i need help with a. b. and c.​

The approximate angle is $\approx 135^{\circ}$, rounded to the nearest degree

\underset{v}{\rightarrow} - 3\underset{w}{\rightarrow} = (7 \cdot 4, 7 \cdot 2) - (3 \cdot 1, 3 \cdot -3) = (28, 12). The result in component form is (28, 12).

The exact magnitude of \underset{v}{\rightarrow} is $\sqrt{4^2 + 2^2} = \sqrt{20}$ and the exact magnitude of \underset{w}{\rightarrow} is $\sqrt{1^2 + (-3)^2} = \sqrt{10}$.

The dot product \underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow} is (4 \cdot 1) + (2 \cdot -3) = -10.

proj_{\underset{w}{\rightarrow}}(\underset{v}{\rightarrow}) = (\frac{\underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}}{\Vert \underset{w}{\rightarrow} \Vert^2})\underset{w}{\rightarrow} = (\frac{-10}{10}) \cdot (1, -3) = (-1, 3).

proj_{\underset{v}{\rightarrow}}(\underset{w}{\rightarrow}) = (\frac{\underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}}{\Vert \underset{v}{\rightarrow} \Vert^2})\underset{v}{\rightarrow} = (\frac{-10}{20}) \cdot (4, 2) = (-2, -1). The results in component form are (-1, 3) and (-2, -1).

The angle between \underset{v}{\rightarrow} and \underset{w}{\rightarrow} can be found using the formula $\cos\theta = \frac{\underset{v}{\rightarrow}\cdot \underset{w}{\rightarrow}}{\Vert \underset{v}{\rightarrow} \Vert \cdot \Vert \underset{w}{\rightarrow} \Vert}$.

Plugging in the values, $\cos\theta = \frac{-10}{\sqrt{20}\cdot\sqrt{10}} = -\frac{1}{\sqrt{2}}$. The exact angle is $\arccos(-\frac{1}{\sqrt{2}})$. Using a calculator, the approximate angle is $\approx 135^{\circ}$, rounded to the nearest degree.

Learn more about Approximate angle

brainly.com/question/2589631

#SPJ4

The area of the garden is given as follows:

A = 20.6925 ft².

The garden has a rectangular format, hence it's area is given by the multiplication of it's length l by it's width w, as follows:

A = lw.

From the image, converting the mixed numbers to decimal, the dimensions of the garden are given as follows:

Hence the area in feet squared is given by the multiplication of these two dimensions, as follows:

A = 7.75 x 2.67

A = 20.6925 ft².

More can be learned about the area of a rectangle at https://brainly.com/question/25292087

#SPJ1

Answer: The ball is dropped from a height of 10 ft, so it first travels down 10 ft until it hits the ground. The distance traveled in this first part is 10 ft.

On the first bounce, the ball rebounds to one-fifth of its previous height, which is 2 ft (since 10/5 = 2). The ball then travels up 2 ft and back down 2 ft to the ground, for a total distance traveled of 10 + 2 + 2 = 14 ft.

On the second bounce, the ball rebounds to one-fifth of its previous height, which is 2/5 ft (since 2/5 x 2 = 4/5). The ball then travels up 4/5 ft and back down 4/5 ft to the ground, for a total distance traveled of 2/5 + 4/5 + 4/5 = 2 ft.

On the third bounce, the ball rebounds to one-fifth of its previous height, which is 4/25 ft (since 4/25 x 2/5 = 8/125). The ball then travels up 8/125 ft and back down 8/125 ft to the ground, for a total distance traveled of 4/25 + 8/125 + 8/125 = 0.32 ft (rounded to two decimal places).

The ball will continue to bounce, getting closer and closer to the ground with each bounce. We can calculate the total distance traveled by summing the distances traveled on each bounce:

10 + 14 + 2 + 0.32 + ...

To calculate the sum of this infinite series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where S is the sum, a is the first term, and r is the common ratio.

In this case, a = 10 (the distance traveled on the first drop), and r = 1/5 (the fraction by which the height decreases on each bounce). Plugging in these values, we get:

S = 10 / (1 - 1/5)

= 12.5

So the total distance traveled by the ball is 12.5 ft.

Step-by-step explanation:

Answer:

x = -10

Step-by-step explanation:

Note that it is a isosceles triangle. This means that the base angles (the angles that are not forged by the congruent sides) are congruent.

It is given that one of the angle measurements are 67°, meaning that ∠A would also be equal to 67. Set the equation:

m∠A = x + 77

67 = x + 77

Isolate the variable, x. Subtract 77 from both sides of the equation:

67 (-77) = x + 77 (-77)

x = 67 - 77

x = -10

x = -10 is your answer.

~

Learn more about solving for variables, here:

https://brainly.com/question/2669109

The amount of copper that is contained in 120 pounds of brass is equal to 78 pounds.

Let the amount of copper be C.

Given the following data:

Quantity of brass = 120 pounds

Percentage of copper = 65%

To calculate the amount of cooper that is contained in 120 pounds of the brass:

In this exercise, you're required to determine how many pounds of copper can be found in 120 pounds of brass. Thus, we would solve for the percentage of copper contained in this type of brass.

[tex]Copper=\frac{65}{100}*120\\\\Copper, c=78 ponds.[/tex]

This is correct because 65% of 120 pounds is equal to 78 pounds. 65% can be expressed as a decimal (0.65) and multiplied by 120 pounds to find the number of pounds of copper contained in 120 pounds of the brass.

learn more about percentages,

https://brainly.com/question/15054857

#SPJ4

Therefore , the solution of the given problem of area comes out to be  48 sq ft + 4.5π sq ft is flower bed area.

Its total size can be determined by calculating how much space is required to completely cover the outside. The nearby surroundings are taken into consideration when calculating the surface of a trapezoidal shape. Something's total dimensions are determined by its surface area. The sum of the borders associated with each of a cuboid's six rectangular edges determines the internal water capacity of the object.

Here,

We must add the areas of the rectangular and semicircular regions to obtain the area of the flower bed visible in the picture.

The size of the rectangle, which is square and measures 8 feet by 6 feet, is:

=> A_rectangular

=> length * width

=> 8 ft × 6 ft = 48 sq ft

The radius of the semicircular area is 3 feet, and its diameter is 6 feet. Since this is only a semicircle, we must split by 2 in order to calculate the area of the semicircle using the formula A = r2.

=> A_semicircle = (πr^2)/2 = (π × 3^2)/2 = 4.5π sq ft

The area of the semicircular and rectangular parts combined gives us:

=>A_flower bed = A_rectangular + A_semicircle

= 48 sq ft + 4.5π sq ft

To know more about area visit:

https://brainly.com/question/2835293

#SPJ1

Jacob's sample suggests that Garrett should expect approximately 80 percentage  of the students in the school to vote for him.

Jacob's sample of 30 students suggests that 24 of them will vote for Garrett, which is an 80% ratio. Applying this ratio to the entire school population, Garrett can reasonably expect that 80% of the students in the school will vote for him. This means that out of the total student population, Garrett can expect approximately 24/30, or 80%, of them to vote for him. This is a useful estimate for how many votes Garrett can expect to receive from the student body. It is important to note, however, that this is only an estimate and may not accurately reflect the actual number of students who will vote for Garrett. Factors such as student opinion or external influences may affect the actual voting results.

Learn more about percentage here

https://brainly.com/question/16797504

#SPJ4

Therefore , the solution of the given problem of amount comes out to be Sylvia's homes insurance covers personal property up to a maximum of $123,250.

aggregate attempting to determine the length of time needed, overall amount or quantity. The amount in front of you or being thought about is very active. the final outcome, its significance, or its meaning. three accountings: principal, interest, and the third. Word versions include amounts, amounting, and amounted. supple word How much something is, how often you possess

Here,

Sylvia's house is covered for $225,000. Accordingly, the coverage for personal belongings is as follows:

The policy offers coverage for personal belongings equal to 55% of the insured value of the home.

=> Personal property coverage = 0.55 x $225,000, or $123,750.

Sylvia, however, has a $500 personal property exemption. This implies that she is responsible for covering the first $500 of the insured loss.

So the amount covered for personal belongings under Sylvia's homeowners insurance is:

=> $123,750 -  $500 is the amount insured for personal property, or

=> $123,250.

Sylvia's homes insurance covers personal property up to a maximum of $123,250.

To know more about amount visit :-

brainly.com/question/8082054

#SPJ1

Landon would need to invest approximately $1,150 to reach a future value of $3,250 in 18 years with an interest rate of 6.6% compounded daily.

To determine how much Landon needs to invest, we can use the compound interest formula, which is:

A = P(1 + r/n)^(nt)

where A is the future value of the account, P is the principal amount (the amount Landon needs to invest), r is the interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the interest rate is 6.6% or 0.066, the account is compounded daily, so n = 365, and t = 18. We want to find the principal amount, P, that will result in a future value of $3,250.

Substituting these values into the formula, we get:

3,250 = P(1 + 0.066/365)^(365*18)

Simplifying the right-hand side of the equation, we get:

3,250 = P(1.000181)^6,570

Dividing both sides by (1.000181)^6,570, we get:

P = 3,250 / (1.000181)^6,570

Using a calculator, we can evaluate this expression to find that:

P ≈ $1,150.52

To learn more about interest rate click on,

https://brainly.com/question/22810238

#SPJ4

If you add 5 to each data point in a set of data with a mean of 50 and a standard deviation of 10, the mean of the new set of data will become 55. The standard deviation of the new set of data will remain the same at 10.

The term standard deviation is frequently used in statistics to quantify the dispersion or spread of a set of data. The standard deviation is a measure of the amount of variation or dispersion of a set of data values from the mean. Standard deviation is denoted by the symbol s or σ (sigma).

The term mean or arithmetic mean is used in statistics to refer to the value that represents the central tendency of a data set. It is computed by dividing the sum of all data values into a data set by the total number of data points. The formula for computing the mean is given as:

mean = (sum of data values) / (total number of data points)

When you add 5 to each data point in a data set with a mean of 50, the sum of all data values in the data set will increase by (5 * n), where n is the total number of data points. Consequently, the new mean will be given as:

new mean = (sum of new data values) / (total number of data points)

⇒ [(sum of old data values) + (5 * n)] / n ⇒ (50n + 5n) / n ⇒ 55

When you add a constant value to each data point in a data set, the measure of central tendency, i.e., mean, median, and mode will also be shifted by the same constant value. This is because the sum of all data values in the data set increases by the product of the constant value and the total number of data points, n.

The measure of variability or spread, i.e., range, interquartile range, variance, and standard deviation, however, remains the same because it is independent of the location of the data values in the data set. Therefore, adding a constant value to every data point in a data set does not change the spread of the data set but shifts the measure of central tendency to a new value.

Hence, the mean of the new dataset will increase by 5, from 50 to 55, and the standard deviation of the new dataset will remain the same at 10.

To know more about the "mean" and "standard deviation": https://brainly.com/question/26941429

#SPJ11

Answer:

28

Step-by-step explanation:

4 cubed means 4 x 4 x 4, which is 64.

6 squared means 6 x 6, which is 36.

So,

4 cubed - 6 squared = 64 - 36 = 28.

Answer:

The box alone weighs 6 kg

Step-by-step explanation:

Let, weight of Apple be x, Oranges be y, Guavas be z nd box a.

A box of Apple weighs 270kg and 500g i.e270.5kg

a+x =270.5---(1)

A box of oranges weighs 192.5kg

a+y=192.5---(2)

A box of guavas weighs 245

a+z=245---(3)

Fruits together weigh 690 kg

x+y+z=690---(4)

Combining (1),(2),(3), we get

3a+x+y+z=708---(5)

From 4&5

3a+690=708

3a=18

a=6

So the box weighs 6 kg

Graphs allow us to show that the following is true: D. Both plans will be costing the same when 50 texts are sent is accurate.

The graph is just a organised representation of the data. It helps in our understanding of the data. The numerical information gathered through observation is referred to as data.

The answer is that both plans are same in price when 50 texts are sent because both lines intersect at a cost of $22.5 for 50 texts, indicating that they are equal in price.

The other options are not right:

A-plan Hiroto's costs more than Emilia's plan when more than 50 messages are sent. This is untrue, as you can see from the graph that Emilia's line is higher after 50 texts, indicating that her plan is more expensive.

B-When 22 messages are sent, the cost of both plans is the same. This is false because when 22 texts are sent, the lines do not cross at the same spot.

C-When more than 22 SMS are sent, Emilia's is more expensive than Hiroto's plan. This is untrue because Hiroto's plan is more expensive until they send 50 messages, which is the only time they cost the same. At that moment, Emilia's plan costs about $15.5 and Hiroto's plan costs about $21.

To know more about graphs, visit:

https://brainly.com/question/17267403

#SPJ1

The complete question is:

Hiroto's texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia's plan costs  $10 per month and $0.25 per text. Using the graph below,  which statement is true?

A. Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.

B. Both plans cost the same when 22 texts are sent.

C. Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.

D. Both plans cost the same when 50 texts are sent.

We get the equation as : 5y + 70 = 395 if  the computer for 5 hours and charged her $70 for parts. The total was $395.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's use the variable "y" to represent the cost of labor per hour.

The technician worked on the computer for 5 hours, so the cost of labor would be 5y. Additionally, the technician charged $70 for parts. The total cost was $395. We can set up the following equation to represent the context:

5y + 70 = 395

This equation represents the total cost Sadie paid for the repair, which includes the cost of labor and parts.

Alternatively, we can use a tape diagram to represent the context. We can draw a rectangle and divide it into two parts, one representing the cost of labor and the other representing the cost of parts. The length of the labor part would be Five times the cost per hour (5y), and the length of the parts part would be $70.

]The length of the whole rectangle would represent the total cost ($395). We can label the unknown cost per hour as "y".

Therefore, we get the equation as : 5y + 70 = 395 if  the computer for 5 hours and charged her $70 for parts. The total was $395.

To learn more about Algebraic expression from given link.

brainly.com/question/953809

#SPJ1

The area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.

What is polygon?

A polygon is a two-dimensional geometric shape that is made up of straight lines connecting a sequence of points, which are called vertices.

To find the area of a regular polygon with 12 sides and a radius of 4 units, we can use the formula:

Area = (1/2) * perimeter * apothem

The perimeter of the polygon can be found by multiplying the number of sides by the length of each side. Since the polygon is regular, all sides are of equal length. Let's call this length "s".

s = 2 * r * sin(π/n) where r is the radius and n is the number of sides

s = 2 * 4 * sin(π/12)

s = 1.38 (rounded to two decimal places)

The perimeter of the polygon is:

P = 12 * s

P = 16.56 (rounded to two decimal places)

To find the apothem, we can use the formula:

apothem = r * cos(π/n)

apothem = 4 * cos(π/12)

apothem = 3.77 (rounded to two decimal places)

Now we can calculate the area of the polygon:

Area = (1/2) * P * apothem

Area = (1/2) * 16.56 * 3.77

Area = 31.28 square units (rounded to two decimal places)

Therefore, the area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.

To learn more about polygons from the given link:

https://brainly.com/question/24464711

#SPJ1

Answer:

52 miles

Step-by-step explanation:

Matthew runs 20 miles in the first week. We want to increase this number by 4 each week. For this question we will use m for a variable for miles.

This will look like

20 + 4m = total miles ran

if he ran 8 miles, we will enter this number into the variable m.

20 + 4 × 8 = 52

The total miles Matthew ran was 52 miles after 8 weeks.

The growth rate given by value of dR / dc at C = 2 is 0.0021 (approx).

The given formula is, R(C) = 1.35c / (0.29 + c)

=> R(C) = 1.35c / 0.29 + 1.35c / c

Take the derivative of R with respect to c: R(C) = 1.35c / 0.29 + 1.35c / c

Differentiating with respect to c, dR / dc = 1.35(0.29 + c) - 1.35c / (0.29 + c)2dR / dc

= 1.35(0.29 + c - c) / (0.29 + c)2dR / dc

= 1.35(0.29) / (0.29 + c)2

At C = 2,dR / dc = 1.35(0.29) / (0.29 + 2)2= 0.002129

A bacterial growth rate is given by the equation R(C) = 1.35c / (0.29 + c).

We know that R(C) = 1.35c / (0.29 + c) dR / dc = 1.35(0.29 + c - c) / (0.29 + c)2dR / dc = 1.35(0.29) / (0.29 + c)2dR / dc = 1.35(0.29) / (0.29 + 2)2dR / dc = 0.002129

To know more about growth rates, refer here:

https://brainly.com/question/13870574#

#SPJ11

Answer: y=28

Step-by-step explanation:

The coordinates of the foci of the ellipse given by 4x² + y² = 64 are (0, 0).

To find the coordinates of the foci of the ellipse given by the equation 4x² + y² = 64, we can compare it to the standard form of an ellipse:

(x²/a²) + (y²/b²) = 1

In this case, the equation 4x² + y² = 64 can be rewritten as:

x²/(8²) + y²/(8²) = 1

Comparing the equation to the standard form, we find that a = 8 and b = 8. The foci of the ellipse can be calculated using the formula:

c = sqrt(a² - b²)

For our ellipse, c = sqrt(8² - 8²) = sqrt(64 - 64) = 0.

Since c = 0, the foci coincide with the center of the ellipse. Thus, the coordinates of the foci are the same as the center of the ellipse.

Therefore, the coordinates of the foci of the ellipse given by 4x² + y² = 64 are (0, 0).

For more details of coordinates of the foci:

https://brainly.com/question/29089916

#SPJ2

Answer:

Step-by-,step explanation:

s.,s

Suki spent a total of $17 on rides, food, and parking at the carnival.

The problem states that Suki took $20 to the carnival and spent some portion of it on rides, food, and parking. The first step is to figure out what fractions of her money she spent on each of these things.

The problem tells us that she spent one half of her money on rides, 1/4 of her money on food, and 1/10 of her money on parking. We can write this mathematically and use the multiplication :

Suki spent 1/2 x $20 = $10 on rides

Suki spent 1/4 x $20 = $5 on food

Suki spent 1/10 x $20 = $2 on parking

To find the total amount that Suki spent on rides, food, and parking combined, we simply add up these three amounts:

Total spent = $10 + $5 + $2 = $17

Learn more about multiplication here

brainly.com/question/30391645

#SPJ4

The answer is 0.68.b) To find the probability that a randomly selected worker is married but not a college graduate, we need to subtract the probability that the person is married and a college graduate from the probability that the person is married.

The probability that a randomly selected worker is neither married nor a college graduate is the complement of the probability that they are either married or a college graduate. The equation for the complement is 1 - P(A).1 - (0.59 + 0.39 - 0.2)1 - (0.78 - 0.2)0.22. The answer is 0.68.b) To find the probability that a randomly selected worker is married but not a college graduate, we need to subtract the probability that the person is married and a college graduate from the probability that the person is married. The equation is P(A ∩ B) = P(A) × P(B|A).0.591 - 0.196 = 0.394.The answer is 0.394.c) To find the probability that a randomly selected worker is either married or a college graduate, we can use the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B).0.59 + 0.39 - 0.196 = 0.784.The answer is 0.784.

Learn more about Probability

brainly.com/question/11234923

#SPJ11

Shandra has cοllected apprοximately 93.67 grams οf the trace element.

The amοunt οf trace element refers tο the tοtal quantity οr mass οf a particular substance οr element that is present in a given sample οr substance. Tο find the amοunt οf trace elements, we can use the fοrmula:

       Amοunt οf trace element = cοncentratiοn × vοlume

where the cοncentratiοn is the amοunt οf the trace element per unit vοlume, and the vοlume is the tοtal vοlume οf the sample.

Here we have

A water sample shοws 0. 066 grams οf sοme trace element fοr every cubic centimeter οf water.

Shandra uses a cοntainer in the shape οf a right cylinder with a radius οf 5. 7 cm and a height οf 13. 9 cm tο cοllect a secοnd sample

As we knοw the vοlume οf a right cylinder, V = πr²h

Substituting the given values, we get:

V = π(5.7 cm)²(13.9 cm)

V = 1419.34 cm³

Since the cοncentratiοn οf the trace element is 0.066 g/cm³,

Find the number οf trace elements in the sample by multiplying the vοlume οf the sample by the cοncentratiοn:

Amοunt οf trace element = cοncentratiοn × vοlume

Amοunt οf trace element = 0.066 g/cm³ × 1419.34 cm³

Amοunt οf trace element = 93.67 g

Therefοre,

Shandra has cοllected apprοximately 93.67 grams οf the trace element.

Learn more about Amount of trace element

https://brainly.com/question/29229935  

#SPJ1

On average, slightly more dogs attended the Level 2 class than the Level 1 class.The mean number of dogs attending the Level 1 class was 7.92, and the mean number of dogs attending the Level 2 class was 9.48.

The box plots provided show the results of Julia's two dog training classes. The Level 1 class helps dogs learn the basics, while the Level 2 class focuses on more advanced commands. From the box plots, we can see that the Level 1 class was attended more consistently than the Level 2 class, with the majority of classes having between 5 and 10 dogs attending. The Level 2 class, on the other hand, had more variability in attendance, with some classes having up to 18 dogs and other classes having as few as 3. The median number of dogs attending the Level 1 class was 8, while the median number of dogs attending the Level 2 class was 10. The mean number of dogs attending the Level 1 class was 7.92, and the mean number of dogs attending the Level 2 class was 9.48. This indicates that, on average, slightly more dogs attended the Level 2 class than the Level 1 class.

Learn more about average here:

https://brainly.com/question/30873037

#SPJ4

50 dozen donuts should be produced before your average cost per dozen drops to $2.45

Let x be the number of dozen donuts produced.

The total cost to produce x dozen donuts is:

Total cost = cost of raw materials + overhead costs

Total cost = 0.65x + 0.55x

Total cost = 1.20x

The average cost per dozen can be expressed as:

Average cost per dozen = Total cost / number of dozens

2.45 = 1.20x / x

To solve for x, we can cross-multiply and simplify:

2.45x = 1.20x

x = 50

Therefore, you must produce 50 dozen donuts before your average cost per dozen drops to $2.45.

To know more about dozen click here:

brainly.com/question/22813421

#SPJ4

The coordinates of the reflected quadrilateral A'B'C'D can be determined by reflecting the coordinates of the original quadrilateral ABCD across the x-axis.

A reflection across the x-axis is a transformation that flips an object across the line x = 0. This means that the points in the object will be reflected across the x-axis. The coordinates of the reflected quadrilateral A'B'C'D can be determined by reflecting the coordinates of the original quadrilateral ABCD across the x-axis .Let us consider the original quadrilateral, ABCD, with coordinates A(x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4). Then, the coordinates of the reflected quadrilateral A'B'C'D are A'(-x1, y1), B'(-x2, y2), C'(-x3, y3) and D'(-x4, y4).For example, if the coordinates of quadrilateral ABCD are A(3, 5), B(7, 6), C(4, 8) and D(9, 2), then the coordinates of the reflected quadrilateral A'B'C'D will be A'(-3, 5), B'(-7, 6), C'(-4, 8) and D'(-9, 2).Therefore, the coordinates of the reflected quadrilateral A'B'C'D can be determined by reflecting the coordinates of the original quadrilateral ABCD across the x-axis.

Learn more about quadrilateral here

https://brainly.com/question/13805601

#SPJ4

Answer:

? is equal to 8

Step-by-step explanation:

16/20= 0.8

0.8x10= 8

8/10=0.8

OR YOU COUPLE DIVIDED 16 BY TO AND 20 BY 2

Answer:8/10

Step-by-step explanation:when you divide 16 by 20, you get 0.8. So turn 0.8 into a fraction with 10, you get 8/10. (I’m not that smart, mb if I get something wrong.)

The square form of the given equation as per quadratic equation is: x²=7.

What is the quadratic equation?

A quadratic equation is an equation where the variable has the highest degree of 2.

Given equation:

⇒ [tex]3x^{2} -12 =9[/tex]

⇒ [tex]3x^{2} -12 -9=0[/tex]

⇒ [tex]3x^{2} -21 =0[/tex]

⇒ [tex]3x^{2} =21[/tex]

⇒  [tex]x^{2} =7[/tex]

Therefore, the square form of the given equation is x² = 7

To know more about quadratic equation, visit:

brainly.com/question/12279188

#SPJ9

The religious make-up of the United States Congress is reflective of that in the general population.

Answer:Yes, the religious make-up of the United States Congress is reflective of that in the general population.The steps to test whether the distribution of religion among U.S. adults differs significantly from that among the 114th U.S. Congress with an α = 0.01 level of significance are given below:First, calculate the expected frequencies for Mormon and Unaffiliated using the formula:Expected frequency = (total sample size) x (proportion)Expected frequency of Mormons = (1500) x (0.030) = 45Expected frequency of Unaffiliated = (1500) x (0.019) = 28.5Next, calculate the chi-square statistic using the formula:Chi-square = ∑ [(observed frequency - expected frequency)² / expected frequency]To find the observed frequency - check the frequency table below.Religion Frequency Expected Contribution Protestant 772 858.0 8.620 Catholic 368 460.5 18.580 Mormon 34 45.0 8.690 Orthodox 12 13.5 0.167 Jewish 46 78.0 13.128 Other 61 16.5 120.015 Unaffiliated 207 28.5 149.969The degrees of freedom for the chi-square test = (number of categories - 1) = 7 - 1 = 6Finally, compare the calculated chi-square statistic with the critical value from the chi-square distribution table with 6 degrees of freedom at α = 0.01 level of significance. If the calculated chi-square statistic is greater than the critical value, then the null hypothesis is rejected and we conclude that the distribution of religion among U.S. adults is significantly different from that among the 114th U.S. Congress. If the calculated chi-square statistic is less than or equal to the critical value, then the null hypothesis is accepted, and we conclude that the distribution of religion among U.S. adults does not differ significantly from that among the 114th U.S. Congress.

Learn more about Religious

brainly.com/question/305333

#SPJ4

If a normal distribution has mean of 57 and standard deviation as 20, then the z-score for x=50 is -0.35 .

In order to find the z-score for x=50, we can use the formula : z = (x-μ)/σ ;

Where x is = 50, "μ" is = mean of the distribution , and "σ" is = standard deviation of the distribution ;

In this case , x = 50 , mean(μ) = 57 and standard deviation(σ) = 20;

Substituting in the values,

We get,

⇒ z = (50-57)/20,

Simplifying, We get,

⇒ z = -0.35

So, the z-score for x=50 is -0.35.

Interpretation of the z-score is that :

The z-score represents the number of standard deviations that a given value (in this case, x=50) is from the mean of the distribution (μ=57).

A negative z-score means that the value is below mean. In this case, x=50 is 0.35 standard deviations below the mean of 57.

Learn more about Standard Deviation here

https://brainly.com/question/15904637

#SPJ4

The given question is incomplete, the complete question is

A normal distribution has mean of 57 and standard deviation as 20. Find and interpret the z-score for x=50.