Write a linear function for the data in the table.
X
y
0
8
1
4.5
2
1
3
-2.5
4
-6

The measures of angles of a rhombus are ∠KNL = 90° , ∠KJL = 50° , ∠MLK = 100° and ∠JKM = 40°

A Rhombus has four sides of the same length, its perimeter can be determined using the formula Perimeter = 4a, where "a" stands for the side's length.

When the two diagonals of a rhombus are known,

The perimeter = 2√p² + q²

where 'p' and 'q' are the diagonals.

Given data ,

Let the rhombus be represented as JKLM

where MK and JL are the diagonals and N is the midpoint of intersection

The measure of MK = 24

The measure of JL = 20

The measure of NK = 12

The measure of ∠MJL = 50°

Now , the diagonals of a rhombus bisect each other , so

NK = MK/2 = 12

And , NL = JL / 2 = 10

Now , to calculate the measure of ML ,

In triangle MNL, ∠N = 90°

MN = NK = 12 , NL = 10

Using Pythagorean theorem of triangles , we get

ML² = MN² + NL²

ML² = 12² + 10²

ML² = 244

ML = √244

On simplifying the equation , we get

ML = 2√61 = 15.62

The measure of ML = measure of JM = 15.62 ( all sides are equal )

The measure of ∠KNL = 90° ( diagonals of a rhombus are perpendicular bisectors )

∠KJL = ∠MJL (diagonals bisect angles)

The measure of ∠KJL = 50°

∠MJK = ∠KJL + ∠MJL = 50 + 50 = 100°

∠MJK = ∠MLK (opposite angles are equal)

The measure of ∠MLK = 100°

∠NJK + ∠JNK + ∠JKM = 180° (sum of angles in triangle)

50 + 90 + ∠JKM = 180

The measure of ∠JKM = 40°

∠JKL = 2 x ∠JKM (diagonal bisect angle)

The measure of ∠JKL = 2 x 40

The measure of ∠JKL = 80°

∠JKL = ∠JML (opposite angles are equal)

The measure of ∠JML = 80°

Hence , the measures of rhombus is solved

To learn more about rhombus click :

https://brainly.com/question/4321700

#SPJ9

The p-value of the test statistic is 0.0401, which is less than the commonly used significance level of 0.05.

In statistical analysis, hypothesis testing is an essential method used to make inferences about population parameters using sample data. In this case, a hospital director wants to test a claim that the percentage of insured patients is less than the expected percentage.

The alternative hypothesis is that the percentage of insured patients is less than the expected percentage. To test this hypothesis, the director will use a one-tailed z-test for proportions. The test statistic is calculated as:

z = (p - P) / √(P(1-P) / n)

where p is the sample proportion, P is the expected proportion under the null hypothesis, and n is the sample size.

In this case, the sample proportion is 115/230 = 0.5, and the expected proportion is not specified. However, since the null hypothesis is that the percentage of insured patients is equal to the expected percentage, we can use the observed percentage of 55% as a reasonable estimate of the expected percentage. Thus, P = 0.55.

Plugging in these values, we get:

z = (0.5 - 0.55) / √(0.55 * 0.45 / 230) = -1.74

p-value = -1.74/0.069 = 0.0401

Trough this one we have identified that the test statistic's p-value is 0.0401, indicating that it is below the widely accepted significance level of 0.05.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true.

To know more about percentage here

https://brainly.com/question/13729841

#SPJ4

Answer:

13.0898597466511 or 13.09

Step-by-step explanation:

The height of the rectangle must be greater than 4 inches if the perimeter of the rectangle is greater than 30 inches.

In geometry, a rectangle is a quadrilateral with four right angles, and opposite sides are equal in length. The perimeter of a rectangle is the total distance around it.

Let's assume that the height of the rectangle is x inches. According to the problem, the base is 7 more than its height, which means the base is (x + 7) inches.

Now, we can calculate the perimeter of the rectangle using the formula:

Perimeter = 2(length + width)

In a rectangle, the length and width are the same as the base and height, respectively. So, in our case, the perimeter of the rectangle will be:

Perimeter = 2(x + (x + 7)) = 4x + 14

As we are given that the perimeter of the rectangle is greater than 30 inches, we can write the inequality:

4x + 14 > 30

Solving for x, we get:

4x > 16

x > 4

To know more about perimeter here.

https://brainly.com/question/6465134

#SPJ4

The Larger number is 8

What is a linear equation in one variable?

The fundamental equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown graphically. A mathematical statement is simply represented by a linear equation.

Given that, the sum of two numbers is 14 and the larger number is four less than twice the smaller number

let the larger number be 'a' and the smaller be 'b'

from the question,

a + b = 14 .....eq 1

a = 2b - 4 .....eq 2

By substituting eq 2 in eq 1:

2b - 4 + b = 14

3b - 4 = 14

3b = 14 + 4 = 18

b = 6

a = 2b - 4 = 2*6 - 4 = 8

Therefore, The two numbers are 8, 4

To learn more about linear equations in one variable, refer to the link below:

https://brainly.com/question/28555579

#SPJ1

The angle that completes the law of cosines is 62°.

Option D is the correct answer.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

The law of cosines in a triangle states that,

c² = a² + b² - 2ab cos C

Where c is the side opposite to ∠C.

Similarly,

a² = b² + c² - 2bc cos A

b² = a² + c² - 2ac cos B

Now,

289 + 64 - 272 cos __ = 15²

17² + 8² - 2 x 17 x 8 cos 62 = 15²

289 + 64 - 272 cos 62 = 15²

Thus,

The angle that completes the law of cosines is 62°.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ9

The complete question.

289 + 64 - 272 cos __ = 15²

Answer:

To find out which rental car company is cheaper, you need to compare the cost for the same number of miles driven. Let's say you drive a total of "m" miles.

The cost for renting a car from Lou's Garage is 50 + 0.1m dollars.

The cost for renting a car from Jerry's Garage is 25 + 0.05m dollars.

To determine which option is cheaper, you need to compare these two expressions and find out which one is less. To do this, you can subtract the second expression from the first expression:

50 + 0.1m - (25 + 0.05m) = 25 + 0.05m

This equation shows that the cost of renting a car from Lou's Garage is 25 + 0.05m dollars more expensive than renting a car from Jerry's Garage for the same number of miles driven. Therefore, Jerry's Garage is the cheaper option.

The only option that represents an object with volume is; Option D: Water Bottle

An object that will have volume is a 3-D object which means that it has length, width and height. Thus, 2D objects cannot have a volume.

Let us access the given options;

A) Baseball diamond: This refers to the baseball field because of the shape of the infield. Thus, it has only length and width and is a 2D shape which doesn't have a volume.

B) Floor Rug: A floor rug, is a plane shape which means it s a 2D shape which doesn't have a volume.

C) A piece of paper: This is a plane shape which means it s a 2D shape which doesn't have a volume.

D) Water Bottle: This is a 3D shape that has length, width and height and as such it has volume.

Read more about Volume of objects at; https://brainly.com/question/463363

#SPJ1

Answer:

x = 1/3

Step-by-step explanation:

64^2x+1 = 1024
4^3(2x+1) = 4^5

Since the bases are the same, two expressions are only equal if the exponents are also equal.

3 (2x + 1) = 5

Divided each term by 3

2x + 1 = 5/3

2x = 2/3

x = 1/3

The probability that the actress will need to attend more than 5 try-outs is approximately 0.478.

Since the outcomes of each try-out are independent,

As per the given information,

Number of try-out is 0.15

probability means the possibilities.

We can model the number of try-outs needed to get an offer as a geometric random variable with the probability of success p = 0.15.

Let X be the number of tryouts needed to get an offer.

Then, X follows a geometric distribution with parameter p=0.15, and the probability of needing to attend more than 5 try-outs is:

[tex]P(X > 5) &= 1 - P(X \leq 5)[/tex]

=[tex]1 - \sum_{k=1}^{5} P(X=k)[/tex]

= 1 [tex]- \sum_{k=1}^{5} P(X=k)[/tex]

= [tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]

=[tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]

=  0.478

Hence the number of possibility required to attend more than 5 try-outs is approximately 0.478.

For such questions on probability

https://brainly.com/question/25870256

#SPJ4

Answer:

Step-by-step explanation:

first, write down on paper 3 5/12 - 8/12 then convert the mixed fraction into a more straightforward form. so 3 5/12 equals 37/12. then you do 37 - 8 = 29 so then change it into a fraction and the answer is 29/12. if you what it as a mixed fraction then it would be 2 5/12

The circumference of a circle is equal to 2π multiplied by its radius. Therefore, the circumference of a circle with a radius of 15 cm is equal to 2π multiplied by 15 cm, or 30π cm.

When the outside temperature is 30°F, the sales is $414.13

When the sale is $1,993.33, the outside temperature is 78°F

Since the equation y = 32.9x - 572.87 can be used to model the relationship between sales at a local ice cream shop, y, in dollars, and the outside temperature, x, in degrees Fahrenheit (F).

Thus, when the outside temperature is 30°F, the sales can be estimated by substituting x = 30°F into the equation and solving for y. That is:

y = 32.9x - 572.87

y =  32.9(30) - 572.87

y = 987 - 572.87

y = $414.13

Thus, when the sale is $1,993.33, the outside temperature can be estimated by substituting y = $1,993.33 into the equation and solving for x. That is:

y = 32.9x - 572.87

1,993.33 = 32.9x - 572.87

32.9x = 1,993.33 + 572.87

32.9x = 2566.2

x = 2566.2/32.9

x = 78°F

Learn more about model equation on:

https://brainly.com/question/29458424

#SPJ1

The probability of both events is the sum minus the intersection. The answer should be rounded to two decimal places.

To calculate the probability of someone using a cell phone while driving or had no speeding violation, first calculate the individual probabilities of each event. The probability of someone using a cell phone while driving is P(cell phone) and the probability of someone having no speeding violation is P(no speeding violation). Then, add these two probabilities together, P(cell phone) + P(no speeding violation). This will give you the total probability of both events occurring. Finally, subtract the probability of the intersection, which is the probability of someone using a cell phone while driving and having no speeding violation. This will give you the total probability of someone using a cell phone while driving or having no speeding violation. Round the answer to the hundredths place.

Learn more about probability here

https://brainly.com/question/30034780

#SPJ4

Answer:

x= 39.549°

Step-by-step explanation:

please review answer.

The value of $×$ is 3.14 units

Perimeter is the distance around the edge of a shape. The algebraic sum of the length of each side is the perimeter of that shape. We have formulas available for the various shapes in geometry.

The perimeter of a square is expressed as 4l

The circumference of a circle = 2πr

This means that;

4l = 2πr

4l = 2× 3.142 × 2

4l = 12.57

divide both sides by 4

l = 12.57/4

l = 3.14 units(nearest hundredth)

therefore the value of the side length is 3.14 units

learn more about perimeter from

https://brainly.com/question/19819849

#SPJ1

The given statement about the disjunction is true.

A compound statement with two distinct statements (disjuncts) connected by the wedge symbol (v) is called Disjunction.

Given is the statement -

(S~T) v (~U.W)

The given statement about the disjunction is true.

Therefore, the given statement about the disjunction is true.

To solve more questions on disjunctions, visit the link below -

https://brainly.com/question/20893557

#SPJ1

Answer: To find out how much you would pay for 2.5 kg of tomatoes at $1.50 per kg, we need to multiply the weight of the tomatoes by the price per kg:

Cost = 2.5 kg x $1.50/kg

   = $3.75/kg x 2.5 kg

   = $9.38

So, you would pay $9.38 for 2.5 kg of tomatoes at $1.50 per kg.

Step-by-step explanation:

Answer:

r = 8

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

given a₁ = 3 and a₃ = 192 , then

a₁ = 3 → (1)

a₁r² = 192 → (2)

divide (2) by (1) on both sides

[tex]\frac{a_{1}r^2 }{a_{1} }[/tex] = [tex]\frac{192}{3}[/tex] ( cancel a₁ on numerator/ denominator of left side ), then

r² = 64 ( take square root of both sides )

r = [tex]\sqrt{64}[/tex] = 8

Mackenzie's reimbursement for a business trip would be $736.50 per mile when she drives of a total of 982 miles with $0. 75 per mile.

Mackenzie's reimbursement for driving 982 miles for business can be calculated by multiplying the number of miles driven by the reimbursement rate per mile.

Mackenzie's company reimburses her $0. 75 per mile which is rate per mile.

Reimbursement = miles driven x rate per mile

Filling the value in above equation.

So,

Reimbursement = 982 miles x $0.75/mile

Reimbursement = $736.50

Therefore, Mackenzie's reimbursement for driving 982 miles with the rate of $0. 75 per mile for business would be $736.50.

To know more about reimbursement :

https://brainly.com/question/25307180

#SPJ4

3 is the minimum number of guesses required to guarantee that you know the number.

If we use a binary search approach, we can guess the number in a minimum number of steps.

First, we guess the middle number, which is 8. If the answer is higher, we can eliminate all the numbers from 1 to 8, because they are lower than the answer.

Then we guess the middle number of the remaining numbers, which is 12. If the answer is lower, we can eliminate all the numbers from 12 to 15, because they are higher than the answer.

We have now eliminated half of the remaining numbers, and we are left with 6 and 7. We can guess either of these numbers, and we will know the answer with a total of three guesses.

Therefore, we can guarantee that we know the number in three guesses using this binary search approach.

To learn more about minimum here:

https://brainly.com/question/21426575

#SPJ4

Bob needs to buy 500 kg of sand.

What is the ratio?

A ratio is a quantitative relationship between two numbers, quantities, or values that expresses how many times one is contained in the other. Ratios are typically expressed in the form of "a to b" or "a:b" and can be represented as fractions or decimals.

Since the ratio of cement to sand to stone is 1:2:3 by weight, the total weight of the ingredients needed to make one bag of dry concrete is:

Cement: 1/6 of 30 kg = 5 kg

Sand: 2/6 of 30 kg = 10 kg

Stone: 3/6 of 30 kg = 15 kg

To make 50 bags of dry concrete, Bob will need 50 times these amounts:

Cement: 5 kg x 50 = 250 kg

Sand: 10 kg x 50 = 500 kg

Stone: 15 kg x 50 = 750 kg

Hence, Bob needs to buy 500 kg of sand.

To learn more about the ratios, visit:

https://brainly.com/question/12024093

#SPJ1

To get 77 marks on a quiz the student has to spend approximately 3 hrs.

The expected quiz score if a student spends no time on homework is 55.

What is meant by a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, occasionally referred to as a "linear equation of two variables."

It is given that y = 7.2x + 55

where y is the expected quiz score.

x is the number of hours spent on homework that week.

If the value of y=77

77=7.2x+55

22=7.2x

x is approximately 3 hrs.

If the student spends no time on their homework:

x=0

y=0+55

y=55.

Therefore to get 77 marks on a quiz the student has to spend approximately 3 hrs.

The expected quiz score if the student spends no time on home work is 55.

To learn more about linear equations, refer to the link below:

https://brainly.com/question/2030026

#SPJ1

Answer:

2,2 but i could be wrong

Just wanted to say he's correct, it's 2, 2

The graplh shows that it will take 3.33 weeks to pay up the money borrowed

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function as as follows

c = money borrowed from your parents =  $50.00

m = you are paid $15 per week to walk the dog for 20 minutes each weekday = $15

x = number of weeks

y = amount remaining

The equation is

y = 15x - 50

From the graph the pay will be completed at x = 3.33 (3.33, 0)

Learn more on  linear models at :

https://brainly.com/question/29650903

#SPJ1

a. The percentage of the department faculty have 5 or more years of service is 76%

b. Probability that a faculty member chosen at random has between 5 and 35 years of service is 0.4.

c. The probability the representative will have less than 5 years of service given that the person has less than 15 years of service is 0.7.

The histogram is used to estimate probability of a categorical variable or probability of frequency of a particular class interval, and there is no gap among the bars of the histogram.

(a) The per cent of the department faculty have 5 or more years of service is calculated as follows,

The number of department faculty have 5 or more years of service is 38 and total frequency 50, therefore the required probability is:

P(x > 5) = 38/50 = 0.76 = 76%

(b) The probability (in decimal form) of representative will have between 5 and 35 years of service is given as,

P(5 < X < 35) = 20/50 = 0.4 = 40%

(c) The probability the representative above will have less than 5 years of service given that the person has less than 15 years of service is calculated as follows,

P(X < 5 | X < 15) = 28/40 = 0.7

Learn more about Histogram at:

https://brainly.com/question/30354484

#SPJ4

For complete question, see the figure.

Answer:

20×5=100

380-100=280

280÷120=2 and 40 remain

40÷20=2

Answer:

213 ft^2

Step-by-step explanation:

In this problem, we can create a larger rectangle that engulfs this image with a few missing pieces on the corners. The area of that rectangle would be 18ft * 17 ft = 306 ft^2. The sum of the missing pieces is 2ft * 7ft + 5ft * 6 ft + 7ft * 7ft  = (14 + 30 + 49)ft^2 = 93 ft^2. So, the area of this figure is 306 - 93 = 213 ft^2

ANSWER: S=173ft^2

_._._._._._._._._._._._.