b = 10 and h = 4.

A = 4*10 = 40.

The area of a semi-circle is A =1/2 πr². Substitute r = 5 since the diameter is 10.

A =1/2 π5² = 12.5π = 39.25.

Add the two areas together.

39.25 + 40 = 79.25

Answer:

No solution

Step-by-step explanation:

Each side of the equation,once distributed, has 5x.

The 5x's cancel out to x= x-5

Which is incorrect and has no solution.

Answer:

No solution

Step-by-step explanation:

Let B = the weight of box B

Let 2B = the weight of box A

Let 2B + 30 = the weight of box C

B + 2B + 2B + 30 = 640

5B = 610

B = 122 pounds, weight of box B

2B = 2(122) = 244 pounds, weight of box A

2B + 30 = 2(122) + 30 = 274 pounds, weight of box C

hope this helps

Answer: 90b (grams)

Step-by-step explanation:

Given statement : A box weighs 90 grams.

Let b denotes the number of boxes, then the weight of b boxes will be :-

[tex]\text{Total weight of b boxes}=b\times\text{Weight of one box}\\\\\Rightarrow\ \text{Total weight of b boxes}=b\times90\\\\\Rightarrow\ \text{Total weight of b boxes}=90b[/tex]

Hence, the expression for the weight  ( in grams) of b boxes : 90b

Answer:

Francesco can achieve this amount by investing at an APR of 7.14% compounded annually , or 7% compounded every six months or 6.95% compounded quarterly

Step-by-step explanation:

This question can be solved using the concept of compounded interest

The formula for amount obtained when a principal of p was invested at a rate r compounding n times a year is:

[tex]Amt = p(1+\frac{r}{100n})^n[/tex]

Here p = 70000, amt = 75000,

So when compounded annually, n=1

[tex]Amt =p(1+\frac{r}{100n})^n\\75000=70000(1+\frac{r}{100})^1\\\frac{15}{14}=1+\frac{r}{100}\\\frac{1}{14}=\frac{r}{100}\\r = \frac{100}{14}=7.14[/tex]

For compounding every 6 months n=2

[tex]Amt =p(1+\frac{r}{100n})^n75000=70000(1+\frac{r}{200})^2\\\frac{15}{14}=(1+\frac{r}{200})^2\\\sqrt{\frac{15}{14}}=1+\frac{r}{200}\\r = 200*(\sqrt{\frac{15}{14}}-1)=7.01[/tex]

For compounding quarterly n=4

[tex]Amt =p(1+\frac{r}{100n})^n\\75000=70000(1+\frac{r}{400})^4\\\frac{15}{14}=(1+\frac{r}{400})^4\\(\frac{15}{14})^\frac{1}{4}=1+\frac{r}{400}\\r = 6.95[/tex]

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Answer: An APR OF 6.98% compounded quarterly

Step-by-step explanation:

Answer:

25 feet

Step-by-step explanation:

You can superimpose a triangle in this situation.  The height from the ground to the top of the ladder along the wall is one leg of the triangle, the distance the ladder is from the wall is the other leg, and the length of the ladder is the hypotenuse.  

Use Pythagorean theorem to solve, which is a² + b² = c² where a, and b are the legs, and c is the hypotenuse...

We have

7² + 24² = c²

   49 + 576 = c²

       625 = c²

        25 = c          

*Tecnhically the answer is ±25, but it's a length, so we disregard the negative answer.

Answer:

1 Cup = 8 Fluid Ounces

Therefore 13 cups = 13*8 = 104 Fuid Ounces

So 96 Fluid Ounces is LESS THAN 13 cups.

Step-by-step explanation:

410 is your answer, 2 subtractions signs next to eachother make a plus sign, so in the end it’s just 356+54 :)

Answer:

410

Step-by-step explanation:

Answer:

y = 3x + 3

Step-by-step explanation:

The graph passes through the points (-1, 0) and (0, 3).

Slope = m = Δy/Δx = (y₂ - ₁)/(x₂ - x₁) = (3 - 0)/(0 - (-1)) = 3/1 = 3.

The y-intercept (b) is at y = 3.

The equation for a straight line is

y = mx + b

Thus, the equation for your line is

y = 3x + 3

The best model for the given data is likely a quadratic model because the y values increase then decrease and then increase again, a typical pattern of a quadratic model.

To determine which model best fits the given set of data: (-4,-2), (-2,1), (2,-2), (4,3), we need to examine the relationship between the x and y values. Based on the given data, there is not a consistent increase or decrease, which suggests that the best model is not linear.

Quadratic model and cubic model can also be tested as they can capture complex patterns, which makes them a good fit for data that has peaks and valleys, such as our data set.

Upon examining the data, we realize there is a pattern where the value of y increases, then decreases, then increases again which is typically of a quadratic model. Therefore, the best fit for this data set is most likely a quadratic model.

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a) the first and last one : 6x + 9x and 15x

b) second and third one : 4*1 + 4*9y and 4 + 36y

pls mark brainliest!

This is F(n) = 3n

The X is an interger which is holding a value

The relationship between Y and X is 3n as we multiply X by 3 to get the value of Y and is proven yet so.

The rule which represent the function as shown in the table is:

                 [tex]f(n)=3n[/tex]

We are given a table as follows:

  x       2          -1         0

  y       6          -3         0

Now we are asked to find the function which represent these table of values.

a)

    [tex]f(n)=n+3[/tex]

Here x is represented by n and y by f(n)

when n=2 we must have f(n)=6

Hence, we put n=2 in the given expression and check,

[tex]f(2)=2+3=5\neq 6[/tex]

Hence, this is not a correct function.

b)

[tex]f(n)=\dfrac{1}{3}n[/tex]

Again we check for n=2

We have:

[tex]f(2)=\dfrac{1}{3}\times 2=\dfrac{2}{3}\neq 6[/tex]

Hence, it is not a correct expression.

So we are left with option: c)

c)

[tex]f(n)=3n[/tex]

By putting the value of n=2,-1 and 0

we see that the expression matches the table of values.

( since,

when n=2 we have:

[tex]f(2)=3\times 2=6[/tex]

when n= -1 we have:

[tex]f(-1)=3\times -1=-3[/tex]

and when n=0 we have:

[tex]f(0)=3\times 0=0[/tex] )

Hence, this is a correct expression.