Answer:
m∠A ≈ 39.865°
Step-by-step explanation:
C² = 16² + 15² - 2 × 16 × 15 × cos (97°)
=> C = 23.22708085
sin (97°)/23.22708085 = sin A/15
=> sin A = sin (97°) × 15/23.22708085
=> A = \(sin^{-1}\)(sin (97°) × 15/23.22708085)
=> A ≈ 39.865
a recipe calls for 2 cups of flour for every 3 cups of sugar. If you are planning to use 5 cups of flour, how many cups of sugar should you use
Answer:
7½ cups of sugar
Step-by-step explanation:
2 cups of flour needs 3 cups of sugar
1 cups of flour needs 3/2=1.5 cups of sugar
1×5 cups of flour needs 1.5×5=7.5 cups of sugar=7½ cups of sugar ANS
+
-
1. The amount M (in trillions of dollars) of mortgage debt outstanding in the United States from 1990
through 2009 can be approximated by the function M = f(0) = 0.0037(t + 14.979), where t = 0
represents the year 1990.
(a) Describe the transformation of the common function f(x) = x2. Then sketch the graph over the
intervalo s t < 19.
(b) Rewrite the function so that t = 0 represents the year 2000. Explain how you got your answer.
(c) Use the model from part (b) to predict the mortgage debt in the year 2014.
The give quadratic function is dilated by the given coefficient, and shifted
horizontally to the left.
(a) The transformation of the common function f(x) are;
f(t) is made more wider than f(x) f(t) is shifted more to the left than the common function f(x).Please find attached the required graph created with MS Excel
(b) Where t = 0, represent the year 2,000 we have;
f(t) = 0.0037·(t + 24.979)²(c) The mortgage debt in the year 2014 is M ≈ $5.622 trillion
Reasons:
The given function is f(t) = 0.0037·(t + 14.979)²
Year 1990 is t = 0
(a) The given common function is; f(x) = x²
The transformation of the quadratic function are;
The coefficient 0.0037 widens the common function such that f(t) is wider
than f(x).
The constant, 14.979 added to the variable, t, shifts the graph of the
common function horizontally to the left.
Therefore;
f(t) is wider and shifted to the left more than the common function f(x)Please find attached the required graph over the interval 0 ≤ t ≤ 19 created with MS Excel.
(b) The amount of mortgage debt in 2,000 is given as follows;
With t' = 0 represent the year 2,000, we have;
At year 1990, t' = -10
Which gives, t' = t + 10
From which we have;
f(t) = 0.0037·(t + 14.979)² = 0.0037·(t' + 10 + 14.979)² = 0.0037·(t' + 24.979)²
Therefore;
The function with t = 0 representing the year 2,000 is presented as follows;
f(t) = 0.0037·(t + 24.979)²
(c) In the year 2014, we have;
t = 2014 - 2000 = 14
Which gives;
f(14) = 0.0037·(14 + 24.979)² ≈ 5.622
The mortgage debt in the year 2014 is M ≈ $5.622 trillion dollars
Learn more about transformation of quadratic functions here:
https://brainly.com/question/15105480
?
58 62
28 27 13
13 15 12 11
6 7 8 4 7
4 2 5 3 1 6
Answer:
105
Step-by-step explanation:
First, adding two sequence numbers and that result become upper number
Please Answer the question with the formula and simplification
Answer:
1/2
Step-by-step explanation:
-4 3 15 -14
--- *--- * --- *------
5 7 16 9
Rewriting
-4 3 5*3 -7*2
--- *--- * --- *------
5 7 4*4 3*3
Canceling like terms
-1 1 1*1 -1*2
--- *--- * --- *------
1 1 1*4 1*1
This leaves
2
---
4
1/2
\(answer = \frac{1}{2} \\ solution \\ \frac{ - 4}{5} \times \frac{3}{7} \times \frac{15}{16} \times ( \frac{ - 14}{9} ) \\ = \frac{ - 4 \times 3 \times 15 \times ( - 14)}{5 \times 7 \times 16 \times 9} \\ = \frac{2520}{5040} \\ = divide \: 5040 \: by \: 2520 \: \\ = \: \frac{1}{2} \\ hope \: it \: helps\)
HURRY IM TIMED!!!
Use this formula to solve this word problem. d=r*t Carolina wants to travel on a new maglev in Japan when she takes a trip this summer. If she takes the latest model which travels 352 mph, and it takes her 3.2 hours, how far did she travel? a. 112.6 miles c. 110 miles b. 1126 miles d. none of these
Answer:
352 mph
Step-by-step explanation:
cuz I'm super smart
Answer: 1126.4
Step-by-step explanation:
Rate times time, takes her 3.2 hrs and she travels 352, 3.2 times 352 is 1126.4
As part of a school project, Tim and Jesse decide to build a birdhouse. Tim plans to house bluebirds in his birdhouse and Jesse hopes to attract wrens. Tim decides to make the floor of his birdhouse a square that measures
inches on all sides. The piece of lumber that he uses for the floor is
inches wide. How much will he need to cut off of the width of the board to make the floor?
Answer:
Step-by-step explanation:
344
CAN ANYONE HELP ANSWER THIS
9514 1404 393
Answer:
58
Step-by-step explanation:
The marked points on the graph show that the number of hot cocoas sold decreases by 6 when the temperature goes up by 6 degrees. That is, the line has a slope of -1. The y-intercept is 100, so the equation of the line can be written as ...
y = mx +b . . . . . line with slope m and y-intercept b
y = -x +100
Then for x = 42, the expected value of y is ...
y = -42 +100 = 58
Mei Mei can expect to sell 58 hot cocoas on a day when the high is 42°F.
Answer the following questions about confidence intervals.
(a) What happens to a confidence interval as sample sizeincreases, assuming everything else stays the same?
The width of the interval decreases, since the standard error decreases.The center of the interval decreases, since the standard error increases. The center of the intervalincreases, since the standard error decreases.The width of the interval increases, since the standard error increases.
(b) If we want to use a larger confidence level when creating a confidence interval for a population mean, which of the following happens to our confidence interval?
The interval gets wider, since the standard error decreases.The interval gets narrower, since the t-value required to capture a larger proportion of the sampling distribution of the sample mean gets smaller. The interval gets narrower, since the standard error decreases.The interval gets wider, since the t-value required to capture a larger proportion of the sampling distribution of the sample mean gets larger.
(c) What does the margin of error in a confidence interval for a population mean describe?
It describes the difference between the sample mean and the population mean due to calculation errors by the researchers. It describes the difference between the sample mean and the population mean. Due to the random sampling method, different sample means will be different. It describes the difference between the sample mean and the population mean, due to taking non-random samples involving voluntary response or convenience sampling.It describes how often researchers make a mistake due to response bias or non-response bias.
(d) Why do we use a z-score from a normal distribution in constructing large-sample confidence intervals for a proportion?
For large random samples the data distribution is approximately normal.For any n we use the t-distribution to get a confidenceinterval, and for large n the t-distribution looks like the standard normal distribution. For large random samples the sampling distribution of the sample proportion is approximately normal.The population distribution is normal for large samples.
(e) True or false: The confidence interval for a mean with a random sample of size n = 2000 is invalid if the population distribution is bimodal.
TrueFalse
Answer:
the options are not numbered so I have added each of the correct answers under their corresponding question number. the answers in bold letters are right options from the question.
Step-by-step explanation:
a.)
the width of the interval decreases, since the standard error decreases. this is the answer to this question. this happens to a confidence interval as the sample size gets increased. that is if every other thing remains the same.
b.
the answer to this question is that the interval gets wider since the t value required to Capture a larger proportion of the sampling distribution of the sample mean gets larger. so the last option is the answer to the question.
c.
the margin of error shows the degree of random sampling error that is in the result of a survey. the correct answer to this question is this:
in a confidence interval for a population mean, the margin of error describes the difference between the sample mean and the population mean. Due to the random sampling method, different sample means will be different.
d.
regarding this question, we use a z score because:
For large random samples the sampling distribution of the sample proportion is approximately normal.
e.
the answer to this is false.
thank you!
HELP ME IM TOTALLY LOST AND HAVE A HARD TIME ASKING PEOPLE FOR HELP
Answer:
a. 1,323,002
Step-by-step explanation:
you sailed 0.032 units to the left and found treasure at 0.248 units find where the ship started
HELP?!!!!! Name the space figure you can form from the net.
Answer:
a or b but i think a
Step-by-step explanation:
Select the correct answer.
Using a table of values, approximate the solution to the equation below to the nearest fourth of a unit.
Answer:
3
Step-by-step explanation:
Answer:
Correct Answer for Plato is (3)
Step-by-step explanation:
#Platolivesmatter :)
Hope This Helped XD
Fyi I took the test and got it right too
Find the equation to the line
The equation of the line is y = 2/3x + 1
How to determine the equation of the line?The graph represents the given parameter
From the graph, we have the following points that can be used in our computation:
(x, y) = (0, 1) and (3, 3)
The equation of the line is then calculated using the following equation
y = (y₂ - y₁)/(x₂ - x₁) * (x - x₁) + y₁
Where
(x, y) = (0, 1) and (3, 3)
Substitute the known values in the above equation, so, we have the following representation
y = (3 - 1)/(3 - 0) * (x - 0) + 1
Evaluate
y = 2/3 (x - 0) + 1
So, we have
y = 2/3x + 1
Hence, the line equation is y = 2/3x + 1
Read more about linear equations at
https://brainly.com/question/2030026
#SPJ1
On a piece of paper, use a protractor to construct a triangle with angle measures of 40° and 60º.
What is the measure of the third angle?
Answer:
80
Step-by-step explanation:
every triangle, no matter what shape or size, will have all angles add up to 180 degrees so 180-40-60=80
Find the next three terms of the arithmetic sequence.
a) 9, 12, 15, ... b) 288, 252, 216, ...
Answer:
a) 18,21,24
b)180, 144, 108
Step-by-step explanation:
For a) The pattern seems to be adding up by three, so you do that to find the next three terms: 18, 21, 24
For b) The pattern is subtracting by 36, so subtract by 36 three more times to get: 180, 144, and 108
Sorry if I made any mistakes, currently on mobile.
"Our new
training room can seat 150
employees. If 6 tables consisting of 6
chairs are now taken, what
percentage of our new facility's
seating is full?"
Employee: "At this point, we have
used up
of our new seating
capacity."
The percentage of our new facility's seating is full will be 76%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Initial value - Final value] / Initial value x 100
Our new training room can seat 150 employees.
If 6 tables consisting of 6 chairs are now taken.
Then the number of occupied seats by tables will be
⇒ 6 x 6
⇒ 36
Then the percentage of our new facility's seating is full will be
P = [(150 - 36) / 150] x 100
P = (114/150) x 100
P = 0.76 x 100
P = 76%
The percentage of our new facility's seating is full will be 76%.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ1
what is 2(12) 3/2 in its simpilist form
Answer: 2/12 --> 1/6
3/2 --> 1 1/2
Step-by-step explanation:
2/12 can be simplified by dividing the top by 2 and the bottom by two. 2 is the GCF (greatest common factor) of both 2 and 12.
3/2 is a improper fraction so you have to make it a proper fraction. To do that you get 1 and 1/2. <-- this is for simplest form.
Hope this helped!
A jar contains 8 pennies, 3 nickels, 5 dimes, and 2 quarters. If one coin is chosen from the jar, how many ways are there to get more than 4 cents
Answer: The jar contains a total of 18 coins (8 pennies + 3 nickels + 5 dimes + 2 quarters). To get more than 4 cents, we need to choose a nickel, dime, or quarter. There are 3 nickels, 5 dimes, and 2 quarters, for a total of 10 coins that satisfy this condition. Therefore, there are 10 ways to choose a coin from the jar that is more than 4 cents.
B. PHOTOGRAPHY What is the area of the
matte pictured below?
4 in.
6 in.
1.5 in.
11.5 in.
Answer:
63in^2
Step-by-step explanation:
6 + 1.5 + 1.5 = 9
4 + 1.5 + 1.5 = 7
9 times 7 = 63 in^2
Find the value of y.
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
learn more about similar triangles from
https://brainly.com/question/14285697
#SPJ1
One number is 14 more than another. The sum of the two numbers is 168, find the two numbers
Answer:
77 and 91
Step-by-step explanation:
let x and x+14
x+(x+14)=168
2x=168-14
2x=154
divide both sides by 2
x=77
PLEASE HELP ASAP! For show and tell, Sophie brought 28 trading cards to class. During the day, Sophie got 54 more from her friends. How many trading cards does Sophie have now?
Answer:
84
Step-by-step explanation:
28+54=84
Answer:84
Step-by-step explanation:
Hi! So to start/set up the problem, since Sophie brought 28 cards, that is how many she has so, so far we only have, 28+_=_.
The next step is to add 54 cards since she added that many. Now we have 28+54=_.
The last step is to calculate. 28+54=84.
I don't get it can u please show me how to do it step by step
Step-by-step explanation:
6.)
|x - 6| = 5
x + 6 = 5
x = 5 - 6
x = - 1
7.)
|3x - 7| = 12
3x + 7 = 12
3x = 12 - 7
3x = 5
x = 5/3
8.)
|2x + 9| - 10 = 5
2x + 9 - 10 = 5
2x - 1 = 5
2x = 1 + 5
2x = 6
x = 6/2
x = 3
Simplify
6/19 ÷ 12/38
Answer:
1
Step-by-step explanation:
To divide 2 fractions, you have to use the reciprocal of the latter fraction.
The reciprocal of 12/38 is 38/12
Now you can multiply
6/19*38/12 = 1
i dont understand this
We can Add 7 black beads to make ratio 3 : 1.
Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.
There are three white beads in the picture.
Total beads we will have (b meaning black)b : 3
Ratio black : white beads 3 : 1
Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.
Find common ratio by dividing total by ratio white beads: 3/1 = 3
Multiply ratio black beads by common ratio. 3 X 3 = 9
We need 9 black beads in total.
Check answer
9 : 3
Both sides divisible by 3; reduce ratio
= 3 : 1
Which is Correct ratio
Hence, There will be a total of 9 black beads, but we already have 2 black beads:
(9 total) - (2 original) = (7 to add)
Therefore , we need to add 7 black beads.
Learn more about the ratio visit:
https://brainly.com/question/12024093
#SPJ1
Identify each number between 1.8×100 and 195%
There are no numbers between 1.8×100 and 195%.
What are numbers?The representation of quantities or values using numbers is a fundamental idea in mathematics. They can be applied to measure, compare, compute, and count. Depending on the situation and the chosen notational system, numbers can be represented in a variety of ways, such as digits, words, or symbols.
Based on their attributes and traits, several sorts of numbers can be distinguished in mathematics. The following list includes some of the most typical numbers:
Natural numbers: These are the numbers used for counting, such as 1, 2, 3, 4, 5, and so on.Whole numbers: These are the natural numbers together with zero, such as 0, 1, 2, 3, 4, and so on.Integers: These are the whole numbers together with their negatives, such as -4, -3, -2, -1, 0, 1, 2, 3, 4, and so on.Rational numbers: These are numbers that can be expressed as a fraction of two integers, such as 1/2, 0.75, -2/3, and so on.Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers, such as π (pi), √2 (square root of 2), and so on.Real numbers: These are all rational and irrational numbers together.Complex numbers: These are numbers of the form a + bi, where a and b are real numbers, and i is the imaginary unit, which is defined as the square root of -1.To identify the numbers between 1.8×100 and 195%, we need to convert both numbers to the same unit of measurement.
1.8×100 = 180
195% = 1.95 (since 195% is equal to 1.95 times the original quantity)
Now, we need to identify all numbers between 180 and 1.95. To do this, we can simply list all the numbers that are greater than 180 and less than 1.95, excluding 180 and 1.95 themselves. However, we notice that there are no such numbers, because:
Any number greater than 180 is also greater than 1.95 since 1.95 is less than 2 and 180 is greater than 2.
Any number less than 1.95 is also less than 180 since 180 is greater than 100 (which is 1% of 10,000) and 1.95 is less than 2.
Therefore, there are no numbers between 1.8×100 and 195%.
To know more about numbers, visit:
brainly.com/question/19104371
#SPJ1
Answer:
1 7/8
Step-by-step explanation:
i took the test
???can anyone please help???
Because he wants to mantain a constant rate over the first hours, we can see that on the first hour he should travel 26 miles.
How many miles should he travel in the first hour?The total race is 150 miles, if we discount the last 20 miles (that Jackson will bike as fast as he can) we get:
150mi - 20mi = 130mi
We know that he travels these 130 miles at a constant rate over 5 hours, so the distance that he moves each hour (an particularly the first hour) is given by the quotient between the distance and the time.
R = 130mi/5h = 26mi/h
So he should travel 26 miles in the first hour.
Learn more about constant rates:
https://brainly.com/question/25598021
#SPJ1
Jack borrows $2,700 at a rate of 8.2% per year. How much total will he pay if it takes 3 months to repay the loan?
well, a year has a total of 12 months, so 3 months is really 3/12 of a year.
\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2700\\ r=rate\to 8.2\%\to \frac{8.2}{100}\dotfill &0.082\\ t=years\to \frac{3}{12}\dotfill &\frac{1}{4} \end{cases} \\\\\\ A=2700[1+(0.082)(\frac{1}{4})] \implies A = 2700(1.0205)\implies A=2755.35\)
Rick Rich owns a Mercedes dealership. Mercedes has 5 models, 4 standard options packages, and 5 colors. If Rick wants to immediately be able to deliver any car (model, option package, color), how many cars must Rick have on hand?
Rick would need to have at least 100 cars on hand to immediately be able to deliver any car (model, option package, color).
To immediately deliver any car, Rick Rich's dealership must have all possible combinations of Mercedes models, option packages, and colors in stock.
With five models, four option packages, and five colors, there are 5 x 4 x 5 = 100 possible combinations.
Therefore, Rick would need to have at least 100 cars on hand, each representing a unique combination of model, option package, and color. It's worth noting that having exactly 100 cars on hand would only allow Rick to deliver one of each possible combination, so it may be prudent to have additional inventory on hand to meet demand for more popular combinations.
for such more question on word problem
https://brainly.com/question/1781657
#SPJ11
What is the y-intercept of this quadratic function? f(x)= -x^2
Answer:
x-intercept(s):
( 0 , 0 )
y-intercept(s):
( 0 , 0 )
Step-by-step explanation:
Answer:
(0,0)
Step-by-step explanation:
This has no real starting point. The x-intercept as well as the y-intercept is (0,0).