A line of best fit was drawn for 16 data points. What is the maximum number
of these data points that may not actually be on the line?
OA. 14
OB. 13
O C. 15
OD. 16

Answer:

A,C,E

(if you find a better answer choose that.)

Step-by-step explanation:

This one has two acute angles and one obtuse.

This one is a scalene.

So, tick A,C,E

Answer:

4/15

Step-by-step explanation:

in fractions, the number that goes on top is the dividend (the first number in the division problem) which is 4 in this case and the number that goes on the bottom of the fraction is the divisor, which is 15 in this case. therefore, the answer is 4/15.

The given sample data the Q3=61

We begin by ordering the data from smallest to largest.

Next, find the median of the data.

The data set has 8 values, so the two middle values are 52 and 55.

49 52 52 52 55 55 67 74

Median = (52 + 55) / 2

Median= 53.5

The third quartile (Q3) is the 25th percentile or the median of the upper half of the data.

To find the median of all the values that lie above 53.5.

Q3 = (55 + 67)/ 2

Therefore the Q3=61

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Answer:

-4

Step-by-step explanation:

The equation for slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

m: Slope

(6, 2) = [tex](x_1, y_1)[/tex]

(4, 10) = [tex](x_2, y_2)[/tex]

Substitute these values into the equation:

[tex]m=\frac{10-2}{4-6}=\frac{8}{-2}=-4[/tex]

Therefore the slope is -4.

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of the line that passes through the points? 2 points given

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The formula used here, is [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{\dfrac{10-2}{4-6}}[/tex] | subtract

[tex]\bf{\dfrac{8}{-2}}[/tex] | evaluate

[tex]\bf{-4}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

           [tex]\bf{=Slope\;-4}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Using the z-distribution, it is found that she should take a sample of 97 scores to ensure that the margin of error is below 20.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence by the Empirical Rule the standard deviation is given by:

[tex]6\sigma = 800 - 200[/tex]

[tex]\sigma = 100[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

To ensure a margin of error of 20, we solve for n when M = 20, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]20 = 1.96\frac{100}{\sqrt{n}}[/tex]

[tex]20\sqrt{n} = 1.96 \times 100[/tex]

[tex]\sqrt{n} = 1.96 \times 5[/tex]

[tex](\sqrt{n})^2 = (1.96 \times 5)^2[/tex]

n = 96.04.

Rounding up, she should take a sample of 97 scores to ensure that the margin of error is below 20.

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The point which lies on the graph of the given function is; Choice D; (0, 2).

The point which lies on the graph of the given function; y = 2*3^x is it's y-intercept. The y-intercept which corresponds to the value of y when variable X is set to zero.

Hence, y = 2*3^0;

y = 2 ×1 = 2.

Hence, the point is; (0,2).

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Answer:

[tex]\sf{$a)$} \ x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]

Step-by-step explanation:

Quadratic formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Quadratic equation: ax² + bx + c = 0, where a ≠ 0

Given: 3x² + 9x - 2 = 0

⇒ a = 3, b = 9, c = -2

Substitute the given values into the formula and simplify:

[tex]x=\dfrac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)}\\\\x=\dfrac{-9\pm\sqrt{81+24}}{6}\\\\x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]

Therefore, the correct answer is A.

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In a study of birth orders and intelligence, IQ tests were given to 18 and 19 years old men to estimate the size of the difference, we have that  [tex]|t|=0.618\leq t_c =2.101[/tex] and for this reason, we cannot reject the null hypothesis.

Null and Alternative Hypotheses

[tex]H_o: \mu_{1} = \mu_{2}\\\\Ha: \mu_1 \neq \mu_2 .[/tex]

Since the population standard deviations are unknown, we will apply a t-test on the means of the two populations, using two independent samples.

The degrees of freedom are df = 18, and the significance threshold is set at alpha = 0.05, based on the data presented. If we assume that the population variances are the same, we can calculate the degrees of freedom in this way:

The rejection region for this two-tailed test is R = \{t : |f| > 2.101}

Therefore the Test Statistics is

[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]

[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]

t=0.618

In conclusion. we have that  [tex]|t|=0.618\leq t_c =2.101[/tex]

For this reason, we cannot reject the null hypothesis.

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The values of x for which the expression [tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]is undefined are 0,[tex]\sqrt{41} /2[/tex] and imaginary numbers.

Given Expression :x^2+4x+32/x^2−x−10∗2x^2+4x^3/x^2+3x÷x^2+3x+2/x

We have to find out those values of x for which the expression does not exists.

[tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]

We have to take LCM of the expression which is equal to [tex]x^{3}(x^{2}-x-10)(2x^{2} +4x^{3})[/tex]

LCM is the smallest positive integer that is divisible by both the numbers whose LCM is found.

and it is present in the denominator.

Expression if exists cannot take denominator equal to 0.

So, by putting  LCM equal to zero we find

x=0,x=imaginary numbers and x=[tex]\sqrt{41} /2[/tex].

Hence the given expression have not take values of x=0,[tex]\sqrt{41} /2[/tex], imaginary number.

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Answer:

[tex]2a^{4} + 5a^{3} - 13a^{2} + 19a - 28[/tex]

Step-by-step explanation:

The length of the kite string is 50 ft

The string and the kite form a right triangle.

So, the length can be calculated using Pythagoras theorem as follows:

c^2 = 30^2 + 40^2

This gives

c^2 = 2500

Take the square roots

c = 50

Hence, the length of the kite string is 50 ft

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Answer: Tbh i don’t know anything besides that all the angles are equal to another and you have to prove it. I would just say: “90 degrees = 90 degrees

Sorry mate I can’t help

Step-by-step explanation:

Answer:

(4, -3)

Step-by-step explanation:

A vertex is just a point at which 2 lines going in different directions meet, hence (4, -3)

Answer:

b. y = x - 3

Step-by-step explanation:

The general form of the equation of the line is y = mx + c.

1) Find for m (gradient) using the following formula:

m = y2 - y1 / x2 - x1

Substitute the values into it and solve for m.

m = 2 - 1 / 5 - 4

m = 1 / 1

m = 1

2) Substitute into m of the y = mx + c.

y = 1x + c

3) Choose one the coordinates that the line goes through ((4, 1) or (5, 2)) to find c (y-intercept). I will choose (4, 1). Then, substitute your chosen coordinates into your newfound equation (y = 1x + c)

1 = 1(4) + c

1 = 4 + c

1 - 4 = c

-3 = c

Substitute -3 in place of c.

y = 1x - 3, which can be simplified to y = x - 3. Therefore, the correct choice is b.

Using proportions, it is found that it would take 55 hours for him to make $720.50.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

He is paid $524 for a 40 hour work week, hence per hour he earns?

r = 524/40 = $13.1.

The amount of hours he would need to make $720.50 is given by:

h = 720.50/13.1 = 55.

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Total: 48

DIning Hall: 48(3/8)=18

so theres 30 left for the classes

30/5(#of classes)=6 per class

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

we find the volume as if it were a parallelepiped and we remove the volume of the missing part.

8 * 6 * 10 = 480 cm³

480 - 2 * 3 * 10 = 420cm³

Answer:

2.6 hours

Step-by-step explanation:

Let t be the time that the trains meet.

[tex]90t = 416 - 70t[/tex]

[tex]160t = 416[/tex]

[tex]t = 2.6[/tex]

Answer:

10

Step-by-step explanation:

There are ten zeros therefore in standard form it is 1 x 10 to the power of 10 or [tex]10_{12}[/tex]

Using a system of equations, it is found that the number of golfers in the cafeteria is of 5.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

The number of baseball players is one less than twice the number of golfers, hence:

x = 2y - 1.

Since x = 9:

9 = 2y - 1

2y = 10

y = 5.

There are 5 golfers in the cafeteria.

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Answer:

Surface Area = 378.25

Step-by-step explanation:

Comment

It's not clear whether the figure has 0 1 or 2 lids. Since it is a cylinder, I will assume 2 lids like a can of soup.

Area lids

diameter = 11.4

radius = d/2

radius = 11.4/2

radius = 5.7

Area = pi * r^2

Area = (3.14 * 5.7^2) * 2 There are 2 lids.

Area =   102.01 yd^2

Area body

This is found by finding the circumference of the lid and multiplying by the height

Circumference

C = 2*pi*r

2*r = the diameter

2*r = 11.4

C = 3.14*11.4

C = 35.80

Area body

Area body = C* h

h = 7.8

Area body = 35.80 * 7.8

Area body = 279.24

Total Area = 102.01 + 279.24 = 378.25

Answer:

95%

Step-by-step explanation:

5 player won, meaning 95 player didn't.

This means that 95% of the players didn't win.

The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the distance from the man side of the house to the gutter is 15 m, since the drainpipe comes in lengths of 2.5 m, hence:

Number of drainpipe needed = 15 m / 2.5 m = 6

The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.

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The required quantity of drainpipe is mathematically given as six.

L=6

Generally, Let's say the distance from the male side of the house to the gutter is 15 meters. Since the length of the drainpipe typically comes in increments of 2.5 meters, we may reason as follows:

In conclusion, The required quantity of drainpipe is equal to 15 meters divided by 2.5 meters, which is equal to six.

L=15/2.5

L=6

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The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

41% of adults say cashews are their favorite kind of nut.

P = 41% = 0.41

Q = 1 - P = 1 - 0.41 = 0.59

n = 2

From the binomial distribution:

[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]

a) Exactly​ three

[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]

P(X = 3) = 0.131

b) At least​ four:

P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)

[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]

P(X ≥ 4) = 0.795

c) At most two:

P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)

[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]

P(X ≤ 2) = 0.0733

Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.

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∠A ≅ ∠D , BC≅ EF , AC ≅   DF  , option B , C , F are the correct answer.

CPCTC stands for corresponding parts of congruent triangles are congruent .

This means when two triangles are congruent then the corresponding sides are also congruent.

In the given triangles , Δ ABC ≅ ΔDEF

∠A ≅ ∠D

BC≅ EF

AC ≅   DF

Therefore option B , C , F are the correct options

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Using the Empirical Rule, it is found that:

It states that, for a normally distributed random variable:

Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:

68% are within 1 standard deviation of the mean, hence, out of 100:

0.68 x 100% = 68 scores.

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