Need help with these two questions linear relations.

Answer:

2.28% is the approximate percentage of the population with an IQ greater than 130.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 15

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(IQ greater than 130)

[tex]P( x > 130) = P( z > \displaystyle\frac{130 - 100}{15}) = P(z > 2)[/tex]

[tex]= 1 - P(z \leq 2)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x > 130) = 1 - 0.9772 = 0.0228 = 2.28\%[/tex]

2.28% is the approximate percentage of the population with an IQ greater than 130.

The approximate percentage of the population with an IQ greater than 130 will be 2.28%.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The mean intelligence quotient (IQ) score is 100, with a standard deviation of 15, and the scores are normally distributed.

Then the approximate percentage of the population with an IQ greater than 130 will be

The value of z-score

z = (130 - 100) / 15

z = 30 / 15

z = 2

Then the probability will be

P(x > 130) = P(z > 2)

P(x > 130) = 1 - P(z < 2)

P(x > 130) = 1 - 0.97725

P(x > 130) = 0.02275

Then the percentage will be

P = 0.02275 x 100

P = 2.275%

P ≅ 2.28%

More about the normal distribution link is given below.

https://brainly.com/question/12421652

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Answer:

120

Step-by-step explanation:

you multiply base times height of the rectangle to get 96 then you do 1/2 bh for the triangle to get 24 and then you add them to get 120

The area of the irregular polygon is 120ft^2

We are given that;

The figure with triangle on top and rectangular base

Height of triangle=4ft

Base* height= 12*8

Now,

Area of triangle= 1/2 * base * height

=1/2 * 12 * 4

=24

Area of rectangle= 12 * 8

=96

Total area= 24+96

=120

Therefore, by the given polygon answer will be 120ft^2.

Learn more about polygons;

https://brainly.com/question/9757482

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Answer:

8x(2x - 1)

Step-by-step explanation:

Step 1: Write expression

16x² - 8x

Step 2: Find GCF

We can factor and 8 out of both terms and also an x out of both terms.

GCF = 8x

Step 3: Factor

8x(2x - 1)

To factor the expression [tex]16x^2[/tex] - 8x, the greatest common factor is 8x, resulting in the factored expression 8x(2x - 1).

To factor the expression [tex]16x^2[/tex] - 8x by taking out the greatest common factor (GCF), we first identify the largest factor that divides both coefficients. Here, 8 is the GCF of 16 and 8, and since both terms also include a factor of x, the GCF is 8x. We then divide each term by 8x to find the factored expression:

[tex]16x^2[/tex] ÷ 8x = 2x

-8x ÷ 8x = -1

So, the expression factored by its greatest common factor is 8x(2x - 1).

Answer:

The measure of angle z is 59°.

Step-by-step explanation:

Final answer:

To find the measure of ∠z when ∠x = 123° and ∠y = 51°, add the angles and subtract the sum from 180°.

Explanation:

Given:

∠x = 123°

∠y = 51°

To find ∠z:

Add ∠x and ∠y: 123° + 51° = 174°

Since the sum of angles in a triangle is 180°, subtract the sum of ∠x and ∠y from 180° to find ∠z: 180° - 174° = 6°

Hence, ∠z = 6°.

Answer:

16 pi or approximately 50.24

Step-by-step explanation:

The area of a circle is given by

A = pi r^2 where r is the radius

r = d/2 where d is the diameter

r = 8/2 =4

So plugging into the equation for the area

A = pi (4)^2

A = 16pi

Using 3.14 as an approximation for pi

A = 16*3.14 =50.24

Answer:

[tex]\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}[/tex]

Step-by-step explanation:

The Weight of Ingredients to be used by Chef Selena are:

Total Weight of Food Made, x

[tex]=5\frac{1}{8}+6+4\frac{7}{8}\\=5+6+4+\frac{1}{8}+\frac{7}{8}\\=16 \: Pounds[/tex]

Since each serving is [tex]\frac{1}{2} Pounds[/tex]

Number of Servings of her dish, y

[tex]16 \div \frac{1}{2}\\ =32 \: Servings[/tex]

The two equations needed to solve the problem are therefore:

[tex]\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}[/tex]

Answer:

(-135)/4

Step-by-step explanation:

Evaluate -(3 x^2)/4 - 2 x^2 + x - 12 where x = 3:

-(3 x^2)/4 - 2 x^2 + x - 12 = 3 - 2×3^2 - 3/4×3^2 - 12

3^2 = 9:

3 - 29 - 3/4×3^2 - 12

3^2 = 9:

3 - 2×9 - 3/4×9 - 12

-2×9 = -18:

3 + -18 - 3/4×9 - 12

-3×9 = -27:

3 - 18 + (-27)/4 - 12

Put 3 - 18 - 27/4 - 12 over the common denominator 4. 3 - 18 - 27/4 - 12 = (4×3)/4 + (4 (-18))/4 - 27/4 + (4 (-12))/4:

(4×3)/4 - (18×4)/4 - 27/4 - (12×4)/4

4×3 = 12:

12/4 - (18×4)/4 - 27/4 - (12×4)/4

4 (-18) = -72:

12/4 + (-72)/4 - 27/4 - (12×4)/4

4 (-12) = -48:

12/4 - 72/4 - 27/4 + (-48)/4

12/4 - 72/4 - 27/4 - 48/4 = (12 - 72 - 27 - 48)/4:

(12 - 72 - 27 - 48)/4

12 - 72 - 27 - 48 = 12 - (72 + 27 + 48):

(12 - (72 + 27 + 48))/4

| 1 |  

| 7 | 2

| 4 | 8

+ | 2 | 7

1 | 4 | 7:

(12 - 147)/4

12 - 147 = -(147 - 12):

(-(147 - 12))/4

| 1 | 4 | 7

- | | 1 | 2

| 1 | 3 | 5:

Answer: (-135)/4

Answer:

6 different groups of toy animals

Step-by-step explanation:

In this question, we are to calculate the number of different groups of toy animals Michael can take.

Since we are selecting, this is clearly a COMBINATION question. Now from the question, we are trying to select 5 toy animals from a group of 6 different animals to fit in the bag

The number of ways we can do this is  6C5 ways

Mathematically, if we have to select a number of r items from a group of n items, the number of ways this can be done is;

nCr = n!/(n-r)!r!

Using the case in the question, we have; 6!/5!(6-5)! = 6!/5!1! = 720/120 = 6 groups

Answer:

6 different groups of toy animals

Step-by-step explanation:

The question above can be solved by applying the Combination technique

Combination technique uses the formula:

nCk = n! /k!(n-k)!

Where in the question above:

n = 6

k = 5

Therefore we have , 6C5

= 6! / 5! (6-5)!

= 6!/ 5!(1!)

6! = 6×5×4×3×2×1

5! = 5×4×3×2×1

Hence,

= (6×5×4×3×2×1) / (5×4×3×2×1)(1)

= 6

Hence, Michael can take 6 different groups of toy animals with him on his vacation.

Answer: The fraction that makes up Democrats or Republicans is 49/50.

Step-by-step explanation: There are 100 senators in total. We have 46/100 representing the Democrats, and 13/25 representing the Republicans. The number representing the Republicans can be made into an equivalent fraction of the other simply by multiplying both numerator and denominator by 4 (in order to make the denominator the same, that is 100). Hence the fraction of Republicans is 52/100, while the rest are Independents. The independents are

Ind = 100 - (46/100 + 52/100)

Ind = 100 - 98/100

Ind = 2/100

{Total = 46/100 + 52/100 + 2/100}

{Total = 100/100}

However, the fraction of all senators that are Democrats or Republicans is derived as follows;

Dems = 46/100

Reps = 52/100

Total fraction = 46/100 + 52/100

Total fraction = 98/100

Total fraction = 49/50

Final answer:

To find the fraction of senators who are Democrat or Republican, we add the fractions representing Democrats and Republicans. The fraction is $rac{49}{50}$.

Explanation:

To find the fraction of senators who are Democrat or Republican, we need to add the fractions representing Democrats and Republicans. The fraction of senators who are Democrats is $rac{46}{100}$, and the fraction of senators who are Republicans is $rac{13}{25}$.

To add these fractions, we need a common denominator. The least common multiple of 100 and 25 is 100, so we can rewrite the fractions with denominators of 100. $rac{46}{100}$ is equivalent to $rac{46}{100}  imes  rac{1}{1}$, and $rac{13}{25}$ is equivalent to $rac{13}{25}  imes  rac{4}{4}$ (since $25  imes 4 = 100$).

Now we can add the fractions: $rac{46}{100} +  rac{13}{25} =  rac{46}{100} +  rac{52}{100} =  rac{98}{100}$.

So, $rac{98}{100}$ of the senators are Democrat or Republican, which simplifies to $rac{49}{50}$.

Answer:

1) 25/144 or 0.1736

2) 5/33 or 0.1515

Step-by-step explanation:

Total marbles: 5 + 7 = 12

1) 5/12 × 5/12

25/144

0.173611111

2) 5/12 × 4/11

5/33

0.151515151515

Answer:

1. 25/144

2. 5/33

Step-by-step explanation:

1. There are a total of 12 marbles. The probability of drawing the first marble red is: 5/12. Since we replace the marble, when we draw the second marble, the probability will also be 5/12. So we multiply them together and get: 25/144.

2. Again the probability of drawing the first marble red is 5/12. However, this time we're not replacing. This means that there are 12 - 1 = 11 remaining marbles and 5 - 1 = 4 remaining red marbles. Then the probability of choosing a second red marble is: 4/11. Multiply these two together: (5/12) * (4/11) = 20/132 = 5/33

Hope this helps!

Answer: 84%

Step-by-step explanation:

112 grocery shoppers bought a candy bar and 588 grocery shoppers did not.

Number of grocery shoppers that bought candy bar = 112

Number of grocery shoppers that did not buy candy bar= 588

Total number of grocery shoppers= 112+588 = 700

Percentage of shoppers did not buy a candy bar= 588/700 × 100

= 0.84 × 100

= 84%

Answer:

0.84 = 84%

Step-by-step explanation:

First we need to find the total number of grocery shoppers.

If 112 bought a candy bar and 588 did not, the total number of grocery shoppers is:

588 + 112 = 700

Now, to calculate the percentage of grocery shoppers that didn't buy a candy bar, we make a division between the number of grocery shoppers that didn't buy a candy bar and the total number of grocery shoppers:

588 / 700 = 0.84 = 84%

The rule for reflecting a point over the y-axis is this:

(x, y) ---> (-x, y)

The x term becomes the opposite and the y term stays the same

(3, 4) ---> (-3, 4)

Hope this helped! Let me know if you have any further questions!

~Just a girl in love with Shawn Mendes

Answer:

x+y =13

10x + 9y =122

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations:

The sum of the hours he worked washing cars (x) and the hours he worked walking dogs(y) will be equal to the total hours worked (13)

For the second equation the product of the number of hours he worked washing cars(x) and the price per hour ($10) plus the product of the number of hours he worked walking dogs (y) and the price per hour ($9) will be equal to the total amount earned (122)-

So, the system of equations is:

Where:

x: number of hours Jose worked washing cars

y: number of hours Jose worked walking dogs  

Based on the information given, the equation will be:

Based on the information given, the sum of the hours he worked washing cars and the hours he worked walking dogs will be equal to the total hours worked. Thia can be represented by:

x + y = 13

On the other hand, the product of the number of hours he worked washing cars and the price per hour plus the product of the number of hours he worked walking dogs and the price per hour can be represented with the equation:

10x + 9y = 122

In conclusion, the equation will be x + y = 13 and 10x + 9y = 122.

Learn more about equations on:

https://brainly.com/question/13763238

Step-by-step explanation:

p=5/7-4/7

7p=1

p=1/7

hope it helps

Answer:

Step-by-step explanation:

Answer:

The correct option is;

a. Moderation

Step-by-step explanation:

Here we have that the analysis is to check the hypothesis that drinking caffeine would exacerbate the effect of sleep disturbance caused worry is a form of moderator analysis.

A moderator analysis is one in which we attempt to determine if the  relationship between two investigated variables is dependent on the magnitude or presence of a third variable. We refer to the third variable as the moderator or moderator variable.

I'm guessing 4+-√42 if u can understand it's the last one....

Jake ran 0.534 km in all, if he ran 145 meters before lunch and 389 meters after lunch.

Step-by-step explanation:

The given is,

                  Jake ran 145 meters before lunch.

                  389 meters after lunch.

Step:1

        Total distance ran by Jake,

           Total distance = Jake run before lunch + Jake run after lunch...(1)

        Where,

                    Jake run before lunch = 145 meters

                       Jake run after lunch = 389 meters

        Equation (1) becomes,

                    Total distance = 145 + 389

                                             = 534

                    Total distance = 534 meters

Step:2

        1 kilometer = 1000 meters

        Total distance ran by Jake = 534 meters

                                                     = [tex]\frac{534}{1000}[/tex] kilometers

                                                     = 0.534

      Total distance ran by Jake  = 0.534 km

Result:

         Jake ran 0.534 km in all, if he ran 145 meters before lunch and 389 meters after lunch.

Answer:

0.534

Step-by-step explanation:

I did the work

Answer:

18.9 miles

Step-by-step explanation:

11.90 + 7.9 = 18.9

Answer:

2 2/5

Step-by-step explanation:

-1 3/5 ÷ -2/3

First change the mixed number to an improper fraction

1 3/5 = (5*1 +3)/5 = 8/5

-8/5 ÷ -2/3

Copy dot flip

-8/5 * -3/2

Multiply the numerators then the denominators

24/10

Dividing the top and bottom by 2

12/5

Changing this back to a mixed number

10/5 +2/5

2 + 2/5

2 2/5

Pls mark Brainliest.

Answer:

12/5 or 2 2/5 is the answer.

Step-by-step explanation:

-1 3/5 divided by -2/3.

First, we must turn the mixed fraction into an improper fraction so we are able to perform operations without the hassle of an extra whole.

-1 3/5 = -8/5

Now let's divide. Division is the same as multiplying the dividend by the reciprocal of the divisor. The divisor is the latter, or the number we are dividing the other number by, i.e. -2/3.

The reciprocal of -2/3 is -3/2.

Now let's multiply.

-8/5 * -3/2 = 24/10, which simplifies into 12/5.

12/5 or 2 2/5 is the answer.

Answer:

Car would have traveled [tex]1.283[/tex] miles more with the extra time

Step-by-step explanation:

Given

Speed of the car - [tex]70[/tex] miles per hour

Speed of car in miles per second

[tex]\frac{70}{60* 60}[/tex]

[tex]= 0.0194[/tex] miles per second

Time wasted in talking instead of travelling

[tex]66[/tex] seconds and [tex]513[/tex] milliseconds

Total time wasted in seconds

[tex]66 + \frac{513}{1000} \\66 + 0.513[/tex]

[tex]66.153[/tex] seconds

Distance that would have been traveled in this time instead of talking

[tex]0.0194[/tex] miles per second [tex]* 66.153[/tex] seconds

[tex]= 0.0194 * 66.153[/tex] miles

[tex]= 1.283[/tex] miles

Answer:

undefined

Step-by-step explanation:

We can find the slope of the line using

m = (y2-y1)/(x2-x1)

    = (-2 - -10)/(-1 - -1)

     = (-2+10)/(-1+1)

     = 8/0

When we have a 0 in the denominator the slope is undefined

Answer:

x = 6/5

y = -14/5

Step-by-step explanation:

y = x -4

y - x = -4

y = 6x -10

y - 6x = -10

y - x = -4

y - 6x = -10

_________--

5x = 6

x = 6/5

y - x = -4 | ×6 |

y - 6x = -10 | ×1 |

6y - 6x = -24

y - 6x = -10

__________--

5y = -14

y = -14/5

Brad average typing rate in words per minute is 21

1260 divided by 60 = 21

(In case you meant 30 minutes)

1260 divided by 30 = 42

Based on the diagram shown above, the area of the shaded region rounded to the nearest hundredth is 1.34 square meter.

In Mathematics and Euclidean Geometry, the area of a square can be calculated by using this formula;

A = [tex]s^2[/tex]

Where:

By substituting the given side lengths into the formula, we have;

Area of square, A = 2.5 × 2.5

Area of square, A = 6.25 square meters.

In Mathematics and Geometry, the area of a circle can be calculated by using this formula:

Area of circle = π[tex]r^2[/tex]

Where:

r represents the radius of a circle.

By substituting, we have;

Radius of circle = diameter/2 = 2.5/2

Radius of circle = 1.25 m.

Area of circle = π × [tex]1.25^2[/tex]

Area of circle ≈ 4.91 square meters.

Area of the shaded region = Area of square - Area of circle

Area of the shaded region = 6.25 - 4.91

Area of the shaded region = 1.34 square meter.

The area of the shaded region is Area = 1.34 [tex]m^2[/tex].

To find the area of the shaded region (the area outside the circle but inside the square), we need to calculate the area of the square and the area of the circle, then subtract the area of the circle from the area of the square.

Given:

Side length of the square [tex]\(s = 2.5\)[/tex] meters

Use [tex]\( \pi = 3.14 \)[/tex]

1. Calculate the area of the square:

[tex]\[ \text{Area of the square} = s^2 = 2.5^2 = 6.25 \text{ square meters} \][/tex]

2. Calculate the radius of the circle:

Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square.

[tex]\[ \text{Diameter of the circle} = 2.5 \text{ meters} \][/tex]

[tex]\[ \text{Radius of the circle} = \frac{2.5}{2} = 1.25 \text{ meters} \][/tex]

3. Calculate the area of the circle:

[tex]\[ \text{Area of the circle} = \pi r^2 = 3.14 \times (1.25)^2 \][/tex]

[tex]\[ \text{Area of the circle} = 3.14 \times 1.5625 = 4.90625 \text{ square meters} \][/tex]

4. Calculate the area of the shaded region:

[tex]\[ \text{Area of the shaded region} = \text{Area of the square} - \text{Area of the circle} \][/tex]

[tex]\[ \text{Area of the shaded region} = 6.25 - 4.90625 = 1.34375 \text{ square meters} \][/tex]

Rounded to the nearest hundredth:

[tex]\[\text{Area of the shaded region} \approx 1.34 \text{ square meters}\][/tex]

The complete question is:

Calculate the area of the shaded region. Use 3.14 for pi. Round your answer to the nearest hundredth if necessary.

Area = ____ [tex]m^2[/tex].

Answer:

sin D= 12/15

sin E= 9/15

cos D=9/15

Step-by-step explanation:

Use SOH CAH TOA

Sine= opposite/hypotenuse

Cosine= adjacent/hypotenuse

Tangent= opposite/adjacent

Answer:

The correct answer is 24.

Step-by-step explanation:

Jose wants to have an average mean of 25 points per game in his 6 basket ball matches.

Total points Jose plans to achieve in 6 games is 25 × 6 = 150.

Points score by him in the first five matches are 28, 24, 26, 27 and 21.

Total points in 5 matches is 126.

Thus the points he need to score in his next game to have an average mean of 25 is given by 150 - 126 = 24.