If θ is an angle in standard position and its terminal side passes through the point (-4,1), find the exact value of csc ⁡ � cscθ in simplest radical form.

Answer:

y = - 2x + 12

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 1 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (6, 0 ) , the point it crosses on the x- axis into the partial equation.

0 = - 2(6) + c = - 12 + c ( add 12 to both sides )

12 = c

y = - 2x + 12 ← equation of perpendicular line

GIVEN EQUATION IS y = 1/2x + 1

NOW PERPENDICULAR EQUATION CAN BE WRITTEN AS

Since the line passes through the point (6,0) on the x-axis, we can substitute these values into the equation to solve for k:

Answer: 16 girls

Step-by-step explanation:

Step 1: Calculate the total number of students in the school by multiplying 32 by the ratio of girls to all the students, which is 5:8.

32 x (5/8) = 20

Step 2: Subtract the result from 32 to get the number of girls in the school.

32 - 20 = 12

Step 3: Multiply the result by the ratio of girls to all the students, which is 5:8.

12 x (5/8) = 16

Answer:

If 1 + 1 = 2, then we can say that 1 = 2 - 1. Now, if we have 3x + 5x, we can factor out the common term of x to get: 3x + 5x = (3 + 5)x = 8x So, 3x + 5x = 8x.

Angle R is right angle (QR perpendicular to PT) then ∆PQR ~ ∆TSR   (both are similar triangle).

Triangles with the same shape but different sizes are called similar triangles. To put it another way, the sides and angles of the same triangle are in proportion to each other. This indicates that the shape of one of the triangles would remain unchanged regardless of how much you scaled it up or down. Similar triangles are important in geometry and have numerous practical uses in architecture and engineering.

From the given figure,

Statement                   Reason

∠P = ∠T                      AA similarity theorem

∠R is right angle        QR ⊥ PT

Then ∆PQR ~ ∆TSR   (both are similar triangle)

To know more about triangle, visit:

brainly.com/question/25882965

#SPJ1

Answer:7,6,5

Step-by-step explanation:

So this is how I did it

So the theorem  is

a+b>c

a+c>b

b+c>a

---

Let's now substitute A= 6 and B =2 so It'll look something like

6+2> C

6+C> 2

2+C>6

From there I added like terms

8>C

4<C

2<C

Then from there I noticed the numbers 5,6,7 are the the only whole numbers between 4 and 8. So that's what I'm put as my answer.

Answer:  F(1) = 2. (1)^3 + (1)^2 + 3

                      = 2+1+3

                      = 7

Step-by-step explanation:

Answer:

10% of $10=$1

Step-by-step explanation

1/10=10% hence 10% of $10 is %1

Using the radians we know that the length of the arc in terms of π is s = 1.53 * π * 12 ft or s = 57.60 ft.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, the central angle of degrees must first be converted to radians.

θ(rad) = 275/180 * π = 1.53 rad

Then, by multiplying the Central angle (in rad units) by the circle radius r, the arc length may be determined:

s = θ * r

Changing the θ and r values:

s = 1.53 * π * 12 ft

s = 57.60 ft

Therefore, using the radians we know that the length of the arc in terms of π is s = 1.53 * π * 12 ft or s = 57.60 ft.

Know more about a circle here:

https://brainly.com/question/24375372

#SPJ1

Correct question:

Find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. Express arc length in terms of π. Then round your answer to two decimal places.

Radius, r = 12 feet; Central angle, θ = 275

Sophie deposited approximately $16,516.

The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and so forth are known as whole numbers. They are the figures we use to measure things, such as the quantity of pencils in a box or apples in a basket. In computations like addition, subtraction, multiplication, and division, whole numbers are also employed.

Let's call the amount Sophie deposited "P". After 9 years, the investment would have gone through 18 compounding periods (2 per year for 9 years).

The formula for calculating the future value (FV) of an investment with compound interest is:

[tex]FV = P(1 + r/n)^{(nt)[/tex]

where:

P = the principal (the initial amount invested)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have:

P = unknown (what we're trying to find)

r = 4.2% = 0.042

n = 2 (since the interest is compounded semiannually, or twice a year)

t = 9

So the formula becomes:

[tex]24,575.22 = P(1 + 0.042/2)^{(2*9)[/tex]

Simplifying the right side of the equation:

24,575.22 = P(1.021)¹⁸

24,575.22 = 1.485P

Dividing both sides by 1.485:

P ≈ $16,516

Therefore, Sophie deposited approximately $16,516.

Learn more about whole numbers on:

https://brainly.com/question/13242016

#SPJ1

Answer:

5°

Step-by-step explanation:

The three angles of a triangle add up to 180° (every triangle, always) Since this triangle is a right triangle, one of the angles is a right angle, 90°.

Another angle is given, 85°.

x + 85° + 90° = 180°

x + 175° = 180°

x = 5°

To do this question using mental math, if one angle is 90° the other two angles must add up to 90° (thats the total of 180°) One angle is 85° then the other is 5°

f(w) = 100 + 15t is the function that represents the relationship between w, the number of weeks Jordan kept his money in the account, and t, the total amount in the savings account

It is given to us that Jordan received $100 for a graduation present and deposited it in a savings account. Each week thereafter, he added $15 to the account but no interest was earned.

We need to write an equation represents the relationship between w, the number of weeks Jordan kept his money in the account, and t, the total amount in the savings account:

Graduation present = $100

Amount deposited per week = $15

Let, w be the number of weeks, and t, the total amount in the savings account, therefore, the function is:

f(w) = 100 + 15t

Therefore, f(w) = 100 + 15t represents the relationship between w, the number of weeks Jordan kept his money in the account, and t, the total amount in the savings account

To learn more about functions, click here:

brainly.com/question/12431044

#SPJ4

The 95% confidence interval for the mean difference in the amount absorbed is (0.01, 3.25) ml, with a df of 28. Yes, the interval does not contain zero, suggesting that there is a significant difference between the two brands in the amount absorbed.

To find the 95% confidence interval for the mean difference in the amount absorbed, we can use the formula:

CI = (x1 - x2) ± tα/2 * SE

where x1 - x2 is the difference in means, tα/2 is the critical value from the t-distribution table for a 95% confidence interval with degrees of freedom (df) = 30 - 2 = 28 (assuming equal variances), and SE is the standard error of the difference in means:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

Plugging in the values, we get:

x1 - x2 = 15.63 - 14 = 1.63

s1 = 3.12, n1 = 16

s2 = 2.53, n2 = 16

SE = sqrt[(3.12^2/16) + (2.53^2/16)] = 0.974

tα/2 for df = 28 and α = 0.05 is 2.048.

CI = (1.63) ± (2.048 * 0.974) = (0.01, 3.25)

Therefore, the 95% confidence interval for the mean difference in the amount absorbed is (0.01, 3.25), with df = 28.

This interval suggests that there is a significant difference between brands in the amount absorbed, since the interval does not include 0. This means that we can reject the null hypothesis that the means are equal at a 5% significance level and conclude that the mean amount of water absorbed for brand A is significantly greater than brand B.

To know more about confidence interval:

https://brainly.com/question/29680703

#SPJ4

The cost of one package of tulip bulbs is 11, and the cost of one package of crocus bulbs is 16.

To find the cost of one package of tulip bulbs and one package of crocus bulbs, follow these steps:

Write two equations based on the given information:

Equation 1 (James): 3T + 7C = 145

Equation 2 (Kim): 10T + 14C = 334

Solve the system of equations using the substitution or elimination method. In this case, we'll use the elimination

method by multiplying Equation 1 by 2 to make the coefficients of C the same:

Equation 1 modified: 6T + 14C = 290

Subtract Equation 2 from the modified Equation 1:

(6T + 14C) - (10T + 14C) = 290 - 334
  -4T = -44

Divide both sides by -4 to find the value of T (tulip bulbs):
  T = 11

Substitute the value of T back into Equation 1 to find the value of C (crocus bulbs):
  3(11) + 7C = 145
  33 + 7C = 145

Subtract 33 from both sides:
  7C = 112

Divide both sides by 7 to find the value of C:
  C = 16

So, the cost of one package of tulip bulbs is 11, and the cost of one package of crocus bulbs is 16.

for such more question on cost

https://brainly.com/question/25109150

#SPJ11

Answer:

-16/5 divided by 12/25 is equal to -40/3.

Step-by-step explanation:

Answer:

45 times

Step-by-step explanation:

I hope this helps

Answer: B

Step-by-step explanation: Answer choice B states, that same side interrior angles are supplementary so picture i shows parralel lines. This is trues, as line L and line M have interior angles that are supplementary, meaning that it ends up to 180. This concept is not true for ii, as 106 and 73 angles are not supplementary.

At the 5% significance level, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that the average weight of the vacuums from Nature Abhors is less than 19.64 pounds.

To answer this question, we can use a one-sample t-test, assuming that the population of weights is normally distributed. The null hypothesis is that the true mean weight of the vacuums from Nature Abhors is 19.64 pounds, while the alternative hypothesis is that it is less than 19.64 pounds.

We can calculate the t-statistic using the formula

t = (X - μ) / (s / sqrt(n))

where X is the sample mean (19.33), μ is the hypothesized population mean (19.64), s is the sample standard deviation, and n is the sample size (31).

Since we don't know the population standard deviation, we can estimate it using the sample standard deviation. We calculate the sample standard deviation as follows

s = sqrt(sum((xi - X)^2) / (n - 1))

where xi is the weight of the i-th vacuum in the sample. We assume that the weights are normally distributed, so we can use the t-distribution with (n-1) degrees of freedom to calculate the p-value.

Using a t-table or calculator, we can find the critical t-value for a one-tailed test at the 5% significance level with 30 degrees of freedom to be -1.699.

Plugging in the numbers, we get

t = (19.33 - 19.64) / (s / sqrt(31))

s = sqrt(sum((xi - X)^2) / (n - 1)) = 0.714

t = (-0.31) / (0.714 / sqrt(31)) = -1.84

Since the calculated t-value (-1.84) is less than the critical t-value (-1.699), we can reject the null hypothesis at the 5% significance level. Therefore, we can conclude that there is sufficient evidence to suggest that the average weight of the vacuums from Nature Abhors is less than 19.64 pounds.

Learn more about significance level here

brainly.com/question/13947717

#SPJ4

3120 different types of colorings are possible . Thus, Option C is the correct option. There are 3 cases involved

6! = 720 cases

No rotation is necessary because all permutation are already accounted for.

6 × 5 × 4 × 3 = 360

There are 5 different locations where the pair can be present.

360 × 5 = 1800 one pairs is possible

6 × 5 × 4 = 120

There are 5 rotations in the pentagon so the total number of possibilities is  

120 × 5 = 600 two pairs are possible

now, we add the 3 cases to find the total number of possibilities

720 + 1800 + 600 =  3120

3120 different types of colorings are possible. Thus, Option C is the correct option.

To learn more about Permutation,

https://brainly.com/question/28065038

#SPJ4

After 3 weeks, the dog consumed 3 pounds of food, leaving 7 pounds of food left. Subtracting the amount of food consumed from the initial amount, 10 pounds - 3 pounds = 7 pounds.

After 3 weeks, the dog would have consumed 3 pounds of food (1 pound per week x 3 weeks = 3 pounds).

To find out how many pounds of food are left, we can subtract the amount of food consumed from the initial amount:

10 pounds - 3 pounds = 7 pounds

So there are 7 pounds of food left after 3 weeks.

Expressed in decimal form, it would be 7.0 pounds.

The base-10 numbering system, which employs ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent all conceivable numerical values, is used to express numbers in decimal form. When a number is expressed in decimal form, there can be one or more digits to the left of the decimal point that represent the whole number portion of the value and one or more digits to the right of the decimal point that represent the fractional portion of the value.

To know more about decimal form, visit

brainly.com/question/13964095

#SPJ1

The probability of running out of anchovies before the evening is over is approximately 0.058, or 5.8%. We must presume that the number of pizzas ordered with anchovies follows a binomial distribution with parameters n = 60 (the total number of pizzas) and p = 0.08 in order to answer this issue using the normal approximation for the binomial distribution. (the probability of ordering anchovies on a pizza). 

The standard deviation of this binomial distribution is given by = sqrt(np(1-p)) = sqrt(60 x 0.08 x 0.92) = 2.03, and the mean is given by = np = 60 x 0.08 = 4.8.

Now, we need to determine the likelihood that we will need to prepare more than eight anchovy-topped pies before the evening is through in order to determine the likelihood that we will run out of anchovies. (since we only have enough anchovies for 8 pizzas).

This is equivalent to finding the probability that the number of pizzas with anchovies is greater than 8, or P(X > 8), where X is the number of pizzas with anchovies.

To use the normal approximation for the binomial distribution, we need to standardize the variable X using the standard normal distribution. This gives us:

z = (X - μ) / σ = (8 - 4.8) / 2.03 = 1.57

Using a standard normal table or calculator, we can find the probability that z is greater than 1.57, which is approximately 0.058. Therefore, the probability of running out of anchovies before the evening is over is approximately 0.058, or 5.8%.

To know more about binomial distribution -

brainly.com/question/31197941

#SPJ4

The simple interest rate is therefore 6.25% as the initial principal (P) is 2000 Birr and the final amount (A) is 2500 Birr.

what is interest ?

A creditor assesses interest as a cost to a borrowing in exchange for the use of money; Typically, it is expressed as a portion of the principal amount borrowed. Generally, it is the cost of getting cash.

given

The simple interest formula is

S I = P * r * t,

where I is the interest,

P is the principal (amount of money we start with),

r is the interest rate, and

t is the amount of time in years.

In this instance, we are aware that the initial principal (P) is 2000 Birr and the final amount (A) is 2500 Birr.

The interest rate (r) is constant because we also know that the interest is simple.

We may determine r by using the simple interest formula:

SI = P*r*t= 2500-2000

500 = 2000*r*4

500 = 8000r

r = 500/8000

r = 0.0625

The simple interest rate is therefore 6.25% as the initial principal (P) is 2000 Birr and the final amount (A) is 2500 Birr.

To know more about simple interest visit:

https://brainly.com/question/25845758

#SPJ9

Answer:

A) -⅕.

Step-by-step explanation:

If lines s and t are perpendicular, then their slopes are negative reciprocals of each other. Therefore, if the slope of line s is 5, the slope of line t is -1/5.

So the answer is A) -⅕.

The slope of line T is -1/5, because perpendicular lines have opposite reciprocal slopes, meaning the opposite sign (positive or negative) and flipped (whole number becomes a fraction).

The area of the given rectangle is [tex]32\dfrac{6}{20}[/tex] square feet

For better understanding check the calculation here.

Area of the rectangle is the space inside the given triangle.

Formula: Formula to find the area of the triangle is length times width

Length and width are given as mixed fractions

Lets convert mixed fractions into improper fractions

[tex]\text{Length}=6\dfrac{4}{5} =\dfrac{6\times5+4}{5} =\dfrac{34}{5}[/tex]

[tex]\text{Width}=4\dfrac{3}{4} =\dfrac{4\times4+3}{4} =\dfrac{19}{4}[/tex]

Now we find out the area

[tex]\text{Area}=\text{length}\times\text{width}[/tex]

[tex]\text{Area}=\dfrac{34}{5} \times\dfrac{19}{4}[/tex]

[tex]\text{Area}=\dfrac{646}{20}[/tex]

Now we divide the number and find out the quotient and remainder

[tex]\text{Area}=\dfrac{646}{4}[/tex]

[tex]\text{Quotient}=32[/tex]

[tex]\text{Remainder}=6[/tex]

[tex]\text{Area}=32\dfrac{6}{20}[/tex]

The area of the given rectangle is [tex]32\dfrac{6}{20}[/tex] square feet

Learn more information about Area of rectangle here:

brainly.com/question/21029878

Answer:

It will take 3 days to runn total of 12 Kilometers

Step-by-step explanation:

12(1000) = 12,000 meters

400(10) = 4000 meters/day

12,000/4000 = 3 days

the equation √x = -7 has no real solutions.

Why it is?

There is no real number x that satisfies the equation √x = -7.

The square root of a non-negative real number is always non-negative. Therefore, √x is non-negative for all real numbers x, including x = 0. However, -7 is negative, so the equation √x = -7 has no real solutions.

An equation is a statement that asserts the equality of two mathematical expressions. It generally consists of two sides, left-hand side (LHS) and right-hand side (RHS), which are separated by an equal sign (=). An equation is true when both the LHS and RHS represent the same value or expression.

To know more about equation related question visit:

https://brainly.com/question/29657983

#SPJ1

Complete question:

What is the solution to the equation √x = -7, where √x represents the square root of x and -7 is a negative number?

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the inverse of the function y = 3x, we need to swap the positions of x and y and then solve for y.

Step 1: Swap the positions of x and y

x = 3y

Step 2: Solve for y

Divide both sides by 3

x/3 = y

So the inverse function of y = 3x is x/3.

We can also verify that this is the inverse function by plugging in x/3 for y in the original equation and confirming that we get x:

y = 3x

x/3 = 3x/3

x/3 = x

Therefore, the inverse function of y = 3x is x/3.

Answer:

Step-by-step explanation:

The given function is y = 3x.

To find its inverse, we start by swapping x and y in the equation to get:

x = 3y

Next, we solve this equation for y to isolate it:

y = x/3

Therefore, the inverse of y = 3x is y = x/3.

We can say that approximately 48 villagers (40% of 120) are under the age of 25. This means that just under half of the population in this village is under the age of 25.

According to the pie chart, we can see that the village of 120 people has 20% of its population over the age of 60. To determine the exact number of villagers over 60, we can multiply the total population by the percentage of people over 60:

120 x 20% = 24

So there are 24 villagers over the age of 60 in this village.

As for the percentage of villagers under the age of 25, we can see from the pie chart that 40% of the population falls into this category. However, it is important to note that the question mentions a village of 120 people, while the percentage given in the chart may not reflect this exact number. Therefore, we cannot determine the exact number of villagers under the age of 25 without additional information.

To learn more about Population :

https://brainly.com/question/25630111

#SPJ11

Angles are created by joining the extremities of two rays, with the joint vertex representing the common terminal of the two beams. The value of ∠c= 48.65.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex.

The joint vertex is the common terminal of the two beams.

Given,

AC = 33 cm

AB = 35.75 cm

Hence, The value of ∠C = 48.65.

To learn more about angles, visit

brainly.com/question/2046046

#SPJ1