Solve logx = 6.4 by changing it to exponential form.

a. X= 6.4
b. X= 6.4^10
c. X=-64
d. x= 10^6.4

answer is D

Answer:

D.) Step 6: student needed to add the b value.

Step-by-step explanation:

I got it wrong and it gave me the right answer, which is what i provided, D.

Answer: Step6

Step-by-step explanation:

Answer:

7 boys.

Step-by-step explanation:

Given:

Total number of students in the school = 60

Total number of girls in the school = 33

Total number of students currently studying chemistry = 24

Total number of girls not currently studying chemistry = 16

Question asked:

How many boys are currently studying chemistry ?

Solution:

Total number of girls in the school = 33

Total number of girls not currently studying chemistry = 16

Total number of girls currently studying chemistry = Total number of girls in the school - Total number of girls not currently studying chemistry

Total number of girls currently studying chemistry =  33 - 16 = 17                                                  

Now:-

Total number of boys and girls currently studying chemistry = 24

Total number girls currently studying chemistry = 17

Total number of boys currently studying chemistry = Total number of boys and girls currently studying chemistry - Total number girls currently studying chemistry

Total number of boys currently studying chemistry = 24 - 17 = 7

Therefore, 7 boys are currently studying chemistry.

The height of the pole is 20ft.

Step-by-step explanation:

Let the height of the pole be '(h+6)'

Distance between the pole and Sven = 48ft.

Height of Sven = 6 ft.

Distance between the bird and his eyes = 50 ft.

We can find the value of 'h' using pythogoras theorem,

h = √(2500-2304)

h = √(196)

h = 14 ft.

The height of the pole = h + 6

= 14 + 6

= 20ft.

The height of the pole is 20ft.

Answer:

There will be 1134.6 infected people on April 25 if on March 22 there were 69 case.

Step-by-step explanation:

Given : Equation [tex]15.4x+72[/tex]

To find : Calculate how many infected people there will be on April 25 if on March 22 there were 69 case ?

Solution :

Equation [tex]y=15.4x+72[/tex]

Plug the x value in the equation,

[tex]y=15.4(69)+72[/tex]

[tex]y=1062.6+72[/tex]

[tex]y=1134.6[/tex]

Therefore, there will be 1134.6 infected people on April 25 if on March 22 there were 69 case.

Answer:

c = 30 inch

Step-by-step explanation:

perpendicular (p) = 18 inch

base(b) = 24 inch

hypotenuse (h) = ?

we know by using Pythagoras theorem

h² = p² + b²

h² = 18² + 24²

h² = 324 + 576

h² = 900

h= √900

therefore h = 30 inch

Hope it will help you. :)

Answer:

ST = 12 units

Step-by-step explanation:

Δ RAS and Δ TES are similar triangles, thus the ratios of corresponding sides are equal, that is, noting that SR = 21 - ST, thus

[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{AR}[/tex] substitute values

[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )

6ST = 8(21 - ST)

6ST = 168 - 8ST ( add 8ST to both sides )

14ST = 168 ( divide both sides by 14 )

ST = 12

9514 1404 393

Answer:

  216 J

Step-by-step explanation:

The kinetic energy is given by ...

  KE = 1/2mv^2

  KE = (1/2)(3 kg)(12 m/s)^2 = 216 kg·m²/s² = 216 J

The kinetic energy of the toy is 216 joules.

__

Its potential energy depends on its height.

Answer:216 J Is the answer I just checked

Step-by-step explanation:

Answer:

Correct option:

Fail to reject H₀. There is enough evidence at the 5% level of significance to support the claim.

Step-by-step explanation:

The claim to be tested is:

Claim: μ ≠ 0.

The information provided is:

α = 0.05

σ = 2.62

Sample statistics: = -0.69

n = 60

As the population standard deviation is provided, it can be determined that a z-test for single is used to performed the test.

Decision rule:

If the p-value of the test is less than the significance level, α then the null hypothesis will be rejected and vice-versa.

Compute the p-value as follows:

[tex]p-value=2P(Z<-0.69)\\=2\times [1-P(Z<0.69)]\\=2\times [1-0.7549]\\=0.4902[/tex]

*Use a z-table for the probability.

The p-value = 0.4902 > α = 0.05.

The null hypothesis was failed to rejected at 5% level of significance.Thus, it can be concluded that there is enough evidence at the 5% level of significance to support the claim.

Answer:

f(x) = -15x² + 50x

Step-by-step explanation:

You're given the rocket start at ground level, so we can assume,

f(0) = 0

after 1 second the rocket is 35 feet up.

f(1) = 35

and after 2 second the rocket is 40 ft up.

f(2) = 40

Now you have 2 values to  plug in your formula to solve.

Plug in f(x) = ax² + bx + c and solve:

f(0) = a(0)² + b(0) + c = 0

f(1) = a(1)² + b(1) + c = 35

f(2) = a(2)² + b(2) + c = 40

a(0)² + b(0) + c = 0

a(1)² + b(1) + c = 35

a(2)² + b(2) + c = 40

0 + 0 + c = 0   ,   we got c=0, so substitute it

a + b + c = 35

4a + 2b + c = 40

Solve for a and b

c = 0

a + b + 0 = 35

4a + 2b + 0 = 40   , solve it using elimination

-2a - 2b + 0 = -70

4a + 2b + 0 = 40  

2a + 0 = -30

a = -15   , we got a, solve for b now

a + b + 0 = 35

(-15) + b + 0 = 35

b = 50

Now we got c=0, a=-15, and b=50, plug it back in your equation

f(x) = -15x² + 50x + 0

Answer:

7

Step-by-step explanation:

Answer:

side c = 10.2

A = 52.6°

B = 37.4°

Step-by-step explanation:

c² = 8.1² + 6.2²

c² = 104.05

c = 10.20049018

Using cosine law:

8.1² = 10.2² + 6.2² - 2(10.2)(6.2)cos

cosA = 7687/11648

A = 52.57199409

A = 52.6°

B = 180 - 90 - 52.6 = 37.4°

Given:

The base of the given triangle has two part:

Left( left side of the hypotenuse) = 25

Right ( right side of the hypotenuse) = x

The altitude (h) = 60

To find the value of x.

Formula:

By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,

[tex]\frac{left}{altitude} =\frac{altitude}{right}[/tex]

Now,

Putting,

left = 25, altitude = 60 and right = x we get,

[tex]\frac{25}{60} = \frac{60}{x}[/tex]

or,  [tex](25)(x)=(60)(60)[/tex] [ by cross multiplication]

or, [tex]x= \frac{3600}{25}[/tex]

or, [tex]x=144[/tex]

Hence,

The value of x is 144.

Answer:

x = 144

Step-by-step explanation:

Height Theorem

60² = 25·x

3600 = 25x

x = 3600 : 25

x = 144

Answer:

You should carry 2 other batteries.

Step-by-step explanation:

If the average life of each battery tends to last 6.9 months, and what you need is a year of battery supply, you probably need to carry two batteries.

The battery inside the flashlight has probably already spent much of its half-life.

We are told that the flashlight already has a battery inside, the batteries are discharged inside the flashlight even if the flashlight is not being used.

Which means that the average life of that battery is wearing out.

It would take 2 more batteries in addition to the one already inside the flashlight to supply the need for these for a year.

Answer:

738 cans.

Step-by-step explanation:

To calculate 82% of 900, take 0.82 *900. Your answer will be 738.

Answer:

738 cans

Step-by-step explanation:

900 x .82=738

Answer:

65%

Step-by-step explanation:

Divide 13 by 20:

0.65

Times 100:

65

So 65%

Answer:

4

Step-by-step explanation:

log2(16)

log2(2^4)

4 log2(2)

4 × 1

4

It should be 4

Answer:

1 stack of 60

2 stacks of 30

3 stacks of 20

4 stacks of 15

5 stacks of 12

6 stacks of 10

60 stacks of 1

30 stacks of 2

20 stacks of 3

15 stacks of 4

12 stacks of 5

Prime Factorisation

[tex]60=2^{2}*3*5[/tex]

Step-by-step explanation:

To find the number of stacks you can make just divide the total by the size of the stacks. This also works in reverse.

To find the prime factorisation you just find the factors of the number by dividing it by the largest prime possible.

The monkey can arrange the 60 coconuts into different numbers of stacks, from 1 stack of 60 coconuts to 60 stacks of 1 coconut. The prime factorization of 60 is 2^2 x 3 x 5.

The monkey, who has collected 60 coconuts, can distribute them in various different ways. The distribution depends on the number of coconuts in each stack as well as the total number of stacks. Here are the various possibilities:

Now, for the prime factorization of 60. This involves breaking down 60 into its smallest prime factors, which are 2, 3, and 5. Thus, the prime factorization of 60 is: 22 x 3 x 5

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Answer:

B. 3

Step-by-step explanation:

Answer:

a radius

x-h

y-k

x-h, y-k

Step-by-step explanation:

The standard form of the circle is given by ( x - h )² + ( y - k )² = r²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the equation of circle be C

Let the center of the circle be represented as A ( h , k )

Now , the radius of the circle is = r units

And , standard form of a circle is

( x - h )² + ( y - k )² = r²

when it is a unit circle , the center is at ( 0 , 0 )

S0 , the equation of circle is x² + y² = r²

Hence , the standard form of circle is ( x - h )² + ( y - k )² = r²

To learn more about circle click :

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Answery

y= 2x+2

Step-by-step explanation:

The midpoint is just the average of the coordinates,

M = (1/2) ( (0,2) + (2,8) ) = ((0+2)/2, (2+8)/2) = (1, 5)

Answer: (1,5)

Answer:

(1,5)

Step-by-step explanation:

(0,2) and (2,8)

Midpoint: (0+2)/2, (2+8)/2

2/2, 10/2

(1,5)

Answer:

a) sample size ≥ 30

b) 0.0017

Step-by-step explanation:

a) The central limit theorem states that for population with mean μ and standard deviation σ and take sufficiently large random samples from the population. This will hold provided the sample size is sufficiently large (usually n > 30) for a normal population.

Therefore the sample size should be greater or equal to 30 i.e n ≥ 30.

b) Given that n = 45, μ = 11.4 minutes and σ = 3.2 minutes, the z score (z) is given by the equation:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

Substituting values to get:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }= \frac{10-11.4}{\frac{3.2}{\sqrt{45} } }=-2.93[/tex]

Using the z table:

P(x < 10) = P(z < -2.93) = 0.0017

the probability that a random sample of n=45 oil changes results in a sample mean time of less than 10 minutes is 0.0017

For part (a), a sample size larger than 30 would be sufficient for using the normal model. For part (b), we'd use the standard error and z-score to find the corresponding probability for the sample mean time being under 10 minutes with a sample size of 45.

The questions revolve around the normal distribution model, which is a concept in Statistics, and the sample size needed to use the normal model to make inferences about a population (in this case, the duration of oil changes). For part (a), we must note that the Central Limit Theorem allows us to assume the distribution of sample means will approximate a normal distribution if the sample size is large enough (mostly, n > 30 is sufficient).

Thus, for this particular scenario, a sample size greater than 30 would be adequate. For part (b), using the standard error (standard deviation / sqrt(n)) with n = 45, we can find the z score = (X - μ) / standard error, where X is 10. We consult a normal distribution table or use software to find the probability associated with this z-score, which would be the answer.

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A quadratic function whose zeros are 2 and 7 is [tex]f(x) = x^2 - 9x+14[/tex]

If the zeros of a quadratic function are a and b, the quadratic function will be given as:

f(x)  =  (x  -  a)(x  -  b)

For the function f(x) whose zeros are 2 and 7:

f(x)  =  (x  -  2)(x  -  7)

Expand the equation

[tex]f(x)=x^2-7x-2x+14\\\\f(x) = x^2 - 9x+14[/tex]

Therefore, a quadratic function whose zeros are 2 and 7 is [tex]f(x) = x^2 - 9x+14[/tex]

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Final answer:

A quadratic function with zeros at 2 and 7 can be constructed by multiplying (x - 2) and (x - 7), leading to the function f(x) = (x - 2)(x - 7). A constant 'a' scales the function, which, if not specified, can be assumed to be 1 for simplicity.

Explanation:

The question asks about constructing a quadratic function f with zeros at 2 and 7. In mathematics, a quadratic function is of the form f(x) = ax2 + bx + c, where a, b, and c are constants and a ≠ 0.

To construct a quadratic function with zeros 2 and 7, we utilize the fact that if 2 and 7 are zeros, the function must be divisible by (x - 2) and (x - 7).

Hence, f(x) can be written as f(x) = a(x - 2)(x - 7), where a is a non-zero constant that scales the function.

To determine a, more information about the function is needed, such as a specific value f(x) takes at a certain point.

In the absence of additional information, we can assume a = 1 for simplicity, which gives us the specific quadratic function f(x) = (x - 2)(x - 7).

This function will cross the x-axis at x = 2 and x = 7, making them its zeros.

Answer:

F. Jenny earned 492 points on 6 tests.

Jenny has the same average

math test score as Alisha i.e. 82.

Step-by-step explanation:

Points earned by Jenny = 492

no. of maths tests attempted by Jenny = 6

average maths test score = 492/6

=82

Answer:

1) 14

2) 8

3) 5

4) 11

5) 10

6) 6

7) 10

8) 17

9) 26

10) 18

Step-by-step explanation:

Merry Early Christmas :)

Answer:

By dividing the top number by the bottom.

Step-by-step explanation:

ummmmm

To convert a fraction into a decimal, divide the fraction's numerator by its denominator. Multiplying a decimal by 100 converts it to a percent, and dividing a percent by 100 converts it back into a decimal. This process is used to manipulate numerical values for various mathematical applications.

Converting a Fraction to a Decimal

To convert a fraction into a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). For example, to convert 3/4 to a decimal, you divide 3 by 4, which equals 0.75. If the fraction is not in simplest form, you may first simplify it before dividing. This is a basic mathematical skill that you will use in many areas of math.

To convert a decimal to a percent, you multiply the decimal by 100. For instance, 0.75 multiplied by 100 equals 75%, because you are essentially finding how many 'parts out of 100' are present in the decimal.

In the case of converting percents, to turn a percent into a decimal, you divide by 100. So, taking 75% and dividing by 100 would give you 0.75, which is the original decimal we started with.

Another example is converting 0.0479 into a decimal that's a number between 1 and 10. To do this, we would move the decimal point to the right two places to get 4.79, as specified by the conversion factor which helps in adjusting units or scaling numbers without changing the value.

Answer:

linear and lateral

Step-by-step explanation:

thsts it

Final answer:

A coordinate grid, also known as a Cartesian coordinate system, is a mechanism used in mathematics to define every point in a plane with a pair of numerical values indicating horizontal and vertical positions from an origin. Systems like UTM and SPC are derived from this concept, using a grid to simplify plotting and calculations on a plane surface.

Explanation:

A coordinate grid, or a Cartesian coordinate system, is a tool used in mathematics to specify each point uniquely in a plane by a pair of numerical coordinates. These are typically written as an ordered pair (x, y) where 'x' represents the horizontal displacement and 'y' represents the vertical displacement, both measured from a specific origin point. This system of geometry was developed by René Descartes, hence the name Cartesian.

For example, the origin of a coordinate system is the starting point where both x and y are zero, designated as (0,0). If we move to the right, x increases, and if we move up, y increases. Conversely, moving to the left decreases x and moving down decreases y. So, for instance, the point (3,4) is located 3 units to the right of the origin and 4 units above it.

Plane coordinate systems, like the Universal Transverse Mercator (UTM) and the State Plane Coordinate (SPC) systems, simplify calculations by using a grid pattern superimposed on a flattened representation of the Earth's surface, facilitating easier and more precise location plotting than spherical coordinate systems like latitude and longitude.

Answer:

AB = 24 cm, BC = 6 cm

Step-by-step explanation:

The perimeter of PQRS = 2(8) + 2(2) = 16 + 4 = 20 cm

Given the perimeter of ABCD is 60 cm, then

scale factor = [tex]\frac{60}{20}[/tex] = 3

That is the dimensions of ABCD are 3 times those of PQRS, so

AB = 3 × 8 cm = 24 cm

BC = 3 × 2 cm = 6 cm

Answer:

AB = 24 cm.

BC =  6 cm.

Step-by-step explanation:

The outer rectangle is a dilation of the inner rectangle centered at the origin. Therefore:

The inner and outer rectangles are similar so the ratio of length to width of the outer rectangle is the same as the ratio of length to width of the inner one.

so AB / BC = 8/2 = 4

AB  = 4BC   -------------(1)

Also as the perimeter  = 60

2AB + 2BC = 60.............(2)

Substituting AB = 4BC in equation (2):

2(4BC) + 2BC = 60

10BC = 60

BC = 6 cm.

and AB = 4*6 = 24 cm.

Answer:

61 miles per hour

Step-by-step explanation:

because you need to divide 274.5 by 4.5 to get the average speed per hour.

Answer:

61 miles per hour

Step-by-step explanation:

To find the average speed, divide the miles by the hours

miles/hours

274.5/4.5

61

So, the average speed is 61 miles per hour