The rate of change and the initial value are given as -5 and 27 respectively.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
Given that,
The points for the given linear function are given as (0, 27) and (5, -8) respectively.
The rate of change is equivalent to the slope of the straight line and is given as,
(-8 - 27)/(5 - 0) = -35/7 = -5
Now, the equation of the function can be written as,
(y - 27)/(x - 0) = -5
=> y - 27 = -5x
=> y = -5x + 27
The initial value is given at x = 0 as below,
y = -5 × 0 + 27
= 27
Hence, the rate of change for the function is -5 and its initial value is 27.
To know more about straight line equation click on,
brainly.com/question/21627259
#SPJ2
In the fiscal year of 1991-1992, a total of 109,782 child labor permits were issued, 2/3 of which were males. The monthly average for males is?
Final answer:
The monthly average for males who received child labor permits in the fiscal year of 1991-1992 is approximately 6,099, calculated by multiplying the total permits (109,782) by 2/3 and then dividing by 12 months.
Explanation:
To calculate the monthly average for males who received child labor permits in the fiscal year of 1991-1992, we first determine the total number of permits issued to males. Since 2/3 of the total permits were issued to males, we multiply the total number of permits, 109,782, by 2/3:
Total permits for males = 109,782 * (2/3) = 73,188
There are 12 months in a fiscal year, so to find the monthly average, we divide the total permits for males by 12:
Monthly average for males = 73,188 / 12 ≈ 6,099
Therefore, the monthly average number of child labor permits issued to males was approximately 6,099.
What is the constant of proportionality for the ratios 2 to 3 and 4 to 6?
Answer:2/3
Step-by-step explanation:
Help!!!!!!
A sporting goods store marks up the cost s of soccer balls by 250%. Write an expression that represents the retail cost of the soccer balls. The store buys soccer balls for $5.00 each. What is the retail price of the soccer balls?
(you have to do a expression)
write 91.4 million in both standard form and in scientific notation
91.4 million in standard form is 91400,000.
To express 91.4 million in standard form,
We simply write the number as it is: 91,400,000.
In this form, each place value is clearly represented by its corresponding digit.
In scientific notation, we express the number as a product of a decimal number between 1 and 10, multiplied by a power of 10. For 91.4 million,
It can be written as 9.14 x 10⁷.
In this notation, the decimal point is placed after the first digit, and the power of 10 represents the number of places the decimal point should be moved to the right to obtain the original value.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ6
A person's blood glucose level and diabetes are closely related. let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean m 85 and standard deviation s 25 (diagnostic tests with nursing implications, edited by s. loeb, springhouse press). note: after 50 years of age, both the mean and standard deviation tend to increase. what is the probability that, for an adult (under 50 years old) after a 12-hour fast,
What's the circumference of a circle with a diameter of 30 cm
If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 36 inches, what diameter pizza will reward you with the largest slice? in
We start by expressing the circumference and the size of the slice in terms of the pizza's radius. By setting the pizza slice to be the largest (having an angle of 2π at the centre), we find the radius and hence the diameter of the pizza.
Explanation:The question falls into the area of Circle Geometry. Let's say the radius of the pizza is r inches, the length of the crust is a, and the length of the two straight edges of the pizza slice (each of which is a radius of the circle) are both r.
According to the problem, the perimeter of the pizza slice is given as 36 inches. This sums up the two radii and the length of the crust (a). Therefore, 2r + a = 36.
We know that the crust's length is a fraction of the total circumference of the circle. The whole circle's perimeter is 2πr.
Assuming the angle at the center of the pizza slice is θ (in radians), we have a = θr. θ will be a fraction of 2π depending on the size of the slice.
Substituting θr for a in the equation 2r + a = 36, we get 2r + θr = 36. To get the largest slice, θ has to be as large as possible, 2π.
Replace θ with 2π, we have 2r + 2πr = 36. Solve for r and we find that r = 36/(2+2π). That gives the radius of the pizza. Multiply r by 2 will give us the diameter of the pizza.
Learn more about Circle Geometry here:https://brainly.com/question/27802544
#SPJ12
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 210 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.
The length of the garden is 63 feet and the width is 42 feet.
Explanation:Let's assume that the length of the garden is x feet. According to the problem, the width is two-thirds of the length, so the width is (2/3)x feet.
The perimeter of a rectangle is given by the formula P = 2(l+w), where P is the perimeter, l is the length, and w is the width. In this case, the perimeter is 210 feet, so we have the equation 210 = 2(x + (2/3)x).
Simplifying the equation, we get 210 = 2(5/3)x. By dividing both sides by 2, we find that (5/3)x = 105. Finally, solving for x, we get x = 105 * (3/5) = 63 feet. Therefore, the length of the garden is 63 feet, and the width is (2/3) * 63 = 42 feet.
solve 3x=12? 5,36,4,or 3
1.5 4.5 13.5 40.5.... what is the seventh term in the sequence?
The seventh term in the sequence is 1093.5.
What is Sequence?A sequence in mathematics is a ordered set od objects or numbers which are related with something.
For example, 1, 3, 5, ..... is a sequence of odd numbers.
Given sequence is,
1.5, 4.5, 13.5, 40.5....
There must be a predictable relation between the numbers in order for them to form in a sequence.
It is clear that,
First term = 1.5
Second term = 3 × 1.5
Third term = 3 × 3 × 1.5 = 1.5 (3)²
............
nth term = 1.5 (3)ⁿ⁻¹
seventh term = 1.5 (3)⁷⁻¹ = 1.5 (3)⁶ = 1093.5
Hence the seventh term is 1093.5.
Learn more about Sequences here :
https://brainly.com/question/21961097
#SPJ3
Joe completed 28 math problem from his homework. Joe has done 80% of his homework. How many more math problem does Joe have to complete
0% = 0.8
divide 28 by 0.8
28 / 0.8 = 35 total questions
35 -28 = 7 more questions to do
The ratio of red poms to yellow poms on a float is 5 to 7. If there are 392 yellow poms on the float, how many red poms are there? *
what are partial products of 374 times 510
the back of a moving truck is 4 feet above the ground. A ramp extending from the back of the truck meets the ground 10 feet from the truck. What is the slope of the ramp?
Answer:
20 feet
Step-by-step explanation:
How would you Evaluate. 5⋅4 ^0
the change in the x-coordinates of any two points on a line in the xy-plane is the
Answer
D the run. AP3X
−8x+4y=24
−7x+7y=28
What is the solution?
The Museum of Science in Boston has an exhibit in which metal balls drop down a chute, bounce around, and wind up in one of 21 bins. After 1000 balls have dropped, the heights within the bins clearly follow a bell-shaped curve. The standard deviation is 3 bins.
About how many balls are in bins 1 through 17?
Using the Empirical Rule, we can estimate that about 95% of the balls (950 balls) will fall within the first 17 bins of the bell-shaped distribution, with a standard deviation of 3 bins.
To determine how many balls are in bins 1 through 17 at the Museum of Science in Boston, we can apply the Empirical Rule to the bell-shaped distribution of balls in bins.
Since we have a standard deviation of 3 bins, and a bell-shaped curve approximates a normal distribution, about 95% of the data (balls) will be within two standard deviations of the mean.
Assuming approximately equal distribution across the bins and a large number of trials, bins 1 through 17 would contain slightly less than 95% of the balls, as they represent less than two standard deviations from the mean.
Here is a rough estimate:
Total balls: 1000
Two standard deviations: 95% of 1000 balls = 950 balls
Bins 1 through 17 contain slightly less than 950 balls.
Without the exact mean, we cannot provide a precise number, but we can conclude that about 950 balls will be distributed in bins 1 through 17, give or take, based on the data provided and properties of the normal distribution.
A construction crew needs to build a road that will be 20 miles long. The crew already completed a stretch that is 6.44 miles long and another that is 8.62 miles long.
How much more road does the construction crew need to build?
(A) 2.18 miles
(B) 4.94 miles
(C)11.38 miles
(D)13.56 miles
In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. Three of the 8 are in one family, and want to sit together. How many ways can this happen?
Since 3 members want to sit together, we'll calculate total ways for it and then for remaining seats in each of its case, we'll see in how many ways can those rest of 5 people wants to sit.
The total number of ways those 8 people can sit is 3,991,680 ways.
Given that:Total 14 seats are there in a row in a doctor's waiting room.8 people are waiting to be seated.3 people are of same family and want to sit together.To find:In how many ways can those people sit?
Number of ways in which 3 family members can sit:Since 3 people wants to sit together, then suppose seats are numbered 1,2,3,...,14.
Then those 3 people can choose seats as:
1,2,3
2,3,4
...
...
12,13,14
Total 12 ways.
In each way, those three can sit on those 3 chairs in any order. The number of ways 3 people will arrange themselves is 3! = 6 ways.
Thus:
Total ways those 3 people can sit in = 12 times 6 = 72 ways.
( i did multiplication since for each of 3 seat chosen they were sitting in 6 ways, and this repeated 12 times would end up on 12 times 6 = 72 ways).
Number of ways those remaining 5 people can sit on remaining 11 seats:On remaining seats (14-3 = 11), we have 5 people to sit.
Those people can choose any seat they want to sit on.
Total ways(combinations) they together choose 5 seats is given by: [tex]^11C_5 = 462 [/tex]
For each of those choice of seats, they can arrange themselves in 5! = 120 ways.
Thus, those 5 people can sit in 120 times 464 = 55440 ways.
Since on each choice of those 3 family members , we have 55440 ways of 5 people sitting on remaining 11 seats, thus in total we have:
55440 times 72 = 3,991,680 ways.
Thus, in total, those 8 people can sit in 3,991,680 number of ways in that row of the doctor's waiting room.
Learn more about combinations here:
https://brainly.com/question/10618762
After entering the test scores from her statistics class of 25 students, the instructor calculated the mean and the median of the scores. upon checking, she discovered that the toptop score entered was 73, but it should have been 83. when she corrects this score, how will the mean and median be affected?
what is the volume of a tank that can hold 18 754 Kg of methanol whose density is 0.788g/cm3
The volume of a tank is 23.8m3
that can hold 18 754 Kg of methanol whose density is 0.788g/cm3
Using this formula
Volume=m/p
Let plug in the formula
Volume=18,754 kg/0.788g/cm3
Volume=18,754,000g/0.788g/cm3
Volume=23,799,4924cm2
Volume=23.8m3 (Approximately)
Inconclusion The volume of a tank is 23.8m3.
Learn more here:
https://brainly.com/question/12374560
Order the fractions from least to greatest 5/8, 3/4, 1/2, 9/16
What is 1/5 + 2/3 plz answer this
A grocer has two kinds of tea, one selling for 80 cents per pound and the other selling for 60 cents per pound. How many pounds of each kind must he use to make 50 pounds of tea that will sell for 74 cents per pound?
Answer, There is need to use 35 pounds of 80 cents tea and 15 pounds of the 60 cents tea.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
here, we have,
Imagine what x is tea grocer selling for 80 cents per pound
y is tea grocer selling for 60 cents per pound
{80x+60y
=50*74
=3700
{x+y=50 //*60
{80x+60y=3700
-{60x+60y=3000
20x=700
x=35
y=50-35=15
hence, Answer, There is need to use 35 pounds of 80 cents tea and 15 pounds of the 60 cents tea.
To learn more on percentage click:
brainly.com/question/13450942
#SPJ3
Two well-known aviation training schools are being compared using random samples of their graduates. it is found that 70 of 140 graduates of fly-more academy passed their faa exams on the first try, compared with 104 of 260 graduates of blue yonder institute. in a two-tailed test, the p-value is .0275, so at = .025 we should:
Final answer:
With a p-value of .0275 being greater than the significance level of .025, the decision in a two-tailed test would be to not reject the null hypothesis, indicating insufficient evidence to show a significant difference between the two schools' FAA exam pass rates.
Explanation:
The student is given information about the performance of the graduates from two aviation training schools regarding FAA exam pass rates on the first try. The pass rates are compared using a statistical hypothesis test, and the p-value from this test is .0275. When the level of significance (α) is set at .025, and we are conducting a two-tailed test, we should make a decision about whether to reject or not reject the null hypothesis.
Since the p-value (.0275) is greater than the level of significance (α = .025), the correct decision would be not to reject the null hypothesis. It means that there's not enough statistical evidence to show a significant difference between the FAA exam pass rates of the two schools at the .025 level of significance. This matches the general hypothesis testing rule: if the p-value is less than α, reject the null hypothesis; otherwise, do not reject it.
In the marching band at Hometown High, there are 77 woodwinds and 88 brass. If there is an equal number of woodwind and brass musicians in each row, what is the greatest number of rows in a performance? A) 9 rows B) 11 rows C) 13 rows D) 15 rows
Write four decimals with the digit four in a different place in each ones, tenths , hundredths, and thousandths .Then write a statement that compares the value of the digit 4 in the different decimals
Spring stretches by 21.0 cm when a 135 n object is attached. what is the weight of a fish that would stretch the spring by 62.1
Answer:
399.21 newtons or 40.73 kg
Step-by-step explanation:
In order to solve this you first have to do a rule of threes to calculate how much would the fish will weight compared with the stretching of the spring:
[tex]\frac{21}{162} =\frac{62.1}{weight} \\weight=\frac{62.1*162}{21}=399.21 Newtons[/tex]
So the weight would be 399.21 newtons and it would have 40.73 kilograms in mass.
Find the partial derivatives of the function w=4r2+6s2+