Answer:
[tex]y = mx+b[/tex]
[tex] m =\frac{y_2 -y_2}{x_2 -x_1}[/tex]
[tex] b = y_1 -m x_1[/tex]
Or equivalently:
[tex] b = y_2 - m x_2[/tex]
Step-by-step explanation:
If we are assuming that we have:
x independent variable
y dependent variable
And we want to find an equation of the line, we have the following general expression:
[tex]y = mx+b[/tex]
Where m represent the slope and b the y intercept. The general formula for the slope is given by:
[tex] m =\frac{y_2 -y_2}{x_2 -x_1}[/tex]
Where [tex] (x_1,y_1) , (x_2,y_2)[/tex] are the minimum required points in order to estimate the slope.
In order to find the y intercept we just need to use one of the points selected [tex] (x_1,y_1) , (x_2,y_2)[/tex] and we can solve for b like this:
[tex] b = y_1 -m x_1[/tex]
Or equivalently:
[tex] b = y_2 - m x_2[/tex]
The points (4, -11) and (8, r) lie on a line with slope 2. Find the missing coordinate r.
Following steps and calculations, the missing coordinate r is -3. This point lies on line with slope of 2 along with other given point (4, -11).
Step-by-Step Calculation:
1. Identify the slope formula:
The slope (m) of a line passing through points (x1, y1) and (x2, y2) is calculated as:
m = (y2 - y1) / (x2 - x1)
2. Plug in known values:
We know the slope (m) is 2, points (x1, y1) are (4, -11), and points (x2, y2) are (8, r). Substitute these values:
2 = (r - (-11)) / (8 - 4)
3. Simplify the equation:
2 = (r + 11) / 4
2 × 4 = r + 11
8 = r + 11
4. Isolate r:
8 - 11 = r
r = -3
Rhombus ABCD, with side length 6, is rolled to form a cylinder of volume 6 by taping side AB to side DC. What is sin(angle ABC)?
Final answer:
To find the sine of angle ABC, we need to first find the length of the arc BC, which is equal to the circumference of the resulting cylinder. The circumference can be found by multiplying the diameter of the rhombus, which is equal to the length of side AB, by π (pi). In this case, the circumference is 6π. Using the length of the arc, BC, and the radius of the cylinder, we can find the angle ABC using the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the cylinder.
Explanation:
To find the sine of angle ABC, we need to first find the length of the arc BC, which is equal to the circumference of the resulting cylinder. The circumference can be found by multiplying the diameter of the rhombus, which is equal to the length of side AB, by π (pi). In this case, the circumference is 6π. Since the volume of the cylinder is given as 6, we can use the formula V = πr^2h to find the height of the cylinder. Plugging in the values, we get 6 = πr^2h. Since the radius of the cylinder is half the length of side AB, which is 3, we can solve for h to find that h = 4/π. Using the length of the arc, BC, and the radius of the cylinder, we can find the angle ABC using the formula θ = s/r, where θ is the angle in radians, s is the length of the arc, and r is the radius of the cylinder. Plugging in the values, we get θ = 6π/3 = 2π.
A national polling organization wants to estimate the percentage of all teenagers who believe social security will 'be there' for them. The organization surveys a random sample of 1500 teenagers, and 37% of this sample says that they believe social security will 'be there' for them. In this survey, what is the population of interest?
A) The people in the sample who believe social security will 'be there' for them.B) All teenagers.C) The 1500 teenagers who were surveyed.D) Teenagers who believe social security will 'be there' for them.
Answer: B) All teenagers.
Step-by-step explanation:
In statistical survey , a population is a large group of individuals that share some similar characteristics according to the researchers's point of view or the demand of the study.
When the population very large , then he take a sample of population that represents the whole population.
For example : If a researcher wants know the average weight of women in the university , he will need the data of all women in university which is the population for this study.
As per given : A national polling organization wants to estimate the percentage of all teenagers who believe social security will 'be there' for them.
Here , the population of interest : All teenagers.
Sample : 1500 teenagers
37% : sample proportion of teenagers says that they believe social security will 'be there' for them.
Hence, the correct answer is : B) All teenagers.
Out of 229 racers who started the Eugene marathon, 208 completed the race, 17 gave up, and 4 were disqualified. What percentage of racers did not complete the marathon?
Answer:
9.17% of racers did not complete the marathon.
Step-by-step explanation:
Consider the provided information.
Out of 229 racers who started the Eugene marathon.
208 completed the race, 17 gave up 4 disqualified .
Then total racers who could not complete the marathon is
229-208=21
Now calculate the percentage:
[tex]Percentage=\frac{21}{229}\times 100\\\\Percentage=\frac{2100}{229}\\\\Percentage\approx9.17[/tex]
Hence, 9.17% of racers did not complete the marathon.
Using a metric line, convert the following metric measurement. (Remember to use the same number of significant figures as in the original measurement.) 505 kL expressed in La. 50,500 Lb. 505,000 Lc. 5,050 Ld. 50.5 L
Answer:
B
Step-by-step explanation:
This question is asking to make a conversion from kilolitres to liters.
There is a total of 1000L in 1kL.
Hence to make the conversion from KL to L , we have to multiply the KL by 1000. Hence, for 505KL, its equivalent measurement in L would be 505 * 1000 = 505,000
Hence, 505kL expressed in L is 505,000
)Which polynomial functions have only the roots 1 and 6? Check all that apply.
f(x) = (x – 1)(x – 6)
f(x) = 3(x + 1)(x + 6)
f(x) =(3x – 1)(x – 6)
f(x) = 3(x – 1)(x – 6)
f(x) = 6(x – 1)(x – 6)
the answer is:
f(x) = (x – 1)(x – 6)
f(x) = 3(x – 1)(x – 6)
f(x) = 6(x – 1)(x – 6)
so all you little snow flakes sayin aaahhh no its this aahh no its that sfu cause i just took the evaluation.
Answer:
a,d,e
Step-by-step explanation:
x=1,x-1=0
x=6
x-6=0
if 1,6 are roots then (x-1) and (x-6) are factors of f(x)
Answer:a,d,e
Step-by-step explanation:
When there is a _____ relationship, as values of variable X (e.g., income) increase, values of variable Y (e.g., education level) also increase.
Answer:
When there is a positive relationship, as values of variable X (e.g., income) increase, values of variable Y (e.g., education level) also increase.
Step-by-step explanation:
Consider the provided information.
It is given that the value of variable x increase, and value of variable y also increase.
A positive relationship is when the values increase together or we can say that the value both variable tends to move in same direction. If the value of x increase then the value of y is also increase.
A Negative relationship is when one value decreases as the other increases. Or we can say that the value of x increase the value of y decrease.
Hence, the provided relationship is positive as both values moves in same direction.
When there is a positive relationship, as values of variable X (e.g., income) increase, values of variable Y (e.g., education level) also increase.
Car A travels 702 miles on 12 gallons of gasoline car b travels 873 miles and 15 gallons of gasoline David wants to buy a car with the lowest fuel canister find out the distance traveled by each car per gallon of gasoline then tell which of the two cars AorB David should by
David should buy Car A because it covers more miles in one gallon than Car B
Step-by-step explanation:
Given
Distance traveled by Car A = [tex]d_A = 702\ miles[/tex]
Gallons used by Car A = [tex]g_A = 12[/tex]
Distance traveled by Car B = [tex]d_B = 873\ miles[/tex]
Gallons used by Car B = [tex]g_B = 15[/tex]
In order to find the distance traveled on one gallon, we will divide the total distance by number of gallons
So,
Distance traveled by Car A in one gallon = [tex]\frac{702}{12} =58.5\ miles\ per\ gallon[/tex]
Distance traveled by Car B in one gallon = [tex]\frac{873}{15} = 58.2\ miles\ per\ gallon[/tex]
We can see that Car A travels more distance in one gallon that is 58.5 miles per gallon
So,
David should buy Car A because it covers more miles in one gallon than Car B
Keywords: Fractions, Unit rate
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Car A gets 58.5 miles per gallon, Car B gets 58.2 miles per gallon. David should buy Car A.
Car A: Travels 702 miles on 12 gallons = 702 miles/12 gallons = 58.5 miles per gallon
Car B: Travels 873 miles on 15 gallons = 873 miles/15 gallons = 58.2 miles per gallon
David should buy Car A as it has a slightly higher fuel efficiency of 58.5 miles per gallon compared to 58.2 miles per gallon for Car B.
A college bookstore marks up the price that it pays the publisher for a book by 35 %. If the selling price of a book is $ 87.00 comma how much did the bookstore pay for this book?
Answer:the amount that the bookstore pay the publisher for the book is $64.4
Step-by-step explanation:
Let x represent the amount that the bookstore pay the publisher for the book.
The college bookstore marks up the price that it pays the publisher for a book by 35%. This means that the value of the mark up would be
35/100 × x = 0.35 × x = 0.35x
Therefore, the amount that the bookstore is selling the book would be
x + 0.35x = 1.35x
If the selling price of a book is $ 87.00, then it means that
1.35x = 87
x = 87/1.35 = 64.4
I don't understand how to solve these problems, someone please explain.
Answer:
Step-by-step explanation:
When two triangles are similar, it means that the ratio of their corresponding sides is equal.
Therefore
96/(6x + 28) = 24/25
Crossmultiplying,
1) 96 × 25 = 24(6x + 28)
2400 = 144x + 672
144x = 2400 - 672 = 1728
x = 1728/144
x = 12
2) angle A and angle D is equal because they are alternate angles.
(2x + 6)/(x + 6) = 10/8
Crossmultiplying
8(2x + 6) = 10(x + 6)
16x + 48 = 10x + 60
16x - 10x = 60 - 48
6x = 12
x = 12/6 = 2
3) both triangles are right angle triangles. All angles are similar in both triangles. It also means that all the sides are similar. Therefore
45/30 = 40/x
Crossmultiplying
45 × x = 30 × 40
45x = 120
x = 120/45 = 26.7
In a study commuting patterns of people in a large metropolitan area, respondents were asked to report the time they took to travel to their work on a specific day of the week. What is the individual?a. travel timeb. a personc. day of the weekd. city in which they lived
Answer:
b. a person
Step-by-step explanation:
The conducted study demonstrates the commuting patterns of people. Here, the information is collected from a person about amount of time consumes in travel to their work on a certain day of the week. Thus, here the individual is "a person" because the information is collected from a person about their time travel.
The science club is raising money for a trip to the museum. Tickets to the museum cost $8. Five students already have a membership to the museum, so they will get in for free. The club raised the $296 needed to take all students in the club to the museum.
Answer:there are 42 students in the club.
Step-by-step explanation:
Let s represent the number of students in the club.
Tickets to the museum cost $8. Five students already have a membership to the museum, so they will get in for free. The club raised the $296 needed to take all students in the club to the museum. This means that
8(s - 5) = 296
8s - 40 = 296
8s = 296 + 40 = 336
s = 336/8
s = 42
Jamie bought a load of gravel to cover her driveway. Her brother works for the gravel company and got her a 28% discount. If Jamie paid $357.83 for the gravel (without tax), what would it have cost her without the discount?
Answer:without the discount, it would have cost her $497
Step-by-step explanation:
Let x represent the amount that the gravel would have cost her without the discount.
Her brother works for the gravel company and got her a 28% discount. The value of the discount would be
28/100 × x = 0.28 × x = 0.28x
It mans that the amount that she paid for the gravel is
x - 0.28x = 0.72x
If Jamie paid $357.83 for the gravel (without tax), it means that
0.72x = 357.83
x = 357.83/0.72
x = 496.99
Approximately $497
In year 1, nominal GDP for the United States was $2,250 billion and in year 2 it was $2,508 billion. The GDP deflator was 72 in year 1 and 79 in year 2. Between year 1 and year 2, real GDP rose by:
Answer:
1.6%
Step-by-step explanation:
The real GDP is given by the nominal GDP divided by the GDP deflator, the real GDP for year 1 and year 2, respectively, were:
[tex]GDP_1=\frac{2250}{0.72}\\GDP_1=\$3,125\ billion\\\\GDP_2=\frac{2,508}{0.79}\\GDP_2=\$3,174.68\ billion[/tex]
The percentage change in GDP is:
[tex]P=\frac{3,174.68-3,125}{3,125}\\ P=0.016=1.6\%[/tex]
Between year 1 and year 2, real GDP rose by 1.6%.
A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is fi ve feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile?
Answer:
46 jumps
Step-by-step explanation:
Since the grasshopper is two inches long, and can jump a distance of 40 inches, then its jump ratio is 2:40 = 1:20.
The athlete's body-length is 5 feet 9 inches. We convert this to inches which is 5 × 12 = 60 inches. We then add the remaining 9 inches to make it 60 + 9 = 69 inches. Since our jump ratio for the grasshopper equals that for the athlete, 1:20 = 69: 20 × 69= 69 : 1380. Thus the athlete's jump ratio is 69 inches to 1380 inches.
The athlete wants to cover one mile and we know that 1 mile = 63360 inches. So, we divide the distance the athlete wants to cover(1 mile = 63360 inches) by his jump-length(1380 inches) to get the number of jumps it takes to cover a mile. Number of jumps × jump-length of athlete = one mile, so Number of jumps = one mile/jump-length of athlete = 63360 inches/ 1380 inches= 45.9 jumps ≈ 46 jumps.
It would take the athlete approximately 46 jumps to cover one mile.
To solve this problem, we'll start by establishing the jumping ratio of the grasshopper and then applying that ratio to the athlete to determine how many jumps it would take for the athlete to cover one mile.
First, let's calculate the jump ratio for the grasshopper:
- Grasshopper's length: 2 inches
- Grasshopper's jump length: 40 inches
The ratio of the grasshopper's jump length to its body length is:
[tex]\[ \text{Jump ratio} = \frac{40 \text{ inches}}{2 \text{ inches}} = 20 \][/tex]
Next, let's find the athlete's height in inches:
- Athlete's height: 5 feet 9 inches
- 1 foot = 12 inches
Thus, the athlete's height in inches is:
[tex]\[ 5 \text{ feet} \times 12 \text{ inches/foot} + 9 \text{ inches} = 60 \text{ inches} + 9 \text{ inches} = 69 \text{ inches} \][/tex]
Using the grasshopper's jump ratio, we can determine the distance the athlete could jump:
[tex]\[ \text{Athlete's jump length} = 69 \text{ inches} \times 20 = 1380 \text{ inches} \][/tex]
Now, we need to determine the total number of jumps the athlete would need to cover one mile. First, convert one mile to inches:
- 1 mile = 5280 feet
- 1 foot = 12 inches
Therefore, the distance of one mile in inches is:
[tex]\[ 5280 \text{ feet} \times 12 \text{ inches/foot} = 63360 \text{ inches} \][/tex]
Finally, the number of jumps required for the athlete to cover this distance is:
[tex]\[ \text{Number of jumps} = \frac{63360 \text{ inches}}{1380 \text{ inches/jump}} \][/tex]
Calculating this value:
[tex]\[ \text{Number of jumps} \approx \frac{63360}{1380} \approx 45.92 \][/tex]
Since the number of jumps must be a whole number, we round 45.92 to the nearest whole number:
[tex]\[ \text{Number of jumps} \approx 46 \][/tex]
Therefore, it would take the athlete approximately 46 jumps to cover one mile.
A rectangular painting measures 15 inches by 18 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 90 inches. Determine the width of the frame.
To determine the width of the frame, subtract twice the frame width from the length and width of the outer rectangle and set up an equation based on the perimeter.
Explanation:To determine the width of the frame, we need to first find the dimensions of the inner rectangle formed by the painting. If we subtract twice the frame width from the length and width of the outer rectangle, we get the length and width of the inner rectangle. Let's call the width of the frame 'x'.
The length of the inner rectangle is 15 inches - 2 inches, and the width of the inner rectangle is 18 inches - 2 inches. The perimeter of the inner rectangle is the sum of its four sides, which can be calculated using the
formula P = 2l + 2w. We know that the perimeter of the inner rectangle is 90 inches, so we can set up the equation:
90 = 2(15 - 2x) + 2(18 - 2x)
Solving this equation will give us the value of 'x', which represents the width of the frame.
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Five pounds of candy that is 20% chocolate is combined with a candy that is 40% chocolate. How many pounds of the candy that is 40% chocolate should be used to get a candy that is 25% chocolate?
Answer:
5/3 pounds
Step-by-step explanation:
Five pounds of candy that is 20% chocolate is combined with a candy that is 40% chocolate
Let x be the pounds of candy that is added with 40% of chocolate
5 pounds that is 20%. 20% = 0.2
x pounds that is 40%. 40% = 0.4
mixture is x+5 pounds that is 25%. 25%= 0.25
[tex]0.2(5)+0.4x=0.25(x+5)[/tex]
[tex]1+0.4x=0.25x+1.25[/tex]
Subtract .25x from both sides
[tex]1+0.15x=+1.25[/tex]
Subtract 1 from both sides
[tex]0.15x=0.25[/tex]
divide both sides byu 0.15
x=5/3 pounds
Popcorn is now available in two different cups at a theater; a square pyramid or a cone. They have the same height of 20 cm. The price of each cup is the same. Which cup is the better deal?
Answer:
Square pyramid cup is better deal then Cone cup.
Step-by-step explanation:
Diagram is missing in the question we have attached diagram for your reference.
Given:
height of square pyramid = 20 cm
height of cone = 20 cm
Base of square pyramid = 12 cm
diameter of cone = 12 cm
radius of cone is half of diameter.
radius of cone = [tex]\frac{diameter}{2}=\frac{12}{2} = 6\ cm[/tex]
We need to find the which cup is the better deal.
Solution:
We will first find the volume of both cups and then we can say the the one which has greater volume is the better deal in buying.
Volume of square pyramid is calculated by one third times square of the base times height.
framing in equation form we get;
Volume of square pyramid = [tex]\frac{1}{3}\times 12^2\times20= 960\ cm^3[/tex]
Now we know that;
Volume of cone is calculated by one third times square of the radius times height times π.
framing in equation form we get;
Volume of cone = [tex]\frac{1}{3}\pi r^2h= \frac{1}{3}\pi\times 6^2\times 20 \approx 754cm^3[/tex]
Now we can see that;
Volume of square pyramid cup which [tex]960\ cm^3[/tex] is greater than Volume of cone cup [tex]754\ cm^3[/tex]
Hence Amount of popcorn will be more in square pyramid cup then in cone cup.
Hence Square pyramid cup is better deal then Cone cup.
You are visiting baltimore, MD and a taxi company charges a flat fee of 3.00 for using the taxi and 0.75 per mile. How much woks a taxi ride for 8 miles cost
Answer: the cost of riding the taxi for 8 miles is $9
Step-by-step explanation:
The taxi company charges a flat fee of 3.00 for using the taxi and 0.75 per mile. This means that the total cost of using the taxi and travelling x miles would be
3 + 0.75x
This is the equation representing the situation.
To find the cost of riding the taxi for 8 miles, we would substitute x = 8 in our equation. It becomes
Therefore, the total cost of riding the taxi for 8 miles would be
3 + 0.75 × 8
= 3 + 6 = $9
Cory bought some baseball equipment. He used a coupon for 1/2 off the price of the bat which is $69 and the glove which is $75. Write and evaluate a numerical expression to find the total cost of the bat, the glove, and 3 baseballs which are 5.50 each
Answer:
Step-by-step explanation:
He used a coupon for 1/2 off the price of the bat which is $69. With the coupon applied, the cost of the bat would be 69 × 1/2 = $34.5
He also used a coupon for 1/2 off the price of the glove which is $75. With the coupon applied, the cost of the bat would be 75 × 1/2 = $37.5
Therefore, a numerical expression to find the total cost of the bat, the glove, and 3 baseballs which are 5.50 each would be
34.5 + 37.5 + 3 × 5.5 = $88.5
The total cost of the bat, the glove, and the baseballs is $88.5 and this can be determined by using the given data and arithmetic operations.
Given :
He used a coupon for 1/2 off the price of the bat which is $69 and the glove which is $75.
The following steps can be used to evaluate the total cost:
Step 1 - Find the cost of the bat after the discount.
[tex]= \dfrac{1}{2}\times 69[/tex]
= $34.5
Step 2 - Find the cost of the glove after the discount.
[tex]=\dfrac{1}{2}\times 75[/tex]
= $37.5
Step 3 - Now, evaluate the cost of the baseballs.
[tex]=3\times 5.5[/tex]
= $16.5
Step 4 - Add all the costs to determine the total cost.
= 16.5 + 37.5 + 34.5
= $88.5
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In order to study whether IQ level is related to birth order, data were collected from a sample of 540 students on their birth order (Oldest/In Between/Youngest) and their score on an IQ test.
Which of the following would be a meaningful display of the data from this study?
a. A pie chart
b. A histogram
c. A scatterplot
d. A two-way table
e. Side-by-side boxplots
Answer:
correct answer is e. Side-by-side boxplots
Step-by-step explanation:
given data
IQ test
sample = 540 students
solution
here Side-by-side boxplots that is apply it to the data set with 1 quantitative and 1 categorical variable
Side-by-side boxplots is also very useful in the comparing fundamental information for 2 data set
eg median value and range of value they cover from data
and
Side-by-side boxplots also provide target summary and it analysis the data
so here correct answer is e. Side-by-side boxplots
The relation between the two dataset can be shown by placing the
dataset side-by-side, to give a meaningful display.
Correct response:
The correct option is; e. Side-by-side boxplotsMethod used to make the above selectionThe number of student in the study = 540
The categories of the data = Oldest/In Between/Youngest
The category of the other data collected = Their score on IQ test
Required:
To choose the option that would be a meaningful display of the data
from the study.
Solution:
The number of categories of the order of birth = 3
Therefore, a meaningful display of the order of birth is possible using a boxplot.
The IQ test scores can be categorized as follows;
Maximum test score;75th percentile = Third quartile = Q₃50th percentile = Second quartile = Q₂25th percentile = first quartile = Q₁Minimum test scoreTherefore, the dataset for the order of birth and the dataset for the IQ
test score can be presented side-by-side, thereby providing a
meaningful display.
The correct option is therefore;
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Suppose you buy a car with a value of $8,500. Each year the value of your car will depreciate by 4.7%. How much will your car be worth in 6 years?
A) $11,196.93
B) $6,779.17
C) $7,488.42
D) $6,367.61
Answer:
D
Step-by-step explanation:
y=a(1-r)^n
a is the initial cost of the vehicle
r is the percentage decrease in decimal
n is the number of years.
so y as the final cost is computed as:
8500(1-0.047)^6
we get $6367.61
What kind of transformation is illustrated in this figure?
a. rotation
b. dilation
c. reflection
d. translation
Answer:
translation
Step-by-step explanation:
It is not a rotation not a dilation, not a reflection
Answer:
i think its rotation plz tell me if im incorrect
Step-by-step explanation:
Solve for x. Show all work
3(x + 5) = x - 7
The answer is x equal -11
Answer: x = -11
Step-by-step explanation: First distribute or multiply through the parentheses on the left side of the equation.
When we do this, we get 3x + 15 = x - 7.
Then subtract x to get 2x + 15 = -7.
Then subtract 15 to get 2x = -22.
Then divide both sides of the equation by 2 and we find that x = -11.
A chef uses 12 pounds of butter each day. About how many grams of butter does the chef use each day? Use the conversion factors 16 ounces/1 pound and 28.4 grams/1 ounce
Answer:
The chef uses 5452.8 grams of butter each day.
Step-by-step explanation:
Given:
Chef use 12 pounds of butter each day.
To find the amount of butter in grams used by chef each day.
Conversion units:
1 pound = 16 ounces
1 ounce = 28.4 grams
Solution:
We need to convert 12 pounds of butter in grams of butter.
We will apply unitary method to carry out the conversion.
If 1 pound = 16 ounces
Then, 12 pounds = [tex]12\ pounds\times\frac{16\ ounces}{1\ pound}= 192\ ounces[/tex]
If 1 ounce = 28.4 grams
Then, 192 ounces = [tex]192\ ounces \times \frac{28.4\ grams}{1\ ounce} = 5452.8\ grams[/tex]
Thus, the chef uses 5452.8 grams of butter each day.
Final answer:
convert 12 pounds to ounces (192 ounces) and then multiply by 28.4 to convert ounces to grams, resulting in 5452.8 grams of butter used per day.
Explanation:
To find out how many grams of butter the chef uses each day, we need to convert pounds to ounces and then ounces to grams.
First, we use the conversion factor that there are 16 ounces in a pound. So, for 12 pounds of butter:
12 pounds × 16 ounces/pound = 192 ounces.
Next, we use the conversion factor that there are 28.4 grams in an ounce. So, for 192 ounces of butter:
192 ounces × 28.4 grams/ounce = 5452.8 grams.
Therefore, the chef uses approximately 5452.8 grams of butter each day.
At least ____ % of healthy adults have body temperatures within 22 standard deviations of 98.32degrees°F. (Round to the nearest percent as needed.)
Answer:
95%
Step-by-step explanation:
We are asked to find the percentage of healthy adults have body temperatures within 2 standard deviations of 98.32 degrees°F.
We will use Empirical rule of normal distribution to answer our given problem.
Empirical rule of normal distribution states that 68% of data falls within the first standard deviation from the mean. 95% of data fall within two standard deviations. 99.7% of data fall within three standard deviations.
Therefore, 95% of healthy adults have body temperatures within 2 standard deviations of 98.32 degrees°F.
For triangle JKL, angle JKL measures 90 degrees, and side JL has a length of 260 centimeters. If side JK > side KL, which of the following could be a combination of the lengths of sides JK and KL50 / 100 / 120 / 200 / 240.
Answer:
100/240/260 will be the combination.
Step-by-step explanation:
In a right angle triangle JKL,
∠JKL = 90° and side JL is the hypotenuse of the triangle.
By Pythagoras theorem,
JK² + KL² = JL²
Since JL = 260
Therefore, (JK)² + (KL)²= (260)² = 67600
In the given options, square of two numbers total becomes 67600.
And the possible numbers will be 100 and 240.
(100)² + (240)² = 10000 + 57600 = 67600
Since side JK > side KL
Therefore, measure of JK = 240 cm, KL = 100 cm and JL = 240 cm could be the combination among all values.
In the diagram below triangle abc ~ triangle dec . What is the value of x
Answer:
the answer is D
Step-by-step explanation
the ratio of the triangles is 3:1 (you find that out because 21:7 is simplified to 3:1.
when you plug in 6 as x then you get 18:6 which simplifies to 3:1 also
Triangle P has a base of 12 inches and a corresponding height of 8 inches triangle Q has a base of 15 inches and a corresponding height of 6.5 inches which triangle has a greater area?
Answer:
Triangle Q has the greatest area
Step-by-step explanation:
Answer:
Triangle Q is the greatest
Step-by-step explanation:
The value for P is 48
The value for Q is 48.75
*Remember once we get the area of a triangle we must divided by 2*
Therefore, Q has a greater value then P
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line passes through the points (3 comma 19 )and (7 comma 23 ). Write a linear function rule in terms of x and y for this line.
Answer:
[tex]y=1x+16[/tex]
Step-by-step explanation:
Two given points are (3,19) and (7,23)
f(x)=mx+b
slope is m and b is the y intercept
[tex]slope m =\frac{y_2-y_1}{x_2-x_1} =\frac{23-19}{7-3} =1[/tex]
slope m= 1 (3,19) is (x1,y1)
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-19=1(x-3)[/tex]
[tex]y-19=1x-3[/tex]
Add 19 on both sides
[tex]y=1x+16[/tex]
Final answer:
The linear function rule for the line passing through the points (3, 19) and (7, 23) is found by calculating the slope (which is 1) and using the point-slope form to derive the slope-intercept form y = x + 16.
Explanation:
To write a linear function rule for a line that passes through the points (3, 19) and (7, 23), we need to calculate the slope of the line and use the point-slope form to write the equation.
Finding the Slope (m)
Using the formula for the slope m = (y2 - y1) / (x2 - x1):
m = (23 - 19) / (7 - 3) = 4 / 4 = 1
We can use the point-slope form y - y1 = m(x - x1), where (x1, y1) is a point on the line:
y - 19 = 1(x - 3)
Simplifying this equation to the slope-intercept form (y = mx + b), we get:
y = 1x + 16
Therefore, the linear function rule in terms of x and y for this line is y = x + 16.