Solve 2 2/5 - 1 1/2 .

Answer:

46.4

Step-by-step explanation:

58x0.20 = 11.6

58-11.6= 46.4

hope this helps

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}\)

The error in finding the perimeter of the rectangle is that the length was not calculated correctly, as it is of 5 units.

The perimeter of a rectangle of dimensions l and w is given by:

P = 2l + 2w.

From the graph, the dimensions are given as follows:

Hence the perimeter is:

P = 2l + 2w = 2(5) + 2(3) = 16 units.

The calculated length was of 4, hence the error in finding the perimeter of the rectangle is that the length was not calculated correctly, as it is of 5 units.

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The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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Answer:

0.891

Step-by-step explanation:

sin(63º) = 0.891006..... ≈ 0.89

Answer: 9 is on left of the tiny dotted line of 10. 2 is the tiny dotted line right of 1 and -4 is right of the tiny dotted line of 5.

Step-by-step explanation:

here's a vague picture, hope this makes sense.

While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

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Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

The term "volume" refers to how much general space an object occupies. Unlike mass, volume changes depending on the surroundings. The mass of a substance in a given volume is referred to as its "density." It describes the relationship between mass and volume.

Here,

A cylinder has a volume of V = r2h.

As a result, V = r2[(1/3)]h is obtained by multiplying h by 1/3.

The (1/3) can be moved to the front to obtain V = [(1/3)]r2h because you are free to multiplied in any ratio you choose.

Thus, you would receive one-third of the initial mass.

What would occur if you increased the radius by 1/3 in contrast to this?

Next, you would have

=> V = π[(1/3)r]2h

=> V = π(1/9)r2h

=> V = (1/9)πr2h

You would then possess 1/9 of the volume.

Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

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Answer:

1.691

Step-by-step explanation:

Standard error of the mean is expressed as SEM = S/√n

S is the population standard deviation

n is the sample size (number of observation)

Given S = 27 and n = 255

SEM = 27/√255

SEM = 27/15.97

SEM = 1.691

Hence the standard error of the mean is 1.691

Answer:

x<3/2

Step-by-step explanation:

12x+7<-11

12x<-11-7

12x<-18

x<-3/2

Answer: 1/4

Step-by-step explanation:

Answer:

a) 0.0026

P- value is 0.0026

Step-by-step explanation:

Step(i):-

Given data

first sample size n₁= 80

mean of the first sample  x⁻₁= $6.75

Standard deviation of the first sample   (σ₁) = $1.00

second sample size (n₂) = 60

mean of the second sample( x₂⁻) = $6.25

Standard deviation of the second sample (σ₂) = $0.95

step(ii):-

Test statistic

\(Z = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{\frac{(S.D)_{1} ^{2} }{n_{1} } +\frac{(S.D)_{2} ^{2} }{n_{2} } } }\)  

  Null Hypothesis :H₀: There is no significant difference in wages across the two employers.

x⁻₁= x₂⁻

Alternative Hypothesis :H₁: There is significant difference in wages across the two employers.

x⁻₁≠ x₂⁻

\(Z = \frac{6.75 -6.25 }{\sqrt{\frac{(1^{2} }{80 } +\frac{((0.95)^{2} }{60} } }\)

Z = 3.01

P- value:-

Given data is two tailed test

The test statistic Z = 3.01

First we have to find the Probability of z-statistic

P(Z>3.01) =  1- P( z <3.01)

                 = 1- (0.5 + A(3.01)

                = 0.5 - A(3.01)

             =    0.5 - 0.49865   ( from normal table)

             = 0.0013

P(Z>3.125) = 0.0013

Given two tailed test

   P- value = 2 × P( Z > 3.01)

                 = 2 × 0.0013

                = 0.0026

Final answer:-

The calculated value Z = 3.125 > 1.96 at 0.05 level of significance

null hypothesis is rejected

Conclusion:-

P- value is 0.0026

We are given the following information:

rectangular solid with a square base

surface area = 337.5 cm^2

We are asked to find the dimensions that will give us the maximum volume.

First, we need to represent the dimensions of the given solid. If x = the side of the square base, then we can represent the height as:

So we can express the volume of the solid figure as:

Simplifying the equation, we get:

To find the maximum value of x, we will calculate the derivative of f(x).

Then, we will find the value of x that will make f'(x) = 0.

But because x represents the side of the square base, then we can only accept x = 7.5.

That gives us the height of:

So, the dimensions of the solid figure must be 7.5 cm x 7.5 cm x 7.5 cm.

The form of association that would be found in the variables would be:

As the number of hours spent playing a video game increases, the player is likely to reach higher levels within the game. So positive association.

The number of letters in a person's name and the last digit of their phone number are likely to be unrelated and randomly distributed. There is no association.

As the temperature of the drink decreases, the number of ice cubes in the drink is likely to increase, and vice versa. This is therefore negative association.

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Analyzing the coordinates being provided, the scale factor is found to be 0.5, hence the image of point A(12,4) under the same dilation and the center of dilation as origin is A'(6,2).

A dilation is a transformation in Euclidean space that enlarges or reduces all the points in a figure by a scale factor. In the example given, the dilation maps (6, 10) to (3, 5) with a scale factor of 0.5, and the center of dilation is the origin (0,0). The image of a point A(x,y) under this dilation would be A'(x*0.5, y*0.5). It means the point is scaled down by 0.5 in both x and y coordinate.

The dilation described above can be used in real-world applications such as image processing, where it can be used to reduce the size of an image without losing important details, or to enlarge an image without introducing distortion. It can also be used in architectural design to create smaller or larger versions of floor plans and blueprints. Additionally, it can be used in cartography to change the scale of maps without altering the shape of the features on the map.

Analyzing the given dilation map , mapped from (6,10) to (3,5) ,the center of the dilation being origin. We can see that the scaling factor is 0.5.

So , using the same dilation for point A(12,4), The image of A will be,

A'(12*0.5,4*0.5) = A'(6,2)

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Answer:

y = sec(x-2) - 1

Step-by-step explanation:

We can determine the graph is of a secant by the repeating parabolas. From there, graph sec(x) and add the transformations necessary to replicate the graph.

1. d-b

2. -d -(-b)

3. -d+b

Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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Answer:

They each got about 200 stickers

Step-by-step explanation:

Tracey  needs to have baked 5 pies

What represents a single pie?

Let P represents one single pie that Tracey needs to  bake to cater to her 8 family members

Portion ate by one person=3/5*P

Portion ate by one person=0.60P

8 persons would need to eat=0.60P*8

8 persons would need to eat=4.80P

The fact that a fraction of a pie cannot be baked means that Tracey has to bake 5 pies for  her 8 family members

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The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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Answer: x = ±8

Step-by-step explanation:

x^2 – 64 = 0

Add 64 to each side

x^2 – 64 +64= +64

x^2 = 64

Take the square root of each side

sqrt(x^2) = ±sqrt(64)

x = ±8

Answer:

b) Then z(s) is in the rejection region for H₀. We reject H₀. The p-value is smaller than α/2

c)CI 95 %  =  ( 0.00002 ;  0.09998)

Step-by-step explanation: In both cases, the size of the samples are big enough to make use of the approximation of normality of the difference of the proportions.

Recent Sample

Sample size    n₁  =  1000

Number of events of people with financial fitness more than fair

x₁  =  410

p₁ =  410/ 1000  =  0.4     then q₁ = 1 - p₁    q₁ =  1 -  0.4    q₁  = 0.6

Sample a year ago

Sample size    n₂ =  1200

Number of events of people with financial fitness more than fair

x₂  =  420

p₂  =  420/1200     p₂ = 0.35   q₂  =  1 - p₂    q₂  = 1 - 0.35   q₂ = 0.65

Test Hypothesis

Null Hypothesis                                  H₀              p₁  =  p₂

Alternative Hypothesis                      Hₐ              p₁  ≠  p₂

CI  95 % then significance level  α  =  5%   α  = 0.05    α/2  = 0.025

To calculate p-value:

SE  =  √ (p₁*q₁)/n₁  +  (p₂*q₂)/n₂

SE  =  √ 0.4*0.6/1000 +  0.65*0.35/1200

SE  =  √ 0.00024 + 0.000189

SE = 0.021

z(s) =  ( p₁ - p₂ ) / SE

z(s) = ( 0.4 - 0.35 )/0.021

z(s) = 0.05/ 0.021

z(s) =  2.38

We find p-value from z-table to be   p-value = 0.00842

Comparing

p-value with  α/2   = 0.025

α/2 >  p-value  

Then z(s) is in the rejection region for H₀. We reject H₀

CI 95 %  =  ( p₁  -  p₂ )  ±  2.38*SE

CI 95 %  =  ( 0.05 ± 2.38*0.021 )

CI 95 %  =  ( 0.05 ± 0.04998)

CI 95 %  =  ( 0.00002 ;  0.09998)

CI 95 % does not contain the 0 value affirming what the hypothesis Test already demonstrate

The expression 8x + 4y is not equivalent to 4(2x + 1). Therefore, 8x + 4y = 4(2x + y)

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Let's determine whether the expression 8x + 4y is equivalent to 4(2x + 1).

Let's factorise to know whether the expressions are equivalent.

Therefore, using the common factors,

8x + 4y = 4(2x + y)

Hence, the expression are not equivalent .

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Answer:

30

Step-by-step explanation:

150/5 = 30

30+30+30+30+30 = 150

It is when two Angles add up to 90 degrees

for example 30 + 60

We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.

According to the information we can infer that the parallel line would be AD or CF. Additionally, the perpendicular lines would be CB or FE.

To identify the parallel lines we must look at the figure and find the lines that have the same direction as the line BE and that would never intersect with the segment BE, according to the above, we can infer that the parallel lines would be:

On the other hand, the lines perpendicular to CF would be CB or FE because they make 90° angles with segment CF. Additionally, the face that would be parallel to ABC is DEF.

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