What is the equation of the given line in the point slope -form ?

Answer:

-6, -3

3, 8

Step-by-step explanation:

In order to find the number that are solutions to the compound inequalities, you first solve fr x on each inequality.

First inequality:

[tex]4(x+3)\leq 0\\\\4x+12\leq0\\\\4x\leq-12\\\\x\leq-3[/tex]  interval = (-∞ , -3]

Second inequality:

[tex]x+1>3\\\\x>2[/tex]   interval = (2 , ∞)

The interval solution is (-∞ , -3] U (2 , ∞)

The number that are included in the previous interval are:

-6, -3

or

3, 8

Answer: any except 0

Step-by-step explanation:

Answer:

12, 1

Step-by-step explanation:

12- 6(1)=

12-6= 6

Answer:

She makes conclusion about a population that is not well represented by the sample.

Step-by-step explanation:

The conclusion she is making is about a population that is not well represented by her sample: the population is the homeowners in the nation, but the sample is made of homeowners or only her state.

The population about which she can make conclusions with this sample is the homeowners of her state, given that the sampling is done right.

Answer: The sample is biased

Let's solve the first equation and see if both -6−6minus, 6 and 666 are possible values of ccc.

Hint #22 / 4

\begin{aligned} c^2&=36\\\\ \sqrt{c^2}&=\sqrt{36}&\\\\ c &=\pm 6 \end{aligned}

c

2

c

2

​

c

​

=36

=

36

​

=±6

​

​

Yes, both -6−6minus, 6 and 666 are possible values of ccc for the first equation!

Hint #33 / 4

Let's do the same for the second equation.

\begin{aligned} c^3&=216\\\\ \sqrt[\scriptstyle 3]{c^3}&=\sqrt[\scriptstyle 3]{216}&\\\\ c &=6 \end{aligned}

c

3

3

c

3

​

c

​

=216

=

3

216

​

=6

​

​

No, both -6−6minus, 6 and 666 are not possible values of ccc for the second equation.

Hint #44 / 4

The following equation has both -6−6minus, 6 and 666 as possible values of ccc:

c^2 = 36c

2

=36

The equation that has both -6 and 6 as possible values is c² = 36.

Option A is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

If c is a possible value of 6, then c - 6 = 0.

Similarly, if c is a possible value of -6, then c + 6 = 0.

A)

c² = 36

We can factor this equation as c² - 36 = 0, which gives us (c - 6) (c + 6) = 0. Therefore, both c = 6 and c = -6 are solutions to this equation.

B)

c³ = 216

We can factor 216 as 6³, so c³ - 6³ = (c - 6) (c² + 6c + 36) = 0.

The quadratic factor c² + 6c + 36 does not have any real roots, so the only solution to this equation is c = 6.

Therefore, -6 is not a possible solution to this equation.

Thus,

The equation that has both -6 and 6 as possible values is c² = 36.

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Answer:

Solved below.

Step-by-step explanation:

The data is provided for the starting salary (in $1,000) at some company and years of prior working experience in the same field for randomly selected 10 employees.

(a)

The formula to compute the correlation coefficient is:

[tex]r=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\[/tex]

The required values are computed in the Excel sheet below.

[tex]\begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 10 \cdot 7252 - 97 \cdot 661 } {\sqrt{\left[ 10 \cdot 1335 - 97^2 \right] \cdot \left[ 10 \cdot 45537 - 661^2 \right] }} \approx 0.9855\end{aligned}[/tex]

Thus, the sample correlation coefficient r is 0.9855.

(b)

The slope of the regression line is:

[tex]b_{1} &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 10 \cdot 7252 - 97 \cdot 661 }{ 10 \cdot 1335 - \left( 97 \right)^2} \\\\\approx 2.132[/tex]

Thus, the slope of the regression line is 2.132.

(c)

The y-intercept of the line is:

[tex]b_{0} &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 661 \cdot 1335 - 97 \cdot 7252}{ 10 \cdot 1335 - 97^2} \\\\\approx 45.418[/tex]

Thus, the y-intercept of the line is 45.418.

(d)

The equation of the sample regression line is:

[tex]y=45.418+2.132x[/tex]

(e)

Compute the predicted starting salary for a person who spent 15 years working in the same field as follows:

[tex]y=45.418+2.132x\\\\=45.418+(2.132\times15)\\\\=45.418+31.98\\\\=77.398\\\\\approx 77.4[/tex]

Thus, the predicted starting salary for a person who spent 15 years working in the same field is $77.4 K.

Answer:

Yes correct

Step-by-step explanation:

I think this is correct becase: 2 50

5 55

7 62

etc

these are all correct

Answer:

The answer is

Step-by-step explanation:

For an nth term in an arithmetic sequence

[tex]U(n) = a + (n - 1)d[/tex]

where n is the number of terms

a is the first term

d is the common difference

From the question

a = 15

d = 24 - 15 = 9

n = 61

So the 61st term of the arithmetic sequence is

U(61) = 15 + (61-1)9

= 15 + 9(60)

= 15 + 540

= 555

Hope this helps you.

Answer:

7/2x

Step-by-step explanation:

Well first we need to put,

2x + 7y = 5,

into slope intercept

-2x

7y = -2x + 5

Divide y to all numbers

y = -2/7x + 5/7

So the slope for the given line is -2/7,

the slope of the line that is perpendicular to it is its reciprocal.

Meaning the slope of the perpendicular line is 7/2.

Thus,

the slope of the perpendicular line is 7/2x.

Hope this helps :)

Answer:

The slope of the perpendicular line is 7/2

Step-by-step explanation:

2x+7y=5

Solve for y to find the slope

2x-2x+7y=5-2x

7y = -2x+5

Divide by 7

7y/7 = -2/7 x +5/7

y = -2/7x + 5/7

The slope is -2/7

The slope of perpendicular lines multiply to -1

m * -2/7 = -1

Multiply each side by -7/2

m * -2/7 *-7/2 = -1 * -7/2

m = 7/2

The slope of the perpendicular line is 7/2

Answer:

-2x + y = -1.

Step-by-step explanation:

The slope of the line = rise / run

= (11-9) / (6-5) = 2.

The point-slope form of the line is

y - y1 = 2(x - x1) where (x1, y1) is a point on the line so we have:

y - 11 = 2(x - 6)     ( using the point  (6, 11)

y = 2x - 12 + 11

y = 2x - 1

Convert to standard form:

-2x + y = -1.

Answer:

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

(11,688.68 , 12,511.32)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 17

mean of the sample x⁻ = 12,100

Standard deviation of the sample (S) = 800

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom ν =n-1 = 17-1 =16

[tex]t_{(16 , 0.05)} = 2.1199[/tex]

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

[tex](12,100 - 2.1199\frac{800}{\sqrt{17} } , 12,100 + 2.1199 \frac{800}{\sqrt{17} } )[/tex]

(12,100 - 411.32 , 12,100 + 411.32)

(11,688.68 , 12,511.32)

Answer:

Step-by-step explanation:

I'm not sure what are u asking exactly

Answer:

The rising tide gobbled up the sandcastle that the children had so carefully crafted.

Step-by-step explanation:

personification is when you use human characteristics to describe something non-human.

Answer:

Ans) 42.7%

Step-by-step explanation:

For a continuous probability distribution, a curve known as probability density function contains information about these probabilities.

in the given range -

The probability that a continuous random variable = equal to the area under the probability density function curve

The probability that the value of a random variable is equal to 'something' is 1.

As per the diagram,

Weight of chocolate bar between 4 ounces and 7 ounces is highlighted in the blue part. That area is said to be 0.42739 and the total area under the curve is 1.

Hence required probability

=0.42739/1=0.42739

Ans) 42.7%

Round to nearest tenth of a percent

Answer: No there isn't

Explanation:

A score of 53.7% is quite close to 50% and this is a true or false exam. Charlie could have easily gotten this result by indeed guessing and not studying. This test mark is therefore not high enough to disregard the teachers's claim. Were the results to be significantly high enough above 50% then it could be said that indeed Charlie does study for his exams.

Answer:2/3

Step-by-step explanation:

Given that the length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. The domain of the function is (0, ∞).

The domain of a function is the set of all possible inputs for the function. In other words, domain is the set of all possible values of x. In this question, x is the width of the rectangle. Width of a rectangle existing in two dimensional space, cannot be negative or zero. Thus it is the set of all positive real numbers, or we say, (0, ∞).

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Answer:

8

Step-by-step explanation:

Because it is equal to the 4 side

Answer:

(a)$29.95

(b)A

Step-by-step explanation:

The​ cost, in​ dollars, of producing x cellphone cases is given by:

[tex]C(x)=-0.05 x^2+55 x.[/tex]

We are required to evaluate: [tex]\dfrac{C(251)-C(250)}{251-250}[/tex]

[tex]C(251)=-0.05(251)^2+55(251)=10654.95\\C(250)=-0.05(250)^2+55(250)=10625\\\text{Therefore:}\\\\\dfrac{10654.95-10625}{251-250}=29.95[/tex]

[tex]\dfrac{C(251)-C(250)}{251-250}=\$29.95[/tex]

The value calculated above represents the additional cost to produce one more item after making 250 items.

Answer:

Option 4

Step-by-step explanation:

The central angles are "Angles in the center"

So,

Central Angles are <AOB, <BOC and <AOC

Answer:

<AOB, <BOC and < AOC

Step-by-step explanation:

There are 3 angles at center O . The largest is <AOC ( = 180 degrees). Thn you have 2 more each equal to 90 degrees.

Answer:

Sides:

Angles:

Step-by-step explanation:

Apply the law of sines to find the sine of [tex]\angle A[/tex]:

[tex]\displaystyle \frac{\sin{A}}{\sin{C}} = \frac{a}{c}[/tex].

[tex]\displaystyle\sin A = \frac{a}{c} \cdot \sin{C} = \frac{103}{159} \times \left(\sin{104^{\circ}}\right) \approx 0.628556[/tex].

Therefore:

[tex]\angle A = \displaystyle\arcsin (\sin A) \approx \arcsin(0.628556) \approx 38.9^\circ[/tex].

The three internal angles of a triangle should add up to [tex]180^\circ[/tex]. In other words:

[tex]\angle A + \angle B + \angle C = 180^\circ[/tex].

The measures of both [tex]\angle A[/tex] and [tex]\angle C[/tex] are now available. Therefore:

[tex]\angle B = 180^\circ - \angle A - \angle C \approx 37.1^\circ[/tex].

Apply the law of sines (again) to find the length of side [tex]b[/tex]:

[tex]\displaystyle\frac{b}{c} = \frac{\sin \angle B}{\sin \angle C}[/tex].

[tex]\displaystyle b = c \cdot \left(\frac{\sin \angle B}{\sin \angle C}\right) \approx 159\times \frac{\sin \left(37.1^\circ\right)}{\sin\left(104^\circ\right)} \approx 98.8[/tex].

Answer:Sqrt(8^2 + 3^2)

Step-by-step explanation:

Answer:

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 13, \sigma = 0.2[/tex]

What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster

We have to find the pvalue of Z when X = 13.36.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13.36 - 13}{0.2}[/tex]

[tex]Z = 1.8[/tex]

[tex]Z = 1.8[/tex] has a pvalue of 0.9641

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Answer:

[tex]153.86 \: {units}^{2} [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]

Answer:

153.86 [tex]units^{2}[/tex]

Step-by-step explanation:

Areaof a circle = πr^2

[tex]\pi = 3.14[/tex](in this case)

[tex]r^{2} =7[/tex]

A = πr^2

= 49(3.14)

= 153.86

Answer: a. 0.1031; fail to reject the null hypothesis

Step-by-step explanation:

Given: Significance level : [tex]\alpha=0.05[/tex]

The test statistic in a two-tailed test is z = -1.63.

The P-value for two-tailed test : [tex]2P(Z>|z|)=2P(Z>|-1.63|)=0.1031[/tex] [By p-value table]

Since, 0.1031 > 0.05

i.e. p-value > [tex]\alpha[/tex]

So, we fail to reject the null hypothesis. [When p<[tex]\alpha[/tex] then we reject null hypothesis  ]

So, the correct option is a. 0.1031; fail to reject the null hypothesis.

Answer:

Step-by-step explanation:

The average weight of a package of rolled oats is supposed to be at least 18 ounces

Null hypothesis: u >= 18

Alternative: u < 18

Using the t-test formula, we have

t = x-u/ (sd/√n)

Where x is 17.78, u = 18, sd = 0.41 and n = 18

t = 17.78-18 / (0.41/√18)

t = -0.22 / (0.41/4.2426)

t = -0.22/ 0.0966

t = -2.277

Since, this is a left tailed test, at a significance level of 0.05, the p value is 0.01139. Since the p value is less than 0.05, we will reject the null hypothesis and conclusion that the true mean smaller than the actual specification.

Answer:

X = 2

Step-by-step explanation:

[tex]if \: {x}^{3} + {3}^{x} = 17 \: we \: can \: conclude \: that \: x \: is \: equal \: to \: two \\ {2}^{3} + {3}^{2} = 8 + 9 = 17[/tex]

Consider the standard form of each of the following options given, and note the hyperbola properties through that derivation -

[tex]Standard Form - \frac{\left(x-5\right)^2}{\left(\sqrt{7}\right)^2}-\frac{\left(y-\left(-5\right)\right)^2}{3^2}=1,\\Properties - \left(h,\:k\right)=\left(5,\:-5\right),\:a=\sqrt{7},\:b=3\\[/tex]

Similarly we can note the properties of each of the other hyperbolas. They are all similar to one another, but only option C is correct. Almost all options are present with a conjugate axis of length 6, but only option c is broad enough to include the point ( 1, - 5 ) and ( 9, - 5 ) in a given radius.

Solution = Option C!

Answer:

[tex]\displaystyle AB \approx 8.39 \text{ inches} \text{ and } AC \approx 13.05 \text{ inches}[/tex]

Step-by-step explanation:

Note that we are given the measure of ∠C and the length of side BC.

To find AB, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

Substitute in appropriate values:

[tex]\displaystyle \tan 40^\circ = \frac{AB}{BC} = \frac{AB}{10}[/tex]

Solve for AB:

[tex]\displaystyle AB = 10\tan 40^\circ \approx 8.39\text{ inches}[/tex]

For AC, we can use cosine ratio since we have an adjacent and need to find the hypotenuse. Recall that:

[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

Substitute in appropriate values:

[tex]\displaystyle \cos 40^\circ = \frac{BC}{AC} = \frac{10}{AC}[/tex]

Solve for AC:

[tex]\displaystyle \begin{aligned} \frac{1}{\cos 40^\circ} & = \frac{AC}{10} \\ \\ AC & = 10\cos 40^\circ \approx 13.05\text{ inches} \end{aligned}[/tex]

In conclusion, AB is about 8.39 inches and AC is about 13.03 inches.

Answer:

D

Step-by-step explanation:

The numbers that are less than 0 are negative. Negative numbers have the "-" sign in front of them so the answer is D.

Answer:

d

Step-by-step explanation:

The other ones will always be positive four

Answer:

21900

Step-by-step explanation:

There are 12 months in a year, so multiply the yearly amount by 12

1825 * 12

21900

Answer:

Bob makes $21,000 in a year.

Step-by-step explanation:

There are 12 months in a year, so if he earns $1,825 every month to get his yearly pay you need to add 1,825 twelve times. Thus, 1,825×12=21,000. Hope this helps!

Answer:

5! = 120

Step-by-step explanation:

5! is basically 5(4)(3)(2)(1).