How can you check to see if two ratios form a proportion? Explain the method you used to find the answer to the previous problem.

We are given this equation

[tex] y=-2x^{2} +2x+2 [/tex]

The vertex form is given by:

[tex] y=a(x-h)^{2} +k [/tex]

Now let us try to convert our equation into vertex form:

[tex] y=-2x^{2} +2x+2 [/tex]

Vertex form is given by:

[tex] y=-2(x-0.5)^{2} +2.5 [/tex]

comparing our equation with vertex form ,

The vertex (h,k) is (0.5, 2.5)

Next we have to find y when x=6, plugging x as 6 in the given equation,

[tex] y=-2(6)^{2} +2(6)+2 [/tex]

y=-58

So at x=6, y=-58.

Answer:

Correct option is D

Scale factor of dilation is [tex]\frac{7}{10}[/tex]

Step-by-step explanation:

Given the two similar figures

Trapezoid RSTV∼trapezoid WXYZ

We have to scale factor of dilation from RSTV to WXYZ.

As the two trapezoid are similar therefore their ratio of corresponding sides gives the scale factor of dilation.

Hence, [tex]\text{scale factor of dilation is=}\frac{WX}{RS}=\frac{WZ}{RV}[/tex]

i.e  [tex]\frac{28}{40}=\frac{35}{50}=\frac{7}{10}[/tex]

Hence, scale factor of dilation is [tex]\frac{7}{10}[/tex]

The probability that a randomly selected group of 36 women will have a mean pregnancy length between 264 days and 266 days is 0.2881. The percentage is 28.81%.

The correct probability that the mean pregnancy length of 36 randomly selected women falls between 264 days and 266 days is given by the cumulative distribution function (CDF) of the normal distribution with a mean of 264 days, a standard deviation of 15 days, and a sample size of 36.

To find this probability, we first need to determine the standard error of the mean (SEM), which is calculated by dividing the standard deviation by the square root of the sample size:

[tex]\[ SEM = \frac{\sigma}{\sqrt{n}} = \frac{15}{\sqrt{36}} = \frac{15}{6} = 2.5 \][/tex]

To find the z-scores corresponding to the mean pregnancy lengths of 264 days and 266 days. The z-score for a value x is calculated by:

[tex]\[ z = \frac{x - \mu}{SEM} \][/tex]

For 264 days:

[tex]\[ z_{264} = \frac{264 - 264}{2.5} = 0 \][/tex]

For 266 days:

[tex]\[ z_{266} = \frac{266 - 264}{2.5} = \frac{2}{2.5} = 0.8 \][/tex]

Now, we look up these z-scores in the standard normal distribution table or use a calculator to find the corresponding probabilities.

The probability of a z-score less than 0 is 0.5, and the probability of a z-score less than 0.8 is approximately 0.7881.

The probability that the mean pregnancy length is between 264 days and 266 days is the difference between these two probabilities:

[tex]\[ P(264 < \bar{x} < 266) = P(z < 0.8) - P(z < 0) \] \[ P(264 < \bar{x} < 266) = 0.7881 - 0.5 \] \[ P(264 < \bar{x} < 266) = 0.2881 \][/tex]

Therefore, the probability that a randomly selected group of 36 women will have a mean pregnancy length between 264 days and 266 days is approximately 0.2881.

To express this as a percentage, we multiply by 100:

[tex]\[ 0.2881 \times 100 \approx 28.81\% \][/tex]

The answer is: 28.81%.

Answer:

8x=32

(4,6)

Step-by-step explanation:

Answer:

n=2 m=7

Step-by-step explanation:

Answer:

[tex]3^{\circ}[/tex]

Step-by-step explanation:

Let x represent the angle of elevation.

We have been given that Jamison takes a 20 foot board and props it up with a one foot block at the far end to make a daredevil jump ramp for his bike.

Upon looking at our attached file, we can see that 20 feet board and 1 foot board forms a right triangle with respect to ground, where side of 1 foot is opposite side and 20 feet side is hypotenuse.

We know that sine relates the opposite side of right triangle to its hypotenuse, so we can set an equation as:

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}(x)=\frac{1}{20}[/tex]

Using arcsin we will get,

[tex]x=\text{sin}^{-1}(\frac{1}{20})[/tex]

[tex]x=2.865983982599^{\circ}[/tex]

Upon rounding our answer to nearest degree we will get,

[tex]x\approx 3^{\circ}[/tex]

Therefore, the measure of the angle of elevation of the ramp is 3 degrees.

the complete question in the attached figure

we know that 

dAB=dAC+dCB

dAC=√((8-1)²+(-2+9)²)=√98

Area triangle ADC=dAC*CD/2

Area triangle DCB=dCB*CD/2

 Area triangle ADC/Area triangle DCB=3/4

[dAC*CD/2]/[dCB*CD/2]=3/4

dAC=(3/4)*dCB-----------------------> equation (1)

dAB=dAC+dCB=√98

dAC=√98-dCB------------------------ > equation (2)

 (1)=(2)

(3/4)*dCB=√98-dCB------------------> (7/4)*dCB=√98

dCB=(4/7)√98

dAC=√98-dCB-------- > √98-(4/7)√98-----à (3/7) )√98

dAC=(3/7) )√98

find the slope point A (1.-9) and point B (8,-2)

m=(-2+9)/(8-1)=7/7=1-------------- > 45°

 dAC=(3/7)√98

the component  x of dAC  is 

dACx=(3/7)√98*cos45°=(3/7)√98*√2/2=(3/7)√196=3

the component  y of dAC  is 

dACy=dACx=3

 the coordinates of the point C are

 point A(1.-9)

Cx=Ax+dACx----------> 1+3=4

Cy=Ay+dACy----------> -9+3=-6

 the coordinates  C(4,-6)

 the answer is C(4,-6)

Answer:

C(4,-6) is correct on plato

Step-by-step explanation:

Answer:

the answer is 192in

Step-by-step explanation:

The solution for the below equation is required:

4x + 6 - x = 2x + 3

The work done by the Jermaine is presented below :

4x + 6 - x = 2x + 3

5x + 6 = 2x + 3

Instead of adding 4x with -1x to make it 3x , he added 4x with 1x to make it 5x.

So, the correct option is

Jermaine did make an error. He should have combined 4x and -1x to make 3x

3x + 6 = 2x + 3

Hope it helps..!!

Answer:

Step-by-step explanation:

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc is th

Final answer:

To maximize the product of two numbers with a fixed sum of 156, we set up an equation for the product, differentiate, and find that the maximum product is obtained when both numbers are 78.

Explanation:

To find two positive real numbers whose product is a maximum and whose sum is 156, we need to use the concept of optimization in calculus. This involves taking the derivative of the function representing the product of the two numbers and setting it equal to zero to find the critical points. Since the sum of the numbers is fixed at 156, we can express one number in terms of the other, for example, x and 156 - x. The product of these two numbers is x(156 - x). To find the maximum product, we differentiate this function with respect to x:

[tex]\frac{d}{dx} [x(156 - x)] = 156 - 2x[/tex]

Setting this derivative equal to zero gives us 156 - 2x = 0, solving for x we find-

x = 78.

This gives us the two numbers as 78 and 78, because the sum must be 156 and the other number would be 156 - 78. To confirm that this gives a maximum, we would test the second derivative or use the first derivative test. However, by symmetry, when the sum of two numbers is fixed, their product is maximized when the two numbers are equal. In this case, both numbers are 78.

Answer:

It is given that Suria has x apples and Oranges.

Which means ,total number of fruits which includes apple and Orange is equal to x.

Suppose, number of Oranges Suria has = A

And, Number of Apples  Possessed by Suria= B

→Number of Oranges +Number of Apple=x

→ A + B =x

So,total number of apples and Oranges does Suria have altogether = x

The expression x²-14x+31=63 is a quadratic equation. To solve it, you must order it:

 x²-14x+31-63=0

 x²-14x-32=0

 Then, you must apply the quadratic formula, which is shown below:

 x=(-b±√(b^2-4ac))/2a

 So you have the values of a,b and c:

:

 a=1

 b=-14

 c=-32

 When you substitute those values in the quadratic formula, you obtain:

 x=(-(-14)±√((-14)^2-4(1)(-32))/2(1)

 x1=-2

 x2=16

 So, the correct option is the third one: x=-2 or x=16

Answer:

6 lb 4 oz

Step-by-step explanation:

Since, 1 lb = 16 oz,

Here, the given phrase,

The sum of 36 ounces and 4 pounds,

[tex]= 36\text{ oz}+4\text{ lb}[/tex]

[tex]=36\text{ oz}+64\text{ lb}[/tex]

[tex]=100\text{ oz}[/tex]

Again,

1 oz = 1/16 lb,

[tex]100\text{ oz}=\frac{100}{16}=6.25\text{ lb} = 6\text{ lb}+0.25\text{ lb}=6\text{ lb }4\text{ oz}[/tex]

Hence, The sum of 36 ounces and 4 pounds is 6 lb 4 oz

Second option is correct.