How much juice does a 2 inches long 4 inches tall and 1. 5 inches wide hold?

Answer:

20

Step-by-step explanation:

2x=40 so once you divide both sides by 2 you get x=20

Answer:

5 months

Step-by-step explanation:

Jason's original weight = 120 pounds

Let the no. of months be m

If he gains 10 pounds in each moth , then his weight in m months will be = 10m

His total weight will be= 120+10m  -----(1)

Gerardo's original weight = 150 pounds

If he gains 4 pounds in each month , then his weight in m months will me =4m

His total weight will be = 150+4m-----(2)

Equating (1) ans(2)

120+10m=150+4m

=>10m-4m=150-120

=>6m=30

=>m=\(\frac{30}{6}\)

=>m=5

It will take 5 months for Jason to weigh the same as Gerardo

(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".

(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c).  it is ambiguous.

(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:

S → aaaaaA | aaaaS | bS | aA | bA | ε

A → aA | bAb → bB | ε

B → bB | aB | ε

The above CFG generates the language that has at least five "a's" and any combination of "b's".

(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:

S → AbC | AcB | BCa | CBa

A → aA | ε

B → bBb

B → bBbBbBb

C → cC | ε

C → cC | ε

The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.

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Answer:

3 batches

Step-by-step explanation:

First simplify 1/2 into 3/6

which into 1/6 makes three which means Mark can make 3 batches of cookies.

(If Mark had a full pound he could make 6 batches of cookies)*

Have a good day. :)

Hope this helps!

(brainliest would be appreciated)

Answer:

3 batches

Step-by-step explanation:

Answer:

Length is 29 feet. Width is 20 feet.

Step-by-step explanation:

We know that the rectangular garden is fenced on all sides with 98 feet of fencing.

In other words, our perimeter is 98 feet.

Remember that the formula for perimeter is:

\(P=2(l+w)\)

Since we know our perimeter, substitute 98 for P:

\(98=2(l+w)\)

Now, we also know that our width is 9 feet shorter than our length.

So, whatever our length is, we subtract 9 to acquire the width. In other words:

\(w=l-9\)

We now have a system of equations. To solve for both w and l, we can use substitution.

Let's substitute our second equation into the first. This yields:

\(98=2(l+(l-9))\)

First and foremost, let's divide both sides by 2 to simplify. This gives us:

\(49=l+(l-9)\)

Combine like terms on the right:

\(49=2l-9\)

Add 9 to both sides. So:

\(58=2l\)

Divide both sides by 2. Therefore, our length is:

\(l=29\)

Since our width is 9 feet shorter than our length, our width is 29 - 9 or 20 feet.

So, our length is 29 feet and our width is 20 feet.

And we're done!

Sophia did Calculus test better ompared to the rest of her class, as her z-score for Statistics  was lower than her z-score for Calculus

We know that the formula for the z-score is: \(z=\frac{x-\mu}{\sigma}\)

where x is the observed value

μ is the mean of the sample

σ is the standard deviation of the sample

Sophia got a 95% on her statistics. The grades had a mean of 87%, with a standard deviation of 7%

So, her z-score for statistics would be:

\(z_s=\frac{95-87}{7}\\\\z_s=1.14\)

She got a 91% on her calculus mid-term. The grades had a mean of 85%, with a standard deviation of 47%

So, her z-score for statistics would be:

\(z_c=\frac{91-85}{4}\\\\z_c=1.5\)

Since her z-score for Statistics  was lower than her z-score for Calculus,  she did Calculus test better.

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3 cm 3 mm = 3.3 cm, 2 cm 5 mm = 2.5 cm, 4 cm 5mm = 4.5cm

The combined heights of the boxes are 3.3 + 2.5 + 4.5 = 10.3(cm)

-> There is 35 - 10.3 = 24.7(cm) above the boxes in the drawer left.

Answer: 3 books

Step-by-step explanation: if she reads three books each day as 15 days pass, she would have read 45 books. 3 x 15 = 45. hope this helps

Answer:

3 books each day

Step-by-step explanation:

45 books

15 days

45÷15 =3

Answer:

4 x 10^6

Thanks! Have a great day! :)

Answer:

22.61°

Step-by-step explanation:

Answer:

a. less than

b. finding a part of the number

c. greater than

d. finding more than the whole of the number

e. equal to

f. keeping the number the same

Step-by-step explanation:

I'm going in left to right (standard English reading) order.

Answer:

When you multiply a number by a fraction less than 1, the product is less than the original number because you are finding a part of the number.

When you multiply a number by a fraction that is greater than 1, the product is greater than the original number because you are finding more than the whole of the number.

When you multiply a number by a fraction that is equal to 1, the product is equal to the original number because you are keeping the number the same.

Answer:

Ok, what's your statistic problem?

Step-by-step explanation:

In the given diagram, using the intersecting secant theorem, the length of c is 2 cm

From the question, we are to determine the length of segment c

From the intersecting secant theorem, we have that

If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion

Thus,

In the given circle, we can write that

a × b =  c × d

Substitute the values

3 × 12 = c × 18

36 = c × 18

Divide both sides by 18

36 / 18 = (c × 18) / 18

2 = c

Therefore,

c = 2

Hence, the length of c is 2 cm

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midpoint =(X1+X2)/2 ,(Y1+Y2)/2

therefore=

( -1+-3)/2, (-2+13)/2

=(-4/2,11/2)

=(-2,5.5)

The distance between the hyperplane (5 + 3x1 + 4x2 = 0) and the origin is 1.

To find the distance between a hyperplane and the origin, we can use the formula for the distance between a point and a plane.

In this case, the hyperplane is defined by the equation 5 + 3x1 + 4x2 = 0.

To find the distance between the hyperplane and the origin, we can substitute the coordinates of the origin (0, 0) into the equation of the hyperplane and calculate the absolute value of the result:

Distance = |5 + 3(0) + 4(0)| / √(3^2 + 4^2)

= |5| / √(9 + 16)

= 5 / √25

= 5/5

= 1

Therefore, the distance between the hyperplane (5 + 3x1 + 4x2 = 0) and the origin is 1.

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Answer:

Step-by-step explanation:

8/14: 4/7, 16/28, 32/56

Answer:

x = -30

Step-by-step explanation:

Subtract the 13

7x - 30 = 8x

Subtract the 7x

-30 = x

Answer:

x=2

Step-by-step explanation:

Add 8x to both sides.

7x−17+8x=13

Combine 7x and 8x to get 15x.

15x−17=13

Add 17 to both sides.

15x=13+17

Add 13 and 17 to get 30.

15x=30

Divide both sides by 15.

x=30/15

Divide 30 by 15 to get 2.

x=2

For this problem, we are given a triangle with a line that bisects its base BC on point D. We need to determine DB using the fact that CB is equal to 6.8.

A bisector divides a segment in two equal parts. Since the line I bisects the segment CB, then it divides this segment in two equal parts such as:

Since the value of CB is equal to 6.8, we have:

The value of DB is equal to 3.4 cm.

The number of gallons of paint the hotel will need to buy is (b) 10 gallons

From the question, we have the following parameters that can be used in our computation:

The composite figure of a pool

The surface area is calculated as

Surface Area = Rectangular Prism + Half Cylinder - Common Area

Using the above as a guide, we have the following:

Surface Area = 2 * (10 * 10 + 10 * 50 + 50 * 10) + 22/7 * 2.5 * (2.5 + 4) - 5 * 4

Evaluate

Surface Area = 2231

For the number of gallons, we have

Gallons = 2231/200

Evaluate

Gallons = 11.2

The closest to this is 10

Hence, the number of gallons is 10

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The result (recurrent value), A = sum j=1 to 89 ln(j), is true for every n. This is the desired result.

As in T(n) = T(n/2) + n, T(0) = T(1) = 1, a recurrence or recurrence relation specifies an infinite sequence by explaining how to calculate the nth element of the sequence given the values of smaller members.

We can start by proving the base case in order to demonstrate the first portion through recurrence. Let n = 1. Next, we have:

Being true, ln(a1) = ln(a1). If n = k, let's suppose the formula is accurate:

Sum j=1 to k ln = ln(prod j=1 to k aj) (aj)

Prod j=1 to k aj * ak+1 = ln(prod j=1 to k+1 aj)

(Using the logarithmic scale) = ln(prod j=1 to k aj) + ln(ak+1)

Using the inductive hypothesis, the property ln(ab) = ln(a) + ln(b)) = sum j=1 to k ln(aj) + ln(ak+1) = sum j=1 to k+1 ln (aj)

(b), we can use the just-proven formula:

A = ln(1, 2,...) + ln + ln (89)

= ln(j=1 to 89) prod

sum j=1 to 89 ln = ln(prod j=1 to 89 j) (j).

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Solution,

9x/7-6x=15

or,9x=15(7-6x)[ cross multiplication]

or,9x=105-90x

or,9x+90x=105

or,99x=105

or,X=105/9

X=1.06

Hope it helps

Good luck on your assignment

Answer:

8 plates

Step-by-step explanation:

The reason for this is because 15 and 9 are both divisible by 3. 15 divided by 3 is 5 and 9 divided by 3 is 3. 5+3= 8. Therefore, you will need 8 plates.

The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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Answer:

Step-by-step explanation:

Product of slope of perpendicular lines = -1

6x + 5y = 30

Write this equation in y = mx + b  form

        5y = -6x + 30

          y = \(\frac{-6}{5}x+\frac{30}{5}\)

          \(y=\frac{-6}{5}x + 6\)

Slope of this line m₁ = -6/5

m₁ * m₂ = -1

      m₂ = -1÷m₁ = -1 * \(\frac{5}{-6}\)  

\(m_{2}=\frac{5}{6}\)     & (-6 , -7)

Equation of the required line: y - y₁ = m (x - x₁)

\(y - (-7) = \frac{5}{6}(x - [-6])\\\\y + 7 = \frac{5}{6}x + 6 *\frac{5}{6}\\\\y = \frac{5}{6}x +5-7\\\\y=\frac{5}{6}x-2\)

Answer:

a.

y = (x+6) (x-2)

=x^2-2x+6x-12

=x^2+4x-12

=(x+6) (x-2)

b. x = (-6) (or) x=2

Answer:

Step-by-step explanation:

From the figure attached,

A helicopter is flying at a height 'h' and angle of elevations from two islands C and B are 35° and 15° respectively.

Let the measure of BD = x miles

From ΔABD,

tan(15) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{h}{x}\)

h = x.tan(15) ---------(1)

From ΔACD,

tan(35) = \(\frac{h}{12-x}\)

h = (12 - x).tan(35) ------(2)

By equating the values of h from equations (1) and (2),

x.tan(15) = (12 - x).tan(35)

\(\frac{x}{12-x}=\frac{\text{tan}35}{\text{tan}15}\)

\(\frac{x}{12-x}=2.613\)

x = 2.613(12 - x)

x + 2.613x = 31.386

3.613x = 31.386

x = 9.914 ≈ 9.9 miles

From equation (1),

h = x.tan(15)

  = 9.9[tan(15)]

  = 2.65 ≈ 2.7 miles

Therefore, helicopter is flying at the vertical height = 2.7 miles and horizontal distance of the helicopter from the island B = 9.9 miles.

Answer:

2.7

Step-by-step explanation:

I took the quiz and got it right :)