Which equation represents the line that passes through the point (9,4) and is perpendicular to the graph of 5x+y=30?

The percentage of students that like country are in grades 9-10 will be 61%. The Option D.

In order to get percentage of students that like country and are also in grades 9-10, we must look at the intersection of the "Country" row and the "Grades 9-10" column which has a frequency of 55.

After that, we will divide the frequency by the total number of students that like country which is (90).

The percentage of students that like country are in grades 9-10 will be:

= (55/90) x 100

= 0.61111111111 * 100

= 61%

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The value of the test statistic is t = -2.15.

To test whether the manufacturer's claim of 31.3 mpg is accurate, we can use a one-sample t-test. The null hypothesis is that the true mean mpg of the van is equal to the manufacturer's claim of 31.3 mpg, while the alternative hypothesis is that the true mean mpg is different from 31.3 mpg.

The test statistic for a one-sample t-test is calculated as

t = (x - μ) / (s / √(n))

where x is the sample mean, μ is the hypothesized population mean (31.3 mpg), s is the known standard deviation, and n is the sample size.

Plugging in the values given in the problem, we get:

t = (31.1 - 31.3) / (1.3 / √(140))

t = -0.2 / (1.1 / 11.83)

t = -0.2 × 10.75

t = -2.15

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Answer:

Step-by-step explanation:

We are given with a triangle whose Height is 2 cm and base is 9 cm.

We have to calculate the Area of triangle.

As we know that area of triangle is calculated by,

Area = ½ × base × height

Putting the required values we get,

Area = 1/2 × 2 × 9 (cancel 2 with 2)

Area = 9 cm².

Hence, The area of the triangle is 9 cm².

Answer:

Step-by-step explanation:

4.2

12/(x+5) = 15

We can start by cross-multiplying:

12 = 15(x+5)

Then, we can distribute the 15:

12 = 15x + 75

Next, we can subtract 75 from both sides:

-63 = 15x

Finally, we can divide both sides by 15:

x = -63/15

Therefore, x = -4.2.

Answer:

C

Step-by-step explanation:

If 2 angles are 60, that means the 3rd angle is also 60 because all of the angles of triangle need to add up to 180

The given angles add up to 120 so we subtract 120 from 180, giving us 60

Since all 3 angles are equivalent, the answer is C

Answer: C.

Step-by-step explanation:

60+60=120. Therefore, since a triangle's have to sum to 180 degrees, the last angle is 180-120=60. Since all angles are equal it is an equiangular triangle.

Answer:

b = 5, a = 10.

Step-by-step explanation:

sin 60 = 5√3 / a

√3/2 =  5√3 / a

a =   5√3 / √3/2

  =   5√3 * 2/ √3

  =  10

By pythagoras:

10^2 =   (5√3)^ 2 + b^2

100 = 75 + b^2

b^2 = 25

b = 5

Answer:

To factor the expression 12x^2 - 8x - 15 by grouping, we need to rewrite it as a sum of two terms, each of which has a common factor. One possible way to do this is:

12x^2 - 8x - 15 = (4x - 5)(3x + 3)

To check if this is correct, we can use the distributive property to expand the product (4x - 5)(3x + 3), which gives:

(4x - 5)(3x + 3) = 12x^2 + 2x - 15

We can see that this is equivalent to the original expression 12x^2 - 8x - 15, so the factoring is correct.

To obtain this factored form by grouping, we can group the first two terms and the last two terms of the expression:

12x^2 - 8x - 15 = (12x^2 - 18x) + (10x - 15)

We can then factor out the GCF from each group:

12x^2 - 8x - 15 = 6x(2x - 3) + 5(2x - 3)

Notice that the terms 6x and 5 have a common factor of (2x - 3). Factoring out this common factor, we get:

12x^2 - 8x - 15 = (2x - 3)(6x + 5)

Therefore, the expanded form of 12x^2 - 8x - 15 that can be used to factor the expression by grouping is:

(2x - 3)(6x + 5)

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To maximize the probability of selecting a black ball if one ball is chosen at random from one of two buckets containing 50 black and 50 white balls, all 50 black balls should be put in one bucket and the other bucket should contain 49 white balls and 1 black ball.

To maximize the probability of selecting a black ball, you need to ensure that there are more black balls in one of the buckets than in the other.

Here's one possible way to divide the balls

Put all 50 black balls in one bucket (Bucket A).

Put 49 white balls and 1 black ball in the other bucket (Bucket B).

With this arrangement, Bucket A has a 100% chance of yielding a black ball if a ball is chosen at random, and Bucket B has a slightly less than 50% chance of yielding a black ball (specifically, a 1/50 chance, since there is only 1 black ball among the 50 balls in that bucket).

Therefore, the overall probability of selecting a black ball from one of the two buckets is maximized using this arrangement.

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Answer: The function that is NOT increasing for all values of x is A. f(x) = x^2

Answer:

Darcy can choose 1 pair of earrings out of 16, 1 bracelet out of 11, and 1 ring out of 9. The number of possible combinations is the product of these choices:

16 * 11 * 9 = 1,584

Therefore, Darcy could buy 1,584 different combinations of 1 pair of earrings, 1 bracelet, and 1 ring.

The congruency theorem that would match the triangles shown is AAS. Option B

The Angle-Angle-Side (AAS) congruence theorem states that two angles and one side of one triangle must match two angles and one side of another triangle in order for two triangles to be considered congruent.

To put it another way, two triangles are said to be congruent if their included sides (the sides between the two angles) and their two neighboring angles are both identical.

Thus looking at the triangles we can see that two angles and one side are the same for the both triangles.

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The value of the digit 4 in 46,278 is 4000/400 = 10 times the value of the digit 4 in 24,350.

To calculate the value of a digit in a number, you need to determine its place value. In 46,278, the digit 4 is in the thousands place, which means its value is 4 x 1000 = 4000. In 24,350, the digit 4 is in the hundreds place, which means its value is 4 x 100 = 400.

To find how many times the value of the digit 4 in 24,350 is contained in the value of the digit 4 in 46,278, we simply divide 4000 by 400, which gives us 10. Therefore, the value of the digit 4 in 46,278 is 10 times the value of the digit 4 in 24,350.

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b) 'The probability of success remains the same from trial to trial' is true for a binomial distribution.

A binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where the probability of success remains constant from trial to trial.

The Poisson distribution, on the other hand, is a discrete probability distribution that describes the number of events occurring in a fixed interval of time or space, where the events are rare and random, and the mean number of events per interval is constant.

The number of possible outcomes in a binomial distribution depends on the number of trials and the number of possible outcomes in each trial, and there is no specific requirement for a minimum number of outcomes.

The value of T is not relevant or defined in the context of a binomial distribution.

Correct Question :

Which is true for a binomial distribution?

a) It approximates the Poisson distribution

b) The probability of success remains the same from trial to trial

c) There are ten or more possible outcomes

d) The value of T Is equal to 1.50,

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Answer:

D

Step-by-step explanation:

The answer is D

To find this answer you find the need to find the equation of the lines. The equation of the first line is [tex]-\frac{5}{2} + 40[/tex] . I found this because I looked at the rise/run or how much the graph is moving up or down. In this graph, it is moving down by 1. But the graph is incremented by 5 so the rise is 5. Next, the graph is moving left by 2 so the slope is -5/2. The y-intercept is 40 because it is the place where the line hits the y-axis.

The next equation for the line is repeating the same steps and you get [tex]-\frac{5}{3}+15[/tex].  

The next part would be the solution of the lines. The solution is where the two lines intersect. The lines intersect at (6, 25). Only answer D has all these parts correct.

Answer: P = 1800 + 60n

$3240

Step-by-step explanation:

her pay (P) would start at 1800, and she would gain 60 dollars for every copy (N) she sells.

Draw the conclusion that there is insufficient evidence to support a relationship between gender and World Series viewing based on the findings of the chi-square test.

Use a chi-square test of independence to evaluate whether gender and World Series viewership are independent variables.

Let's begin by calculating the predicted frequencies for each cell based on the supposition that gender and World Series viewing are unrelated. The formula is as follows:

Expected frequency = (row total  x column total) / grand total

Expected frequencies table:

Male | 60.5 60.5 121

Female | 39.5 39.5 79

Total | 100 100 200

Next, we can calculate the chi-square test statistic using the formula:

χ² = Σ (observed frequency - expected frequency)2 / expected frequency

where the sum is taken over all cells in the table.

Calculating the chi-square test statistic:

χ² = ((57 - 60.5)2 / 60.5) + ((64 - 60.5)2 / 60.5) + ((43 - 39.5)2 / 39.5) + ((36 - 39.5)2 / 39.5)

= 0.36 + 0.36 + 0.36 + 0.36

= 1.44

Finally, we need to compare the calculated chi-square value with the critical value from the chi-square distribution with (rows - 1) x (columns -

1) degrees of freedom at a chosen level of significance. For a 2x2 contingency table, the degrees of freedom are (2-1) x (2-1) = 1.

The critical value is 3.84 at a 5% level of significance and one degree of freedom. We fail to reject the null hypothesis that gender and viewing the World Series are independent since our calculated chi-square value of 1.44 is lower than the crucial value of 3.84.

Therefore, We can draw the conclusion that there is insufficient evidence to support a relationship between gender and World Series viewing based on the findings of the chi-square test.

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Answer:

x+16=y

Step-by-step explanation:

[tex]x=y-16\\x+16=y[/tex]

(b) and (c) are correct

value of sin 55 = cos 55

sin 72 = cos 18

Paul will earn $1,500 after 30 days of work.

A work wages means the fixed regular payment earned for work or services which is typically paid on a daily or weekly basis.

To find out how much Paul will earn after 30 days, we wlll multiply his daily earnings by the number of days he works which gives us:

= $50/day x 30 days

= $1500.

Full question "Let assume Paul earns $50 every days. At that rate, how much will Paul earn after 30 days?".

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Answer:

In parallelogram PSQSR, Pq represents the length of the side PQ.

Since PSQR is a parallelogram, opposite sides are equal in length. Therefore, Pq is equal in length to the side SR, which is opposite to Pq in the parallelogram.

So, if the length of SR is given, then Pq is also equal to that length. If the length of SR is not given, then Pq cannot be determined.

Step-by-step explanation:

(c) 336, After being struck with a hammer, a gong vibrates 48 vibrations in the first second.

In each second thereafter, it makes 6/7 as many vibrations as in the previous second. To find the total number of vibrations the gong makes before it stops vibrating, you can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r), where 'a' is the first term and 'r' is the common ratio.

In this case, a = 48 (vibrations in the first second) and r = 6/7 (the fraction of vibrations in each subsequent second).

Sum = 48 / (1 - (6/7))
Sum = 48 / (1/7)
Sum = 48 * 7
Sum = 336

So, the gong makes 336 vibrations before it stops vibrating. The correct answer is (c) 336.

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The value of the x in the given octagon is 26.

Given is regular polygon with 8 sides, we need to find the measure of the x,

Since, the polygon is 8-sided therefore, it is an octagon,

The sum of the interior angles of a polygon =

= (number of sides - 2) × 180°

= (8-2) × 180°

= 6 × 180°

= 1080°

Therefore, one angle = 1080° / 8 = 135°

Therefore,

135° = 6x-21

135°+21 = 6x

6x = 156

x = 26

Hence, the value of the x in the given octagon is 26.

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Answer: it’s -0,6 which is C

Step-by-step explanation:

The length of the midsegment x is given as follows:

x = 9.

The value of x for this problem are obtained considering the triangle midsegment theorem, which states that the midsegment of the triangle has a length that is equals to half the length of the base of the triangle.

The length of the base of the triangle in this problem is given as follows:

18 units.

Hence the length of the midsegment x is given as follows:

x = 0.5 x 18.

x = 9 units.

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Answer: 5/12

Step-by-step explanation:

2/3 - 1/4

Find equivalent fractions that have the same denominator.

2/3 is the same as 8/12

1/4 is the same as 3/12

8/12 - 3/12 = 5/12

5/12

Answer:

See explanation

Step-by-step explanation:

Combine terms into a single fraction

-1/2 (-3x/2 + 6x + 1) - 3x

Find common denominator

-1/2 (-3x/2 + 2⋅6x / 2 + 2/2) - 3x

Multiply the numbers

-1/2 (-3x/2 + 12x / 2 + 2/2) - 3x

Combine like terms

-1/2 (9x + 2/2) - 3x

Distribute

-9x-2 / 2 ⋅ 2 - 3x

Multiply

-9x-2 / 4 - 3x

Solution

-21x-2 / 4

If an equation is expressed in vertex form, then the vertex can be found by simply reading off the values of the constants h and k. Specifically, the vertex is located at the point (h, k).

To find the axis of symmetry, you can use the equation of symmetry, which is x = h. This represents a vertical line that passes through the vertex and divides the parabola into two symmetric halves.

Answer:

Step-by-step explanation:

The formula is

y=a(x-h)+k

(h,k) is your vertex

h is inside with x, key is to take opposite sign

k is outside so take as is

EX 1.

y=2(x-4)+3

vertex (4, 3)

EX 2.

y=3(x+8)-2

vertex(-8,-2)

For, axis of symmetry, that's where you can fold it in half that happens at your vertex but to describe the line of axis of symmetry that comes from your x value in your vertex

so for

EX1.

x=4   is your axis of symmetry , just take your x value of vertex

EX2

x= -8 for axis of symmetry

The x-intercept is 5.5 and the y-intercept is -7.5 for the given line.

The point on a graph where a line or curve meets the y-axis or x-axis is referred to as an intercept in mathematics and statistics. It also goes by the names y-intercept and x-intercept.

The intercept is the value of y when x is 0 in a linear equation of the form y = mx + b. When the independent variable (x) is zero, the value of y is represented by the intercept term (b). Similarly, the x-intercept indicates the value of x when y is zero, and the constant term (a) reflects the value of x when the dependent variable (y) is zero in an equation of type x = a + by.

The x-axis is cut at point 5.5 by the straight line and the y-axis is cut by the line at -7.5.

Therefore, the x-intercept is 5.5 and the y-intercept is -7.5.

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