Find the missing length.

probability = favourable outcomes/total outcomes

you need 1 banana, out of 4 and there are total of 6 items so probability will be 4/6

when you take out 1 banana, there are 3 banana left and total of 5 items

so probability of this action will be 3/5

now, next action is taking out another banana.

this is NOT an independent event.

so by we will multiply the probabilities of these events according to rule of products.

so the answer is [tex] \frac{4\cdot3}{6\cdot5}=\frac25[/tex]

or 2×100/5=40%

Answer:

The properties of right angle triangle are as follows

Answer:

-14

Step-by-step explanation:

5-y=19

collect all the like terms on one side

-y=19-5

when 5 moves over the the other side of the equation it becomes a negative

-y=14

divide both sides by a negative sign

y=-14

Answer:

the answer is 3

Step-by-step explanation:

Answer:

(5*7)-f

Step-by-step explanation:

Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]

Algebraic expression is the combination of terms that consists of numbers  and variables connected by arithmetic operators.

Given statement is 5 times the quantity 7 minus a number f in an algebraic expression.

We need to write it in an algebraic expression

5 times a quantity. for product we use multiplication sign

For addition we use + sign and for difference we use minus sign .

5 times the quantity 7 means 5 multiplied by 7

[tex]5 \cdot 7[/tex]

5 times the quantity 7 minus a number f  

subtract f from the expression we got

[tex]5 \cdot 7 -f[/tex]

Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]

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Hey there! I'm happy to help!

A line of symmetry is a line that cuts a figure in half so that it is the same on both sides. We cannot do a vertical line because one side is different than another. We could do a horizontal line where y=3 the whole time. This would cut the shape in half so it is the same on both sides.

Therefore, the equation for the line of symmetry in this figure is y=3.

Have a wonderful day! :D

The horizontal line y = 3 is the required equation of line that makes the symmetric figure.

A line of symmetry is a line that splits a figure in two and makes the two halves identical.

In the given figure,

One side is different from the other, we are unable to draw a vertical line.

A horizontal line with y = 3 throughout could be drawn. This would split the form in half, making both sides identical.

Therefore, line y = 3 is the equation of line that will make figure symmetric.

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Answer:

3.2 cm = h

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

where b is the base and h is the height

b = 10  and the area is 16

16 =1/2 *10 *h

16 = 5h

Divide each side by 5

16/5 = 5h/5

3.2 cm = h

the expression is "2 + 8." To find the quotient of 12 and 6, divide 12 by 6. The result is 2.

Step 1: Add 8 to the quotient.

Now, add 8 to the quotient found. The expression is "quotient + 8."

Step 2: Write the final expression.

The final expression that represents "8 more than quotient of 12 and 6" is "quotient + 8."

So, the expression is "2 + 8."

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Answer:

1209

Step-by-step explanation:

| - 403 | × | - 3 |

= | 403 | × | 3 |

= 403 × 3

= 1209

Answer:11

Step-by-step explanation:

g(2)=-7

f(-7)=11

Answer:

f(g(x))= 11

Step-by-step explanation:

This question asks us to find f(g(x)) when x=2. Therefore, we can substitute 2 in for x.

f(g(x)), x=2

f(g(2))

First, we must find g(2).

We know that g(x)= -2x-3. We can plug 2 in for each x and solve.

g(x)= -2x -3, x=2

g(2)= -2(2)-3

First, multiply -2 and 2.

g(2)= -4-3

Then, subtract 3 from -4.

g(2)= -7

Let's return to our function: f(g(2)). We know that g(2)= -7. Thus, we can substitute -7 in for g(2).

f(g(2)), g(2)= -7

f(-7)

Now we must find f(-7). We know that f(x)= -x+4. We can plug -7 in for x and solve.

f(x)= -x+4 , x= -7

f(-7)= -(-7) +4

f(-7)= 7+4

Add 7 and 4

f(-7)= 11

Our final answer is: f(g(x))= 11

Answer:

Approximately 13.4 units.

Step-by-step explanation:

To find the distance between two points, use the distance formula. The distance formula is:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

x₁ and y₁ is one coordinate while x₂ and y₂ is the other.

Let (-3,10) be x₁ and y₁ and let (3,-2) be x₂ and y₂. Plug in the numbers and simplify:

[tex]d=\sqrt{(3-(-3))^2+(-2-10)^2}\\ d=\sqrt{6^2+(-12)^2} \\d=\sqrt{36+144} \\d=\sqrt{180}\\ d=\sqrt{36\cdot5}=6\sqrt{5}\approx13.4164[/tex]

Edit: Typo

Answer:

100

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

Let lines be drawn from D to F (line DF) and from F to G (line FG) as shown in the diagram attached.

∠FDE = ∠FGE (angles in the same segment).

Also, ∠EFD = ∠EGD (angles in the same segment)

∠FDE + ∠EFD = ∠FGE + ∠EGD = ∠FGD

Adding ∠FED on both sides gives:

∠FDE + ∠EFD + ∠FED = ∠FGD + ∠FED

But ∠FDE + ∠EFD + ∠FED = 180° (sum of angles in a triangle)

Therefore ∠FGD + ∠FED = 180°

m∠G + m∠E = 180° (sum of opposite angles in a cyclic quadrilateral is 180°)

a) 4x +6

Add up all the sides to calculate perimeter

Answer:

a) 6x + 6

b) 15 x 24

c) see explanation

Step-by-step explanation:

a) 2x + x + 3 + 2x + x + 3 = 6x + 6

b) 6x + 6 = 78

6x = 72

x = 12

2(12) = 24

(12) + 3 = 15

15 x 24

c) 2x(x + 3) = 2x² + 6x

2(12)² + 6(12) = 288 + 72 = 360

15 x 24 is also 360

Answer:

1. 3 yards= 9 feet

2. 78 cups=5 gallons

3. 72 inches = 2 yards

4. 80 ounces = 5 pounds

5. 84 inches = 7 feet

6. 24 feet = 8 yards

7. 40 pints = 5 gallons

8. 16 cups = 5 quarts

9. 144 inches = 4 yard

10. 48 ounces = 3 pounds

The answer is Like terms.

Answer:

90 degrees

Step-by-step explanation:

Add them together. 58+32=90

90 degrees

add them togather

Answer:

Estimated=189

Exact=190.026

Step-by-step explanation:

Estimated values

20.7 to nearest whole number= 21

9.18 to nearest whole number= 9

Product means multiplication

Estimated product of 20.7 and 9.18

=21×9

=189

Exact product of 20.7 and 9.18

=20.7 × 9.18

=190.026

It has 3 decimal places

Answer:

The estimated product of 20.7 and 9.18, after rounding both factors to the nearest whole number,

is

✔ 189

.

The exact product of 20.7 and 9.18 has

✔ 3

decimal places.

Step-by-step explanation: Hope this helps(:

Answer:

144°

Step-by-step explanation:

Complement angles add up to 180°

Therefore.....

x=4(180-x)

x=720-4x

5x=720

x=144°

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The measure of the given angle is 40.

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.

for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.

Let the given angle be represented by x.

Now, the complement of this angle will be,

Complement angle = (90 - x)

Further, it is given that 4 times the complement of this angle is equal to 200°. Therefore, we can write,

4(90 - x) = 200

360 - 4x = 200

-4x = -360 + 200

-4x = -160

x = -160 / -4

x = 40

Hence, the measure of the given angle is 40.

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Answer:

9/8 or 1.125

Step-by-step explanation:

We want to find the area of a rectangular postage stamp

The area of a rectangle can be found by multiplying the length by the width

Given length: 3/2

Given width: 3/4

Area = 3/2 * 3/4 = 9/8 or 1.125

The area of a 2D form is the amount of space within its perimeter. The area of the stamp in square inches is 1 1/8 inches².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given that a rectangular postage stamp has a length of 3/2 inches and a width of 3/4 inch. Therefore, the area of the stamp in square inches is,

Area of the stamp = Length × Width

                              = 3/2 inches × 3/4 inches

                              = 9/8 inches²

                              = 1 1/8 inches²

Hence, the area of the stamp in square inches is 1 1/8 inches².

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Answer:

373.66 cm².

Step-by-step explanation:

The following data were obtained from the question:

Pi (π) = 3.14

Radius (r) = 7 cm

Slant height (l) = 10 cm

Surface Area (SA) =?

The surface area of the cone can be obtained by using the following formula:

SA = πr² + πrl

SA = (3.14 × 7²) + (3.14 × 7 × 10)

SA = (3.14 × 49) + 219.8

SA = 153.86 + 219.8

SA = 373.66 cm²

Therefore, the surface area of the cone is 373.66 cm².

Answer:

C

Step-by-step explanation:

Okay, here we have a reduction in the number of students by 20% from 2010 to 2011.

In 2011, we had k students, so we want to calculate the number of students we had in 2010.

Let the number of students present in 2010 be x

So mathematically;

x - 20% of x = k

x - 0.2(x) = k

0.8x = k

x = k/0.8

x = k * 1/0.8

x = k * 1.25

x = 1.25k

Answer:

x = 11.5 hours

Step-by-step explanation:

Set up a proportion:

[tex]\frac{460}{8}[/tex] = [tex]\frac{661.25}{x}[/tex]

661.25/460 = 1.4375

Multiply 8 by 1.4375 to find x:

8(1.4375) = 11.5

x = 11.5 hours

Answer:

Step-by-step explanation:

This a right triangle so we will use the Pythagorian theorem. x is the hypotenus.

■■■■■ Pythagorian theorem ■■■■■

● x^2 = √10^2 + √10^2

● x^2 = 10 + 10

● x^2 = 20

● x = √20 yd

Answer:

9.8 units

Explanation:

According to Pythagoras theorem, the square of length of the hypotenuse is equal to the sum of squares of lengths of other two sides.

Let the third side be x units.

Then,

x² + 10² = 14²

=> x² + 100 = 196

=> x² = 196 - 100

=> x² = 96

=> x = √96

=> x = 4√6

=> x = 9.79....

=> x = 9.8 (Rounding to the nearest tenths)

So, the length of the third side is 9.8 units.

Answer:

11 terms.

Step-by-step explanation:

We are given the arithmetic sequence:

17, 13, 9, ...

And we want to find the number of terms required such that the sum is -33.

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]

Where k is the number of terms, a is the first term, and x_k is the last term.

The desired sum is -33. The first term is 17 as well. Thus:

[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]

Simplify:

[tex]-66 = k(17 + x_k)[/tex]

We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:

[tex]x_ n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

The initial term is 17 and the common difference is -4. Hence:

[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]

Then the last term is given by:

[tex]x_k = 17 - 4(k-1)[/tex]

Substitute:

[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]

Since we cannot have a negative amount of terms, we can ignore the second solution.

Therefore, the given sequence must have 11 terms such that it sums to -33.

Answer:

Here is 2 methods

Step-by-step explanation:

1) we use excel to find n=11 for lasy students

2) mathematical method

[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]

[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]

Answer:

A is the answer

Step-by-step explanation:

Answer:

the answer is A.

Step-by-step explanation:

Answer:

MN = 3

Step-by-step explanation:

The following are congruent to each other as each pair are tangents of a circle drawn from the same external point:

PQ = QJ = 1

JK = KL = 4 - 1 = 3

MN = ML

Thus, ML = KM - KL

ML = 6 - 3 = 3

Therefore, MN = ML = 3 (both are tangents drawn from the same external point, M.

Answer:

[tex]\frac{64}{27}[/tex] cm³

Step-by-step explanation:

The volume (V) of the prism is calculated as

V = lbh ( l is length, b is breadth and h is height ), thus

V = [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{4^3}{3^3}[/tex] = [tex]\frac{64}{27}[/tex] cm³

Answer:

Step-by-step explanation:

I am more than happy to answer anymore questions. If needed an explanation I can put one in the comments.