What is the value of log6 49?

Round your answer to two places.

Answer:

4% per annum

Step-by-step explanation:

Recall :

Simple interest = principal * rate * time

Given that :

Time = 3 ; simple interest = 84 ; principal = 700

84 = 700 * rate * 3

84 = 2100 * rate

Rate = 84 /2100

= 0.04

= 0.04 * 100% = 4% per annum

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Explanation:

Compare the given equation to the vertex form y = a(x-h)^2 + k

You'll see that a = 3, h = 4 and k = 7

The vertex is (h,k) = (4,7)

The value of 'a' determines if the parabola opens upward or downward. Since a > 0, it opens upward. This furthermore leads to the vertex being the lowest point on the parabola.

The value of 'a' also determines how vertically stretched or compressed the parabola is.

Answer:

1. The vertex of the graph of the function is (-4, 7)

2. The vertex represents a minimum value

3. The equation represented by the new graph is g(x) = (x + 4)² + 1

Step-by-step explanation:

The given quadratic function is given in vertex  form, y = a·(x - h)² + k, as follows;

g(x) = (x + 4)² + 7

1. By comparing the given quadratic function and the vertex form of a quadratic equation, we have;

a = 1, h = -4, and k = 7

The vertex of the graph of the function, (h, k) = (-4, 7)

2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value

3. Shifting the graph 6 units down from where it is now will give;

The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)

h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c

c = k + a·h²

Therefore, initial value of the constant term, c = -1×(-4)² + 7 = 23

After the shifting the graph 6 units down, c = 23 - 6 = 17

∴ k = 1 = -a·(-4)² + 17

∴ -16/16 = -1 = -a

a = 1

Therefore, the equation represented by the new graph is g(x) = (x + 4)² + 1.

Answer:

29/6

Step-by-step explanation:

Answer:

82.5inches.

Step-by-step explanation:

A=1/2bh

=1/2×15×11

=82.5

Answer:

82.5 in.²

Step-by-step explanation:

[tex]A=\frac{1}{2} bh[/tex]

[tex]A=\frac{1}{2}(15)(11)[/tex]

[tex]A=\frac{1}{2}(165)[/tex]

[tex]A=82.5 in.^{2}[/tex]

Answer:

y = 0, y= -7

Step-by-step explanation:

[tex]y(-7-y) = 0\\=> y =0\ ,\ -7 -y =0 => y = -7[/tex]

Answer:

60.5

Step-by-step explanation:

Answer:

600 butter : 2000 flour : 200 sugar : 400 currants = 72 cakes

120 cakes could be made with 1 kg of butter

Step-by-step explanation:

Here, 72 cakes = 6 dozen cakes

( since 12 cake = 1 dozen cake ).

a. First calculate quantity of each ingredient per dozen by dividing each by 1.5 (18/12).

• Butter - 150/1.5 = 100 g per dozen

For 6 dozen :

100g x 6 = 600 g

• Flour - 500/1.5 = 333.33 g per dozen

For 6 dozen :

333.33 g x 6 = 2000 g

• Sugar - 50/1.5 = 33.33 g per dozen

For 6 dozen :

33.33 x 6 = 200 g

• Currants - 100/1.5 = 66.67 g per dozen

For 6 dozen :

66.67 x 6 = 400 g

b. It is given that,

150g butter is required to make = 18 cakes

Then by using unitary method, we get,

1 g of butter is required to make = 18/150 cakes

Since, 1 Kg = 1000 g

Then,

1000 g of butter is required to make = (18/150) × 1000

= 120 cakes

Hence, with 1 kg of butter 120 whole cakes can be made.

Hope this answer helps you :)

Have a great day :)

Mark brainliest

Hi there! Use the difference of two squares formula below:

[tex] \large \boxed{ {x}^{2} - {y}^{2} = (x + y)(x - y)}[/tex]

You need to know that what number times itself and get 16. 16 comes from 4×4 or 4².

Then,

[tex] \large{ {x}^{2} - 16 = (x + 4)(x - 4)}[/tex]

[tex] \large{(x + 4)(x - 4) = 0}[/tex]

Solve the equation for all real values of x.

[tex] \large{x = 4, - 4}[/tex]

If you don't like using a formula. You can do this:

[tex] \large{ {x}^{2} - 16 = 0} \\ \large{ {x}^{2} = 16} \\ \large{x = \pm \sqrt{16} } \\ \large{x = \pm 4}[/tex]

If you remember the square root well, the square root of 16 is 4×4. Pull out the two 4's and thus the square root of 16 is 4.

For the square both sides method above (second method), we can define that:

[tex] \large \boxed{ \large{ {x}^{2} = a \longrightarrow x = \pm a }}[/tex]

Answer

Answer:

56.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

   0 5 6

1 6 9 0 4

 − 0    

   9 0  

 − 8 0  

   1 0 4

 −   9 6

       8

the answer is 56

Answer:

2/3

Step-by-step explanation: 2/3 is just 0.66666 repeating which is greater than 0.6

Answer:

2/3

Step-by-step explanation:

2/3 and 3/5

10/15 and 9/15

Hence, 2/3 is greater

Feel free to mark this as brainliest :D

6.5 / 12 = x / 24

x = 6.5 × 24 / 12

x = 6.5 × 2

x = 13

Answer:

Step-by-step explanation:

x/y=x/y

6.5/12=x/24

do cross multiplication

12x=24*6.5

x=156/12

x=13

Answer:

2 = 10^(2x-1)

Step-by-step explanation:

Imma assume the "," is 10,

So basically, it's just 2 = 10^(2x-1) I think, sorry if I'm wrong tho

Answer:

will you msg me . . . . .. . ..

Answer:

422 cm²

Step-by-step explanation:

Small rectangular prism: 3*4 + 8*3 + 8*3 + 8*4 + 8*4 = 124

Large rectangular prism: 5*7 + 5*7 + 10*5 + 10*5 + 10*7 + (10*7 - 4*3 ) = 298

Total: 124 + 298 = 422 cm²

*Calculate only areas of surfaces showing and add them up

The small rectangular prism has 5, and the large rectangular prism has 6 (with a 4*3 rectangle on its top surface covered)

Answer:

the unit of measure of the conversion factor should be the unit of measure__

A numerator from __ which you want to convert

Answer:

to find the mean you add up all the values to get the sum, count the number of values you have in your data set, then divide the sum by the count

Step-by-step explanation:

Answer:

√24

Step-by-step explanation:

Answer:

[tex] \sqrt{24} [/tex]

as

[tex] \sqrt{25} = 5[/tex]

so

[tex] \sqrt{24} \: is \: nearly \: equal \: to \: 5[/tex]

also it is smaller than 5 and the number shown on the number line is left to 5 so it must be smaller than 5

Answer:

[tex]f(7) = 49[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \left[\begin{array}{cc}3x+5&1.5 <x < 2\\x^2&x>2\end{array}[/tex]

Required

Determine f(7)

To do this, we make use of

[tex]f(x) = x^2[/tex]

Because [tex]7 > 2[/tex]

So, we have:

[tex]f(x) = x^2[/tex]

This becomes:

[tex]f(7) = 7^2\\[/tex]

[tex]f(7) = 49[/tex]

Let's calculate

4/15×285 + 3/20×320 = 124

124 students are participating in these exercises.

7 students is participating

Answer: So how many times can you get 94.2 inces from 1 mile?

How many inches are there in 1 mile?

1 mile = 5280 feet and...

1 foot = 12 inches., so...

1 mile = 5280ft.(12in./ft)

1 mile = 63,360 inches. Finally, you will divide 63,360 inches by 94.2 inches per revolution.

63360%2F94.2+=+672.6revolutions per mile :)

Step-by-step explanation: hope this helped

Given:

The radius of smaller cylinder is 2 m.

The radius of larger cylinder is 8 m.

The height of smaller cylinder is 14 m.

Both cylinders are similar.

To find:

The height of larger cylinder.

Solution:

It is given that the both cylinders are similar to each other.

We know that the corresponding sides of similar figure are proportional.

Let height of the larger cylinder is [tex]h_2[/tex].

[tex]\dfrac{r_1}{r_2}=\dfrac{h_1}{h_2}[/tex]

[tex]\dfrac{2}{8}=\dfrac{14}{h_2}[/tex]

[tex]\dfrac{1}{4}=\dfrac{14}{h_2}[/tex]

On cross multiplication, we get

[tex]1\times h_2=14\times 4[/tex]

[tex]h_2=56[/tex]

Therefore, the height of the larger cylinder is 56 m.

Answer:

(a) Brandon bought 5 gallons of paint for $90.

Step-by-step explanation:

Given

Parvati:

[tex]8\ gallon \to \$144[/tex]

Required

Person with the same paint

First, calculate the unit cost of Parvati's paint

[tex]Unit = \frac{\$144}{8\ gallon}[/tex]

[tex]Unit = \$18/gallon[/tex]

To get the person with the same kind of paint, we simply calculate the unit price.

Whoever has the same unit price as [tex]Unit = \$18/gallon[/tex] have the same kind of paint

Brandon

[tex]Amount = \$90[/tex]

[tex]Size= 5\ gallons[/tex]

So:

[tex]Unit = \frac{Amount}{Size}[/tex]

[tex]Unit = \frac{\$90}{5\ gallons}[/tex]

[tex]Unit = \$18/gallons[/tex]

Brandon has the same paint as Parvati because the unit prices are the same.

Answer: The required sample size = 97

Step-by-step explanation:

If prior population standard deviation is known, then the minimum sample size can be computed as:

[tex]n=(\frac{z^*\times\sigma}{E})^2[/tex]

,where z* = critical z-value

[tex]\sigma[/tex] = population standard deviation

E = Margin of error

As per given,

[tex]\sigma=20,\ E= 4[/tex]

Critical value for 95% confidence = 1.96

[tex]n=(\frac{1.96\times20}{4})^2\\= (1.96\times 5)^2\\= (9.8)^2\\=96.04\approx97[/tex]

Hence, the required sample size = 97

Answer:

E and A

Step-by-step explanation:

Answer:

Step-by-step explanation:

= [tex] ( {p}^{ \frac{1}{2} } )^{3} \times \sqrt{p ^{6} } [/tex]

= [tex] ( {p}^{ \frac{3}{2} } ) \times {p ^{ \frac{1}{2} × 6} } [/tex]

= [tex] ( {p}^{ \frac{3}{2} } ) \times {p ^{ 3} } [/tex]

= [tex] ( {p})^{ \frac{3}{2} + 3} [/tex]

= [tex] ( {p})^{ \frac{3 + 3}{2}} [/tex]

= [tex] ( {p})^{ \frac{9}{2}} [/tex]

Answer:

0.3125 = 31.25% probability that it is not ideal.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either it is a girl, or they are not. The probability of a child being a girl is independent of any other child. This 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.

0.5 probability of a children being a girl:

This means that [tex]p = 0.5[/tex]

If you randomly select a Happyville family that has four children, what is the probability that it is not ideal?

Not ideal is less than two girls, so this is P(X < 2).

Four children means that [tex]n = 4[/tex]. So

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

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

[tex]P(X = 0) = C_{4,0}.(0.5)^{0}.(0.5)^{4} = 0.0625[/tex]

[tex]P(X = 1) = C_{4,1}.(0.5)^{1}.(0.5)^{3} = 0.25[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0625 + 0.25 = 0.3125[/tex]

0.3125 = 31.25% probability that it is not ideal.

Answer:

555

Step-by-step explanation:

Answer:

4 + x = 12

x = 8

Step-by-step explanation:

4 more than a number is 12

4 + x = 12

x = 8

Answer:

Step-by-step explanation:

x/2-5=x/4 +2

x/2-x/4=2+5

x*4-x*2/8=7

4x-2x=8*7

2x=56

x=56/2

x=28

Answer:

J

Step-by-step explanation:

Automatically 1 and 8 are removed as answers since they are too small and go into the negatives, making the other side impossible to be equal. Then just substitute with -20 and 28 and to see which is correct.

Answer:

the x intercepts of the parabola are -2.