Find the size of angle x.
Give your answer in degrees (°).
41°
77°
x
Watch video
36°
Not drawn accurately

The nth term of the given quadratic sequence is expressed as; aₙ = 2n²

To find the nth term, we have to find the relation between the given terms.

Here we see that;

1st term = 2 = 2 × 1 × 1 = 2 × 1²

2nd term = 8 = 2 × 2 × 2 = 2 × 2²

3rd term = 18 = 2 × 3 × 3 = 2 × 3²

4th term = 32 = 2 × 4 × 4 = 2 × 4²

5th term = 2 × 5² = 2 × 50 = 100

Thus, we clearly see a pattern that can represent the nth term as;

aₙ = 2 × n²

aₙ = 2n²

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The parabola's shape is influenced by the separation between its focus and vertex. The parabola becomes wider as the vertex is focused further away (flatter).

A parabola is a plane curve created when a point moves in such a way that the distance it travels from a fixed point to a fixed line. The parabola's directrix serves as the fixed line, while the focus, represented by the letter F, serves as the fixed point. The line through the F and perpendicular to the directrix is the parabola's axis.

2. As illustrated here, the parabola's shape is influenced by the separation between its focus and vertex.

The parabola becomes wider as the vertex is focused further away (flatter).

The parabola becomes thinner as the vertex comes into focus (steeper).

3. If a > 0 in the quadratic equation the parabola opens upward and if a< 0 then the parabola opens downward.

4. The vertex of the parabola is the location where it crosses the axis.

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Answer:

13 months

Step-by-step explanation:

(b)

let C(x) = 431.5 and solve for x , that is

29x + 54.5 = 431.5 ( subtract 54.5 from both sides )

29x = 377 ( divide both sides by 29 )

x = 13

that is cable service for 13 months

If  a petrol station wants to make 100% profit. the cost of fuel per litre at this petrol station is 1.4 pence.

Given, the formula to calculate the cost of fuel per litre:

(1 + 100) X + X 160 C = cost of oil per barrel.

Where :

X = cost of oil per litre

C= rate of fuel duty tax in %.

We know that fuel duty is 50% and oil costs £128 per barrel, so we can substitute these values into the equation:

(1 + 100) X + X 160 * 0.5 = 128

Expanding the equation:

100 X + 80 X = 128

180 X = 128

Dividing both sides by 180:

X = 128/180 = 7/10 = 0.7

So, the cost of oil per litre is 0.7 pence.

The petrol station wants to make 100% profit, so we add the profit to the cost of oil per litre:

0.7 + 0.7 * (100/100) = 1.4 pence

Therefore, the cost of fuel per litre at this petrol station is 1.4 pence.

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Answer:

you cannot cancel (5-5) because it is multiplied to 5 and 4 if the question was 5+(5-5)=4+(5-5) you can cancel 5-5

The reason that we can't cancel out the (5 - 5) is because it is attached to different numbers and as such they must be multiplied first with distributive property.

According to the distributive property of algebra, multiplying the sum of two or more addends by a number will give us the same result as when each addend is multiplied individually by the number and the products are added together.

This also applies to addition as well.

We are given;

5(5 - 5) = 4(5 - 5)

Now, according to the distributive property, we will have to first multiply out the bracket to get a solution. Thus, we can't cancel out the (5 - 5) because it is attached to different numbers and as such they must be multiplied first with distributive property in mind.

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Answer:jjj

Step-by-step explanation:because

On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

[tex]A^2 = B^2 + C^2[/tex]

AC = [tex]\sqrt{14^2 - 9^2}[/tex]

AC  = [tex]\sqrt{196 - 81}[/tex]

AC = [tex]\sqrt{115}[/tex]

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The exponential equation in the form y= a[tex](b)^x[/tex] that can model is y= 500[tex](1.06)^x[/tex].

In mathematics, an exponential function is a relationship of the type

y = [tex]a^x[/tex], where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

Given:

Britney invested $500 in stocks.

After one year, the value of her stocks has increased to $530.

We know the Exponential Function y= a[tex](b)^x[/tex]

As, a= 500, y= 530, x= 1

So, y= a[tex](b)^x[/tex]

530 = 500 [tex](b)^1[/tex]

530 / 500 = b

b= 1.06

So, the exponential equation is y= 500[tex](1.06)^x[/tex]

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The total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.

The formula for calculating the number of unique ways to form three groups comprising of 3, 3, and 2 students is given by:

Number of ways = Number of ways to select 3 first-year students from 5 first-year students x Number of ways to select 3 second-year students from 3 second-year students x Number of ways to select 2 students from 8 students

=[tex]5C3 x 3C3 x 8C2[/tex]

= 10 x 1 x 28

= 280

Therefore, there are 280 unique ways to form three groups comprising 3, 3, and 2 students. This can be seen by considering the total number of possible arrangements of the 8 students into 3 groups of 3, 3 and 2. First, we need to select 3 students from 5 first-year students in 5C3 ways, which is equal to 10. Second, we need to select 3 students from 3 second-year students in 3C3 ways, which is equal to 1. Finally, we need to select 2 students from 8 students in 8C2 ways, which is equal to 28. Therefore, the total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.

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The probability of exactly 5 patients having kidney-related problems is approximately 0.253 or 25.3%.

The probability of a given number of patients having kidney-related problems can be found using the binomial distribution. The binomial distribution models the number of successful outcomes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, each hospital admission is a trial, and the probability of success (having a kidney-related problem) is 0.3 (30%). The number of trials is 10, and we want to find the probability of exactly 5 patients having kidney-related problems.

We can use the formula for the probability mass function of the binomial distribution to find this:

[tex]P(X = k) = (n choose k) * p^k * (1-p)^(n-k)[/tex]

where:

n = 10 (number of trials)

k = 5 (number of successful outcomes)

p = 0.3 (probability of success)

Using the formula, we have:

[tex]P(X = 5) = (10 choose 5) * 0.3^5 * (1-0.3)^(10-5)= 252 * 0.3^5 * 0.7^5[/tex]

= approximately 0.253

So, the probability of exactly 5 patients having kidney-related problems is approximately 0.253 or 25.3%.

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Thirty percent of hospital admissions for diabetic patents are related to problems with the kidneys. in a sample of 10 diabetic hospital admissions, what is the probability that exactly five patients will have kidney related problems?

The value of the number 88 in the ratio of 1:7 will be 11:77.

The ratio is defined as the division of the numbers into two parts according to the requirements. The ratio generally compares one value is how many times the other value.

Given that the £88 is distributed in the ratio of 1:7. The distributed form of the number will be calculated as:-

x + 7x = 88

8x = 88

x = 11

The two values will be,

x = £11

7x = 7 x 11

7x =£77

Therefore, the value of the number 88 in the 1:7 ratio is 11:77.

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Answer:

a. 0.81

b. 0.81

Step-by-step explanation:

Let's assume that the player makes x% of his free throws. Then, the probability that he will make both free throws is (x/100)^2, and he will make at least one free throw is 1 - (1 - x/100)^2.

So if he makes 90% of his free throws, then:

a. The probability that he will make both free throws is (90/100)^2 = 0.81.

b. The probability that he will make at least one free throw is 1 - (1 - 90/100)^2 = 1 - (1 - 0.9)^2 = 1 - 0.19 = 0.81.

The answers to the questions rounded to 4 decimal places are:

a. 0.81

b. 0.81

Answer:

2.57 square meters

Step-by-step explanation:

r = Radius of circle

Area of shaded region = Area of semi-circle:

[tex]= \frac{1}{2}(\pi r^{2})[/tex]

= [tex]\frac{\pi}{2} r^{2}[/tex]

= [tex]\frac{\pi }{2} (1.28m)^{2}[/tex]

= 2.57 [tex]m^{2}[/tex] (Rounded to 2 decimal places)

Answer:

The price of the desk in the furniture store is $202.8

Answer:

2. More time spent on homework results in higher grades.

Step-by-step explanation:

The more time spent on homework pays off in higher grades. If this is incorrect my apologies.

More weight on one side of a balance scale will tip the scale in that direction is relationship is an example of causation.

Causation is the capacity of one variable to influence another.

Causation means that a change in one variable results in a change in another variable.

More weight on one side of a balance scale will tip the scale in that direction.

In this case, adding more weight to one side of the scale will directly cause it to tip in that direction.

There is a correlation between the variables, but it's not necessarily a direct cause-and-effect relationship.

The more education a person has, the more they read suggests that education and reading are correlated, but having more education doesn't necessarily cause a person to read more.

Hence,  More weight on one side of a balance scale will tip the scale in that direction is an example of causation.

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Answer:

The probability of choosing 2 girls from a list of 6 girls and 6 boys can be calculated using combinations.

The number of combinations of choosing 2 girls out of 6 girls is given by the formula: C(6,2) = 6! / (6-2)!2! = 15.

So, the probability of choosing 2 girls is 15 / (C(12,2) = 66) = 15/66 = 5/22.

Therefore, the probability of Mr. Mackinson choosing 2 girls to lead the class field trip is 5/22 or approximately 0.227.

Answer:

Shrub $7

Rose Bush $8

Step-by-step explanation:

First, write them as equations

10r + 4s = $108

5r + s = $47

Next, multiply

10r + 2s = $94

10r + 4s = $108

Then, Subtract

2s = $14

After, Divide

s = $7

Then, plug in and solve

5s + $7 = $47

$40/5s = 8$

$8 = r

$7 = s

Answer: The bushes cost $8 and the shrubs cost 7$

Step-by-step explanation:

For this question you must use system of equations, trial and error will take a very long time.

So yeah, here is how you solve it-

First set up equations (b represents the amount of bushes and s represents the amount of shrubs):

5b + 1s = 47

10b+4s=108

Next you can either solve via elimination or the substitution method. I will show elimination here. Elimination works by slightly modifying one of the equations so that it cancels when it is added to the other equation:

(I modified the first equation)

-4(5b+1s = 47) = -20b-4s=-188

(Then add)

     -20b-4s=-188

  +    10b+4s=108

This equals: -10b=-80

Next you just solve for b:

b=-80/-10

b=8

To then find s, plug b into one of the original equations and solve for s:

(I plugged it into the first equation)

5(8)+1s=47

40+s=47

s=7

So the bushes cost $8 and the shrubs cost 7$

Hope this helps :)

Answer:

b-value is the middle number hope that helps

Step-by-step explanation:

The b-value is the middle number, the number next to the x. The other letters, a and c, are also numbers like b. Each of these can be any number. In combination, they tell you what the quadratic function will look like when graphed

Answer: 7/10

Step-by-step explanation:

multiply 4/5 by 7/8=28/40 or 7/10

Answer: 1/3(6x-12)=2(x-2)

Step-by-step explanation:

The required, approximate volume of the sphere is 113.04 cubic inches.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.

If the radius of the sphere is 3 inches, we can substitute this value into the formula and use 3.14 to approximate π,

V = (4/3) x 3.14 x 3³

V = (4/3) x 3.14 x 27

V = 113.04 cubic inches

Therefore, the approximate volume of the sphere is 113.04 cubic inches.

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a) The probability that a hand will contain exactly 2 wild cards is 0.0246.

b) The probability of choosing a hand with seven yellow cards is 0.00056.

a) To find the probability that a hand will contain exactly 2 wild cards, we need to consider the number of ways we can choose 2 wild cards from 8 and the number of ways we can choose 5 non-wild cards from the remaining 100 cards. The total number of ways to choose 7 cards from 108 is:

C(108, 7) = 85,900,584

The number of ways to choose 2 wild cards from 8 is:

C(8, 2) = 28

The number of ways to choose 5 non-wild cards from the remaining 100 cards is:

C(100, 5) = 75,287,520

Therefore, the total number of ways to choose a hand with exactly 2 wild cards is:

28 * 75,287,520 = 2,108,196,160

The probability of choosing a hand with exactly 2 wild cards is:

2,108,196,160 / 85,900,584 ≈ 0.0246, or about 2.46%

b) To find the probability that a hand contains seven yellow cards, we need to calculate the number of ways we can choose 7 yellow cards from the 25 available, and divide this by the total number of ways to choose 7 cards from the 108 available. The number of ways to choose 7 yellow cards from 25 is:

C(25, 7) = 48,048

The total number of ways to choose 7 cards from 108 is:

C(108, 7) = 85,900,584

Therefore, the probability of choosing a hand with seven yellow cards is:

48,048 / 85,900,584 ≈ 0.00056, or about 0.056%

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The scale of the blueprint is 1 in : 4 ft.

A map scale is the relationship between a distance on a map and the corresponding distance on the earth.

Given that, on a blueprint of a house, the kitchen is 5 inches long, the actual kitchen is 20 feet long, we are asked to find the scale of the blueprint.

Since, the kitchen in the map is 5 in long whereas n earth it is 20 ft long.

Therefore, the ratio =

5 in / 20 ft = 1 in / 4 ft

Hence, the scale of the blueprint is 1 in : 4 ft.

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The amount of money an account with simple interest at an annual rate of 3% would be $750 after 5 years.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

Given that deposit amount is $5,000 in an account that earns simple interest at an annual rate of 3%.

Amount = $5,000

Rate = 3%

Time = 5 years

Therefore, Simple Interest = (Principal × Rate × Time) / 100

Simple Interest = 5,000 × 3% × 5

Simple Interest = 5,000 × 3/100 × 5

Simple Interest = 750

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To represent Brandon's total collection of quarters and dimes, let's use variables.

Let:

q be the number of quarters

d be the number of dimes

The following equations can be used to represent the given information:

The quarters and dimes are worth a total of $9.6:

0.25q + 0.10d = 9.6

The quantity of quarters is 348 less than 8 times that of dimes.

q = 8d - 348

To get a solution for one of the variables, we can use substitution. We may solve for d by substituting the expression for q from equation 2 into equation 1:

0.25q + 0.10d = 9.6

0.25(8d - 348) + 0.10d = 9.6 (substitute q = 8d - 348)

2d - 87 + 0.10d = 9.6

2.10d = 96.6

d = 46

Now that we know d = 46, we can use equation 2 to solve for q:

q = 8d - 348

q = 8(46) - 348

q = 16

Therefore, There are 46 dimes and 16 quarters in Brandon.

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The value of the ratio (new to original) of the perimeters as required in the task content is; 0.5.

The value of the ratio (new to original) of the perimeters as required in the task content is; 0.25.

Recall, a dilation of a point, (x, y) using a scale factor of k is; (kx, ky).

Also; for shapes A and B;

Perimeter (A) / Perimeter (B) = k.

Also, Area (A) / Area (B) = k².

On this note, since the dilation factor of the pre-image is 0.5, it follows that the ratio of the perimeters of the new to original is; 0.5.

Also, the ratio of the area of the new to original is; 0.5² = 0.25.

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The currect option is (b) H0: p = 0.5; Ha: p > 0.5

p represents the population proportion.

A null hypothesis is a statement from the population parameter which is either rejected or accepted (fail to reject) upon testing. It is expressed using the equality sign.

An alternate hypothesis is also a statement from the population parameter which negates the null hypothesis and is accepted if the null hypothesis is rejected. It is expressed using any of the inequality signs.

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. a commentator believes that more than half of all adults favor such a ban. the null and alternative hypotheses you would use to test this claim are

a) H0:p^=0.5;Ha:p^>0.5

(b) H0:p=0.5;Ha:p>0.5

(c) H0:p=0.5;Ha:p<0.5

(d) H0:p=0.5;Ha:p≠0.5

(e) H0:p>0.5;Ha:p=0.5

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On the z-table with a 90% confidence interval, the value 1.645 is called the critical value. The critical value is used to determine the boundary values for the confidence interval.  Correct option is A.

In a confidence interval, we use sample data to estimate the true population parameter with a certain degree of certainty or confidence. The critical value is determined based on the desired confidence level and the degrees of freedom (sample size - 1) of the distribution.

For example, if we want a 90% confidence interval, we use the z-table to find the critical value that corresponds to a probability of 0.05 in the tail of the distribution. The critical value represents the number of standard errors that correspond to the probability in the tail of the distribution.

Once we have determined the critical value, we can use it to find the margin of error for the confidence interval, which represents the range of values within which the true population parameter is likely to lie. The margin of error is calculated by multiplying the critical value by the standard error of the sample statistic.

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Complete question is:

On the z table with a 90% confidence interval, what is 1.645 called? group of answer choices

a. critical value

b. confidence interval

c. margin of error point

d. estimate

Answer:

x = y/(m + 3)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ xm = -3x + y

Then the value of x will be,

→ xm = -3x + y

→ xm + 3x = y

→ x(m) + x(3) = y

→ x(m + 3) = y

→ x = y/(m + 3)

Hence, value of x is y/(m + 3).