Find the value of x
.

Answer:

0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.

Step-by-step explanation:

For each couple, there are only two possible outcomes. Either they paid for their honeymoon, or they did not. The probability of a couple having paid for their honeymoon is independent of any other couple, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

It is known that seventy percent (70%) of married couples paid for their honeymoon themselves.

This means that [tex]p = 0.7[/tex]

You randomly select 9 independent married couples.

This means that [tex]n = 9[/tex]

What is the probability that all married coupled asked stated they paid for their honeymoon themselves?

This is P(X = 9). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 9) = C_{9,9}.(0.7)^{9}.(0.3)^{0} = 0.0404[/tex]

0.0404 = 4.04% probability that all married coupled asked stated they paid for their honeymoon themselves.

Answer:

C

Step-by-step explanation:

We are given the function:

[tex]f(x) = 2x^2 -3x+4[/tex]

And we want to evaluate it for x = 3a.

Substitute:

[tex]f(3a) = 2(3a)^2-3(3a)+4[/tex]

Square:

[tex]f(3a) = 2(9a^2)-3(3a)+4[/tex]

Simplify:

[tex]f(3a) = 18a^2-9a+4[/tex]

Hence, our answer is C.

Answer:

4/3 inches, or 1.33333 inches

Step-by-step explanation:

In terms of the volume of a cube, its side length is the cube root of it. Therefore, for a cube with a volume of 512/216 cubic inches, its side length is equal to ∛(512/216) = ∛(512)/∛(216) = 8/6 = 4/3 inches*

* we know that 8/6 = 4/3 because we can multiply both the numerator and denominator by 1/2 to get this result. If we multiply/divide the numerator or denominator by the same values, the fraction is still the same

Answer:

equation of the line would be y=-3x+7

Step-by-step explanation:

because the line goes 3 up and 1 behind for the next point ad the line is not y intercept 7

Step-by-step explanation:

[tex]\sqrt{10(x-3)} =\sqrt{26}[/tex]

[tex]\sqrt{10x-30} = \sqrt{26} \\\10x-30 = (\sqrt{26} )^2\\10x - 30 = 26\\10x = 56\\x = 56/10\\so, x = 28/5[/tex]

Answer:

The answer is 18 feet...

Step-by-step explanation:

C. 18ft is the answer

Answer:

(b)

Total frequencies:

Multiples of 3 or 5:

Required probability:

(c)

(i) Good limes = GL = 10

(ii) Good fruits = GF = 10 + 8 = 18

(iii) Good apple = GA = 8, Bad lime = BL = 6

Answer:

(x - 2)

Step-by-step explanation:

Given expression is,

[tex]\frac{x^3+3x^2-4x-12}{x^2+5x+6}[/tex]

We have to find the quotient.

x² + 5x + 6) x³ + 3x² - 4x - 12(x - 2

                   x³ + 5x² + 6x

                       -2x² - 10x - 12

                       -2x² - 10x - 12

                                    0

Therefore, quotient of the given expression will be (x - 2).

Answer:

X - 2

Step-by-step explanation:

Answer:

a=9

Step-by-step explanation:

a^3 = 729

Taking the cube root of each side

a^3 ^(1/3) = 729^ (1/3)

a = 9

Answer:

246×17=4182

2460×1700=4182000

(one zero on the end+2 zeroes in the end=3 zeroes in the end on the answer)

16×3=48

0,16×0,3=0,048

(2 numbers after comma+1 number after comma=3 numbers after comma in the answer)

Answer: 1884 cm³

Step-by-step explanation:

cylinder volume = π · r² · h

π · r² · h = 3.14 · 5² · 24 = 3.14 · 25 · 24 = 1884 cm³

Answer:

x is 11

Step-by-step explanation:

[tex]{ \tt{10 + 5 + x = 26}} \\ x = 11[/tex]

Answer:

[tex]U = x[/tex]

[tex]V=10[/tex]

Step-by-step explanation:

Given

[tex](x +3)^2 + 14(x + 3) + 49 = (U + V)^2[/tex]

Required

Find U and V

We have:

[tex](x +3)^2 + 14(x + 3) + 49 = (U + V)^2[/tex]

Expand

[tex]x^2 + 6x + 9 + 14x + 42 + 49 = (U + V)^2[/tex]

Collect like terms

[tex]x^2 + 6x + 14x + 9 + 42 + 49 = (U + V)^2[/tex]

[tex]x^2 + 20x + 100 = (U + V)^2[/tex]

Expand

[tex]x^2 + 10x + 10x + 100 = (U + V)^2[/tex]

Group

[tex][x^2 + 10x] + [10x + 100] = (U + V)^2[/tex]

Factorize each group

[tex]x[x + 10] + 10[x + 10] = (U + V)^2[/tex]

Factor out x + 10

[tex][x + 10][x + 10] = (U + V)^2[/tex]

So, we have:

[tex][x + 10]^2 = (U + V)^2[/tex]

By comparison

[tex]U = x[/tex]

[tex]V=10[/tex]

Answer:

hhhahah

Step-by-step explanation:

eeee

Answer:

[tex]x=32768.000[/tex]

Step-by-step explanation:

One is given the following expression:

[tex]log_2(x)+log_4(x)=5[/tex]

Use the logarithm base change rule, which states the following:

[tex]log_b(y)=\frac{log(y)}{log(b)}[/tex]

Remember, a logarithm with not base indicated is another way of writing a logarithm to the base of (10). One can apply the base change rule to this situation:

[tex]log_2(x)+log_4(x)=5[/tex]

[tex]\frac{log(x)}{log(2)}+\frac{log(x)}{log(4)}=5[/tex]

Factor out (log(x)),

[tex](log(x))(\frac{1}{log(2)}+\frac{1}{log(4)})=5[/tex]

Inverse operations:

[tex]log(x)=\frac{5}{\frac{1}{(log(2)+log(4)}}[/tex]

Simplify,

[tex]log(x)=5(log(2)+log(4))[/tex]

[tex]log(x)=4.51545[/tex]

Now rewrite the logarithm, remember, a logarithm is another way of writing an exponent, in the following format:

[tex]b^x=y\ \ -> log_b(y)=x[/tex]

[tex]log(x)=4.51545[/tex]

[tex]10^4^.^5^1^5^4^5=x[/tex]

[tex]32768.000=x[/tex]

Answer:

4

Step-by-step explanation:

We want to find the highest common factor

Breaking them into factors

28 = 4*7 = 2*2*7

40 = 4*10 = 2*2*2*5

12 = 4*3 = 2*2*3

24 = 3*8 = 3*2*2*2

The factor that appears in all is 2*2

2*2 =4

Answer:

4

Step-by-step explanation:

28÷4=7

40÷4=10

12÷4=3

24÷4=6

7, 10, 3 and 6 cannot be divided by any same number.

D. 2x⁶y²

This is the equivalent expression.

Answer:

30 is your answer

Step-by-step explanation:

32x + 1 = 92x - 1

+1+1=92x-32x

2=60x

x=60÷2

x=30

Answer:

Mala had 14 sweets at the start.

Step-by-step explanation:

7 x 2 = 14

To check, 14/2 = 7. (Dividing by 2 is the same as multiplying by 1/2)

2x - 22 < -8

Add 22 to both sides

2x < 14

Divide both sides by 2

X < 7

Answer:

[tex]2x-22<-8[/tex]

Add 22 to both sides

[tex]2x-22+22<-8+22[/tex]

[tex]2x<14[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}<\frac{14}{2}[/tex]

[tex]x<7[/tex]

OAmalOHopeO

Answer:

10,596 cubic inches

Step-by-step explanation:

The shape of the prism with which the sand castle can be modelled = Square prism

The arrangement of the square prism = One on top of the other

The given height of each prism, h = 6 inches

The side length of the base of the bottom prism, s₄ = 30 inches

The side length of the base of the other prism = The side length of the base of the prism below each prism - 7 inches

Therefore;

The side length of a prism = 7 inches + The side length of the prism above it

Given that the side length of the base prism (The fourth prism), s₄ = 30 inches

The side length of the prism, directly above the base prism (The fourth prism), s₃ = (30 - 7) inches = 23 inches

The side length of the prism, directly above the third prism (The second prism), s₃ = (23 - 7) = 16 inches

The side length of the top most prism, s₁ = (16 - 7) inches = 9 inches

The volume of the sand castle, V = h × (s₄² + s₃² + s₂² + s₁²)

∴ V = 6 × (30² + 23² + 16² + 9²) = 10,596

The volume of the sand castle, V = 10,596 in.³

Heyo!

The volume of the sandcastle above is 10,596 cubic inches.

Hope this helps! If so, please lmk! Tysm and good luck guys!

Answer:

15%

Step-by-step explanation:

As we see, by the time one day passes, we have the amount of weeds as 1650 times 0.85 to the power of 1. We can rewrite 0.85 as 85%. That means that 1650 keeps getting multiplied by 85% to the power of as many days that have passed. 85% can be rewritten again to 1 - 15%. We can see in the equation that the population of weeds decreases by 15% as d, increases, and d is the number of days, so the population of the weeds decreases by 15% each day.

Answer:

tan Z = 4/3

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta= opp / adj

tan Z = 32/24

Divide top and bottom by 8

tan Z = 4/3

Step-by-step explanation:

Volume of 100chocolates:

((12^2 x 15)/3) x 100 =72000

volume of cylinder:

base area x height

base area= πr^2= 5625π

height=volume/base area

height=72000/5625π=4.07 (3sf)

ans: 4.07mm

Answer:

Step-by-step explanation:

1) The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.

Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit

2)If you assume that each break in the stick is uniformly distributed along the length of the stick and is independent of the location of the other break, then the odds are 25% that you will be able to form a triangle with the 3 pieces.

We'll call the length of the stick 1, so each break can occur at a position in the interval [0,1]. Let x and y represent the two breaks. Then we can look at the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is our probability.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square, so the probability that you can form a triangle is 25%

Answer:

solving for x

Step-by-step explanation:

4 or -6

Answer:

x = 4

Step-by-step explanation:

Those absolute value signs are a trick, well at least for this problem. Solve it how you usually would. However, if +2 was -2 or +/-2, then you would need to pay attention. Basically, those signs make the whole equation incased positive no matter what.

Answer:

u is 17√2 and v is 17

Step-by-step explanation:

To find u:

[tex]{ \bf{ \sin( \theta) = \frac{opposite}{hypotenuse} }}[/tex]

feed in the terms:

[tex] \sin(45 \degree) = \frac{17}{u} \\ \\ u = \frac{17}{ \sin(45 \degree) } \\ \\ u = 17 \sqrt{2} [/tex]

To find v:

[tex] \cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]

feed in the terms:

[tex] \cos(45) = \frac{v}{u} \\ \\ v = u. \cos(45) \\ v = (17 \sqrt{2} )÷( \sqrt{2} ) \\ v = 17[/tex]

Answer:

Jeff read 5/28 of a book in 1 hour.

Step-by-step explanation:

The rate given is 5/7 of a book read in 4 hours.

If the questions asks how much he read in 1 hour, it means the answer needed is a unit rate.

A unit rate is a rate per unit. In this case, a rate per hour.

Let’s find how much Jeff read in 1 hour:

5/7 in 4 hours is the rate given so:

5/7 ÷ 4

= 5/7 x 1/4

= 5/28 (already simplified/final answer)

SO, Jeff read 5/28 of the book in 1 hour.

Brainliest? Hope this helped!