Find the value of the trigonometric and simplify the fraction if needed. Thanks!

Answer:

1/7

Step-by-step explanation:

There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7

Answer:

1/7

Step-by-step explanation:

The number from the list that is less than 2 is 1.

1 number out of a total of 7 numbers.

= 1/7

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, ∞).

Learn more about domain of a function here

https://brainly.com/question/13113489

#SPJ2

Answer:

0.65

Step-by-step explanation:

There are 65 student that do sports as 20+20+25=65. In total there are 100 student and you find this by adding up all the values. Now all you do is divide 65/100 and get 0.65 and that is the probability a random student plays sports.

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

Answer:

(190-5a)°

Step-by-step explanation:

Sum of internal angles of a triangle equals to 180°

If the third angle is x, then we have:

The third angle is: (190-5a)°

Answer:

CI: {0.4085; 0.6647}

Step-by-step explanation:

The confidence interval for a proportion (p) is given by:

[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]

Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:

[tex]p=\frac{22}{41}=0.536585[/tex]

Thus the confidence interval is:

[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]

The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}

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:

Do you have an image because I'm a bit confused with you just asking the measure of PSQ.

Step-by-step explanation:

Answer:

$0.60

Step-by-step explanation:

the question ask us to find the amount of the markup on Flora’s roses. The amount of markup is given by:

markup rate x original price = amount of markup

the markup rate is in decimal form

since the original price was $0.05 and the markup price is 80% = 0.80, we have

0.80 x .075 = 0.60

thus, the amount of the markup on Flora’s roses was $0.60

Answer:

12, 1

Step-by-step explanation:

12- 6(1)=

12-6= 6

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:

The answer is 1/1296

Step-by-step explanation:

6^-4 can be written as 1/6⁴

And

1/6⁴ = 1/1296

Hope this helps you.

Answer:

3/10ths of the money

Step-by-step explanation:

Add together the two numbers to get the total.

Josh gets 30 percent and Lucy gets 70 percent.

3/10

Answer:

3/10

Step-by-step explanation:

3+7=10  

Josh=3

Lucy=7

Answer:

2049.

Step-by-step explanation:

2045 - 1983 = 62 years.

So the competition will take place in 1983 + 60 = 2043.

After 2045  the competition takes place in 2049.

Answer:

a) 16xy³

Step-by-step explanation:

For a binomial expansion (a + b)ⁿ, the r+1 term is:

nCr aⁿ⁻ʳ bʳ

Here, a = 4x, b = y, and n = 4.

For the fourth term, r = 3.

₄C₃ (4x)⁴⁻³ (y)³

4 (4x) (y)³

16xy³

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: The answer is B)

B. The independent variable is time​ (t), in​ minutes, and the dependent variable is rental cost​ (r), in dollars. The linear function that models this situation is r equals to r=0.55x+8

Step-by-step explanation:

Step-by-step explanation:

pnotgrt8rthan4 = 3 ÷ 7 × 100

= 42.8571428571 / 43%

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:

Given,

X=2

y=-2

z=3

Now,

[tex]3x + y - z \\ = 3 \times 2 + ( - 2) - 3 \\ = 6 + ( - 2) - 3 \\ = 6 - 2 - 3 \\ = 4 - 3 \\ = 1[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

1

Step-by-step explanation:

3X+Y-Z

Where X = 2, Y = -2 amd Z = 3

=> 3(2)+(-2)-(3)

=> 6-2-3

=> 4-3

=> 1

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:

y = -1/2x + 1/2

Step-by-step explanation:

Step 1: Write in known variables

y = -1/2x + b

Step 2: Find b

2 = -1/2(-3) + b

2 = 3/2 + b

b = 1/2

Step 3: Rewrite equation

y = -1/2x + 1/2

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

Answers:

A ' = (-2, -3)

B ' = (0, -3)

C ' = (-1, 1)

=======================================================

Explanation:

To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.

Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]

Applying this rule to the three given points will mean....

The diagram is provided below.

Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.

Answer:

(-2,-3)...(0,-3)...(-1,1)

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

area of a triangle is length x base

so 6 x 6 = 36

36 divided by 2 = 18

I hope it helps :)

Answer: The area is about 15.59 and is round to the nearest hundredth.

Step-by-step explanation:

An equilateral triangle has three equal sides is just like an isosceles triangle.

So in this case, we know that the base is 6 and since the base is 6 all the other two sides is also 6 .But we do not know the height to find the area so we need to find the height.

The height is the distance of from the base to the tip or top which helps form two right triangles.. And if you divide as  an equilateral triangle into two parts you will form two right triangles. Imagine we have divide the isosceles triangle into two parts to form two right triangles. We will now have a base of 3 instead of 6 and and hypotenuse of 6 .  but we still don't know the height so we need to  find it.

Using the Pythagorean Theorem we could say that a^2 plus b^2 squared is equal to c^2 squared.

We know a as 3 and c the hypotenuse as 6.

so 3^2 + b^2 =6^2  solve for b

  9 + b^2 = 36

 -9               -9

   b^2 = 27

  b= [tex]\sqrt{27}[/tex]  

b= 5.196  

Now we know that b is about 5.196 which is the  height.Now we could find the area by  multiplying  the base by the height.

5.196 * 6 = 31.176  

31.176/2 = 15.588  

Now you could round it to the nearest hundredth to be 15.59  

Answer:

g=22

Step-by-step explanation:

add 8 to both sides

g-8=14

g-8+8=14+8

g=14+8

g=22

The solution of expression g - 8 = 14 is,

⇒ g = 22

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ g - 8 = 14

Now, We can simplify as,

⇒ g - 8 = 14

Add 8 both side,

⇒ g - 8 + 8 = 14 + 8

⇒ g = 22

Thus, The solution of expression g - 8 = 14 is,

⇒ g = 22

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ3

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 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:

The 95% confidence interval for the proportion of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 603, \pi = \frac{142}{603} = 0.2355[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 - 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2016[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 + 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2694[/tex]

The 95% confidence interval for the proportion of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694)

Step-by-step explanation:

yeah,when 15-7=8

the number is 8