4 x3 to the power of 2 divided 6x 3 to the power of 2

The temperature needs to be increased by \(10.8 ^{\circ}F\) for Mrs. Munyai to swim in the pool.

The formula to convert the temperature from Celcius to Fahrenheit is:

\(\textdegree F = (\textdegree C * 1.8) + 32\)

We need to calculate the temperature change of \(6 \textdegree C\) in Fahrenheit:

\(\Delta \textdegree C = 6\\\Delta \textdegree F = \Delta \textdegree C * 1.8 = 10.8\)

The temperature needs to be increased by \(10.8 ^{\circ}F\) for Mrs. Munyai to swim in the pool.

We can calculate the  Fahrenheit temperature of the water and the desired temperature in Fahrenheit:

\(^{\circ}C = 19\\^{\circ}F = (19 * 1.8) + 32 = 66.2\)

\(^{\circ}C = 25\\^{\circ}F = (25 * 1.8) + 32 = 77\)

The current temperature of the pool is \(66.2 ^{\circ} F\) and the desired temperature is \(77 ^{\circ} F\).

Therefore the temperature needs to be increased by:

\(\Delta ^{\circ}F = 77 - 66.2 = 10.8 ^{\circ}F\)

which is the same temperature change we calculated earlier in Fahrenheit.

Therefore, the temperature needs to be increased by \(10.8 ^{\circ}F\) for Mrs. Munyai to swim in the pool.

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Answer:

4

Step-by-step explanation:

x must equal 2 and 2 to the power of 2 is 4

Answer:

4

Step-by-step explanation:

Original equation: 3x-1=5

Add 1 on both sides: 3x=6

Divide by 3 on both sides: x=2

If x=2, then x^2 = 4.

Let me know if this helps!

Answer:

1.3,-12,16

Step-by-step explanation:

Step-by-step explanation:

Vertical angles are equal   r = 70 degrees

Answer:

D) 25 : 1

Step-by-step explanation:

\(\boxed{\bf Volume \ of \ cylinder = \pi r^2h}\)

Cylinder 1:

         \(h_1 = 5 \ cm\\\\r_1 = 3 \ cm\)

Cylinder 2:

           \(h_2 = 5 \ cm\\\\r_2 = 15 \ cm\)

\(Volume \ of \ cylinder2 : Volume \ of \ cylinder1 = \dfrac{\pi * 15 * 15 * 5}{\pi *3*3*5}\)

                                                                       = 25 : 1

Answer:

Look below

Step-by-step explanation:

The mean of the sampling distribution always equals the mean of the population.

μxˉ​=μ

The standard deviation of the sampling distribution is σ/√n, where n is the sample size

σxˉ​=σ/n​

When a variable in a population is normally distributed, the sampling distribution of for all possible samples of size n is also normally distributed.

If the population is N ( µ, σ) then the sample means distribution is N ( µ, σ/ √ n).

Central Limit Theorem: When randomly sampling from any population with mean µ and standard deviation σ, when n is large enough, the sampling distribution of is approximately normal: ~ N ( µ, σ/ √ n ).

How large a sample size?

It depends on the population distribution. More observations are required if the population distribution is far from normal.

A sample size of 25 is generally enough to obtain a normal sampling distribution from a strong skewness or even mild outliers.

A sample size of 40 will typically be good enough to overcome extreme skewness and outliers.

In many cases, n = 25 isn’t a huge sample. Thus, even for strange population distributions we can assume a normal sampling distribution of the mean and work with it to solve problems.

When x is 4, the output of the equation is greater.

The value for x that produces the same output in both the graph and the equation is equal to 6.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of any proportional relationship such as the linear equation (y = 4) is characterized by a straight line that crosses the y-coordinate as shown in the image attached below.

By critically observing the graphs of the equations, we can reasonably infer and logically deduce that they both would produce the same output (dependent value or y-value) at the ordered pair (4, 6).

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Answer:

x < -( 8-2b) /a  a > 0

Step-by-step explanation:

−ax + 2b > 8

Subtract 2b from each side

−ax + 2b-2b > 8-2b

-ax > 8 -2b

Divide each side by -a, remembering to flip the inequality ( assuming a>0)

-ax/-a < ( 8-2b) /-a

x < -( 8-2b) /a  a > 0

Answer: \(x<\frac{-8+2b}{a}\)

                  \(a>0\)

Step-by-step explanation:

\(-ax+2b>8\)

\(\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}\)

\(-ax>8-2b\)

\(\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\)

\(\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)\)

\(ax<-8+2b\)

\(\mathrm{Divide\:both\:sides\:by\:}a\)

\(\frac{ax}{a}<-\frac{8}{a}+\frac{2b}{a};\quad \:a>0\)

\(x<\frac{-8+2b}{a};\quad \:a>0\)

Answer:

0.707106781187

Step-by-step explanation:

I recommend using the website desmos

The solution is:

If my parents are going to pay the 5%, then, they will pay: $2979.

I will need to save $62.06 each month to accomplish my goal.

Here,

I'm going to a 4-year college that will cost $14895/year.

It means that I will need to pay: 14895*4 = $59.580

If my parents are going to pay the 5%, then, they will pay: $2979.

Now, if I want to save my total contribution for all four years, and I have four years to accomplish  the goal, then:

Then, if I have 4 years to pay it. It means I have 4*12 = 48 months.

Then I will need to save $2979./48 = $62.06 each month to accomplish my goal.

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complete question:

You are going to a 4-year college in 4 years that will cost $14,895.00/yr. Your parents expect you to pay 5% of the total cost.

How much do you need to pay for each year of attending?

If you want to save your total contribution for all four years before you start attending college, how much do you need to save each month if you have four years to accomplish your goal?

Answer:

Step-by-step explanation:

If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.

Let 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...

  4s +4l = 288

And the second cake serves ...

  3s +5l = 316

Subtracting 3/4 of the first equation from the second gives ...

  (3x +5l) -3/4(4s +4l) = (316) -3/4(288)

  2l = 100

  l = 50

  4s +4(50) = 288 . . . substitute for l in the first equation

  4s = 88 . . . . . . . . . . subtract 200

  s = 22 . . . . . . . divide by 4

A small tier will serve 22 guests; a large tier will serve 50 guests.

The transformation of f(x) to p(x) is that (a) the graph is reflected and shifted down

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

The functions f(x) and g(x)

In the function equations, we can see that

f(x) = x²

p(x) = -f(x) - 3

So, we have

Vertical Difference = 0 - 3

Evaluate

Vertical Difference = - 3

This means that the transformation of f(x) to p(x) is that f(x) is reflected and shifted down 3 units to p(x).

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18 + 9x = 49

with the use of an equation you can easily find out if 6 weeks of saving up is enough to get the rabbit.

18 + 9(6) \(\neq\) 49

9 x 6 = 54

54 + 18 = 72

you could have enough money in 4 weeks

Answer:

.84

Step-by-step explanation:

geometcdf(.6,2) = .84

Given,

The measure of side AE is 4.

The measure of side EB is 2.

The measure of side DE is 8.

Required:

The measure of line EC.

Answer:

Step-by-step explanation:

Point P is on line segment

O

Q

‾

OQ

​

. Given

O

P

=

6

,

OP=6,

O

Q

=

4

x

−

3

,

OQ=4x−3, and

P

Q

=

3

x

,

PQ=3x, determine the numerical length of

O

Q

‾

.

OQ

​

.

Label known information:

Label known information:

O

P

Q

6

3x

OQ = 4x – 3

O

P

+

P

Q

=

OP+PQ=

O

Q

OQ

6

+

3

x

=

6+3x=

4

x

−

3

4x−3

−

4

x

−4x=

−

4

x

−4x

−

x

+

6

=

−x+6=

−

3

−3

−

6

−6=

−

6

−6

−

x

=

−x=

−

9

−9

−

x

−

1

=

−1

−x

​

=

−

9

−

1

−1

−9

​

x

=

x=

9

9

Plug in value of

x

to find

O

Q

:

Plug in value of x to find OQ:

O

Q

=

4

x

−

3

=

4

(

9

)

−

3

=

33

OQ=4x−3=4(9)−3=33

You can plug

x

into each expression:

You can plug x into each expression:

O

P

Q

6

3(9)

OQ = 4(9) – 3

Simplify:

Simplify:

O

P

Q

6

27

OQ = 33

Final Answer:

Final Answer:

O

Q

=

33

OQ=33

Answer:

And for this case we can begin completing the square like this:

\( f(x) = x^2 +10x + (10/2)^2 +21 -(10/2)^2\)

And after aggrupate the terms we got:

\( f(x) = (x+5)^2 +21 -25 \)

And finally we have:

\( f(X)= (x+5)^2 -4\)

And for this case our vertex would be:

\( (h,k) = (-5,-4) \)

Step-by-step explanation:

For this case we have the following equation given:

\( f(x) = x^2 +10x +21\)

And we want to find a formula in terms in the vertex form given by:

\( f(x) = a(x-h)^2 +k\)

And for this case we can begin completing the square like this:

\( f(x) = x^2 +10x + (10/2)^2 +21 -(10/2)^2\)

And after aggrupate the terms we got:

\( f(x) = (x+5)^2 +21 -25 \)

And finally we have:

\( f(X)= (x+5)^2 -4\)

And for this case our vertex would be:

\( (h,k) = (-5,-4) \)

To rotate a point (x, y) by 270 degrees clockwise about the origin, we can use the following formula:

(x', y') = (y, -x)

where (x', y') are the coordinates of the rotated point.

Using this formula for each of the vertices of RSQ, we get:

R' = (yR, -xR) = (-1, -4)

S' = (yS, -xS) = (-3, -5)

Q' = (yQ, -xQ) = (-1, -3)

Therefore, the coordinates of the vertices of the image RSQ after rotating 270 degrees clockwise about the origin are R'(-1, -4), S'(-3, -5), and Q'(-1, -3).

The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

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Answer:

you can invite 3 members can

The circuit starts at the final AND gate. It has two inputs, one from an OR gate and one from a NOT gate.

The OR gate has two inputs, p and q. If either p or q is high (1), the OR gate will output a high signal. If both p and q are low (0), the OR gate will output a low signal. In this case, we only have the value of p, which is high, so the output from the OR gate is also high.

The NOT gate has one input, q. It inverts the signal, so if q is high (1), the NOT gate will output a low signal (0), and if q is low (0), the NOT gate will output a high signal (1). We don't know the value of q, so we don't know the output from the NOT gate.

Finally, the AND gate takes the outputs from the OR gate and the NOT gate as its inputs. If both inputs are high (1), the AND gate will output a high signal (1). If either input is low (0), the AND gate will output a low signal (0). Since we don't know the output from the NOT gate, we can't determine the output from the AND gate.

So, to summarize, without knowing the value of q, we can't determine the output from the final AND gate.

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The area of the sector in terms of π is 35.6π inches squared.

The area of the sector is approximately  111.6 inches square

The area of sector of a circle is the amount of space enclosed within the boundary of the sector.

Therefore,

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅ = 200 degrees

r = 8 inches

area of the sector = 200 / 360 × 8²π

area of the sector = 200 / 360 × 64π

area of the sector =12800π/  360

area of a sector = 35.6π inches squared

Let's find the area of the sector with π = 3.14

area of a sector = 35.6 × 3.14 = 111.6 inches square

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Answer:

The area of the shaded region is 160.2 in² (to the nearest tenth).

Step-by-step explanation:

The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle.

\(\boxed{\begin{minipage}{4 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}\)

If the circles have the same center, and the inner circle has a radius of 7 in, then the outer circle has a radius of:

\(\implies r = 7 + 3 = 10\; \sf in\)

Therefore, the area of the shaded region is:

\(\begin{aligned}\sf Area_{shaded\;region}&=\sf Area_{outer\;circle}-Area_{inner\;circle}\\&=\pi \cdot 10^2 - \pi \cdot 7^2\\&=100\pi - 49 \pi\\&=51 \pi\\& = 160.221225...\\&=160.2\; \sf in^2\;(nearest\;tenth)\end{aligned}\)

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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Answer:

Corresponding angles are equal so,

m<6= 110° (being the corresponding angle)

.°. m<6= 110°

Hope this helps you!