Answer:
See explanation
Step-by-step explanation:
sin(α + β) = sin α cos β + sin β cos α
sin(α - β) = sin α cos β - sin β cos α
\(\frac{1}{2}\)[ sin(α + β) + sin(α - β)] = \(\frac{1}{2}\)[sin α cos β + sin β cos α + sin α cos β - sin β cos α]
= \(\frac{1}{2}\)[2 sinα cos β]
= sin α cos β = \(\frac{1}{2}\)[ sin(α + β) + sin(α - β)]
Using compatible numbers to estimate, which expression has a quotient of about 70?
O A. 3,424 ÷ 49
OB. 5,358 ÷ 89
O C. 6,409 ÷ 79
O D. 5,238 ÷ 89
Laurie asked 100 of her friends to choose their favorite flower. Fifteen of them chose carnations, 58 chose roses and the rest daises. What percent of her friends chose daises? 73 percent, 58 percent, 15 percent, 27 percent
Answer:
27%
Step-by-step explanation:
remainder of 21 divided by 6
3 21divde by 6, use 3 which is 18. now 21 subtracted by18 is 3
Use the number line below, where RS= 5y +5, ST = 4y + 8, and RT = 67.
a. What is the value of y?
b. Find RS and ST.
R
a. What is the value of y?
y = (Type an integer or a decimal.)
Answer:
y = 6RS = 35ST = 32Step-by-step explanation:
The segment sum theorem tells you the whole is the sum of the parts. That can be used to write an equation for y.
SetupRS +ST = RT
(5y +5) +(4y +8) = 67
SolutionSimplifying, we get ...
9y +13 = 67
9y = 54 . . . . . . . . subtract 13
y = 6 . . . . . . . . . divide by 9
RS = 5y +5 = 5·6 +5 = 35
ST = 4y +8 = 4·6 +8 = 32
The values of interest are ...
y = 6RS = 35ST = 32Question 2
If a = -3,6= 4 and c= -5, then by how much is the product abc greater than the sum a + b + c?
How many 10-letter words real or imaginary can. Be formed from the following letters R,S,P,Q,H,J,S,M,B,A
Answer: 3628800
Step-by-step explanation: there are 10 letters so we multiply each with the other 1x2x3x4x5x6x7x8x9x10 or 10! to know all possible combinations so the answer will be 3628800.
Hope it helped!
Answer:
\(1,814,400\)
Step-by-step explanation:
The number of ways to arrange a word with \(d\) distinct digits is each to \(d!\). Since there are 10 letters, there are \(10!\) permutations initially formed.
However, there is one letter that is repeated, S. We need to account for that fact that switching the placement of the S's does not change the word, as they still appear the same. Therefore, divide \(10!\) by the number of ways you can arrange the 2 S's, which is simply \(2!\). Therefore, our answer is:
\(\frac{10!}{2!}=10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3=\boxed{1,814,000}\)
Find the volume of the figure. Round to the nearest hundredth if necessary. (Figure is not to scale)
Answer:
360 mi^3
Step-by-step explanation:
The figure is composed by two parallelepipeds. For find the volume we have to find the volume of both the solids and the added up the two values
solid 1
length = 11 - 4 = 7 mi
base area = length x width = 7 x 4 = 28 mi^2
V = base area x height = 28 x 6 = 168 mi^3
solid 2
base area = 8 x 4 = 32 mi^2
V = 32 x 6 = 192 mi^3
total volume: 168 + 192 = 360 mi^3
The volume of the figure is 360 mi³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given is a figure where two rectangular boxes are put on top of each other.
Volume of a rectangular prism = L × W × H
Here L is the length, W is the width and H is the height.
The dimensions of the rectangular prism are :
Larger one having L = 11 mi, W = 6 mi and H = 4 mi
Smaller one on top having L = 4 mi, W = 6 mi and H = 8 - 4 = 4 mi.
Volume of the figure = volume of larger box + Volume of smaller box
= (11 × 6 × 4) + (4 × 6 × 4)
= 264 + 96
= 360 mi³
Hence the volume of the figure is 360 mi³.
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A machine is programmed to run an algorithm for 972 hours starting at 9 A.M. on Monday. When will the machine stop running the algorithm.
A) 9 A.M. on Saturday
B) 9 P.M. on Saturday
C) 9 A.M. on Sunday
D) 9 P.M. on Sunday
Using proportions, it is found that the correct option for when the machine will stop running the algorithm is:
B) 9 P.M. on Saturday.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The algorithm runs for 972 hours. Each day has 24 hours, hence we apply the proportion to find the number of days as follows:
972/24 = 40.5 days.
The remainder of the division of 40.5 by 7, as a week has 7 days, is of 5.5, which means that the code will finish running 5.5 days after the 9 A. M. Monday, that is at 9 P. M. on a Saturday, which means that option B is correct.
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A survey of 400 students yielded the following information: 262 were seniors, 215 were commuters, and 150 of the seniors were commuters. How many of the 400 surveyed students were seniors or were commuters?
Out of the 400 surveyed students, 327 were either seniors or commuters.
To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.
According to the information given:
There were 262 seniors.
There were 215 commuters.
150 of the seniors were also commuters.
To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.
Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters
= 262 + 215 - 150
= 327
Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.
It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.
This ensures an accurate count of the students who fall into either category.
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Question about observational study:
The required choice is true of an observational study B, C, and D.
What is Statistic?Statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
Option a is not true of an observational study. In an observational study, the researcher cannot control the variables of interest, unlike in a true experiment where the researcher can manipulate the variables.
Option b is true of an observational study. Since the researcher cannot control the variables of interest, the study is entirely based on observing the subjects and collecting data.
Option c is true of an observational study. The data collected in an observational study is similar to the data collected in a true experiment, and the same statistical methods can often be used to analyze both types of data.
Option d is true of an observational study. Since the researcher cannot control the variables of interest, they have to take advantage of natural variation in the variables to draw conclusions.
Thus, Options B, C, and D are correct.
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Solve this question please for me
f (x) - 2/3x - 7 find the inverse
Find the length of the third side. If necessary, write in simplest radical form.
√39
5
I need help asap please it’s my geometry final!
Answer:
8
Step-by-step explanation:
a² + b² = c²
c² = a² + b²
c² = 5² + (√39)²
c² = 25 + 39
c² = 64
c = 8
Figure ABCD is reflected across the x-axis. What are the coordinates of A′, B′, C′, and D′? Enter your answer by filling in the boxes. A′ (−1, −4) B′ (, ) C′ (−5, −4) D′ (−4, −2)
The coordinates of A′, B′, C′, and D′ for the reflection across the x-axis is given as: A'(2, -3), B'(5, -5), C'(7, -3), and D'(5, -2).
Explain about the reflection across the x-axis?One of the many transformations we can do on a geometric figure is reflection. By using an axis of symmetry, the original position is reversed.The x-coordinate remains constant when a point is reflected across the x-axis, but still the y-coordinate is assumed to correspond to the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).A(2, 3) ⇒ A'(2, -3),
B(5, 5) ⇒ B'(5, -5),
C(7, 3) ⇒ C'(7, -3),
D(5, 2) ⇒ D'(5, -2).
Thus, the coordinates of A′, B′, C′, and D′ for the reflection across the x-axis is given as: A'(2, -3), B'(5, -5), C'(7, -3), and D'(5, -2).
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The correct question is-
Figure ABCD is reflected across the x-axis. What are the coordinates of A′, B′, C′, and D′?
The figure is attached.
10 points, questions is in the picture
Answer:
I think the answer is A
Step-by-step explanation:
If you use the diameter of the circle when drawing you will not get more than one interesection with the circle which will be in the opposite side, repeating this step will just repeat the same circles. But if you use the radius of the circle \(r = AB\) you will get something like the picture attached, bear in mind it's not exact but it helps picture the steps being followed.
The best way to solve this is by experimenting with the compass and following the steps to see the outcome.
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be 95% confident that the sample mean is within 4 IQ points of the true mean.
What is the required sample size?
Answer:
55
Step-by-step explanation:
\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)
Make sure to always round up the required sample size to the nearest integer!
A company that prints Blue Books for exams makes a profit according to the number of books sold. Suppose that the Profit is
Answer:
The answer is not complete. I will explain the concept of profit to you.
Step-by-step explanation:
We can determine profit deducting direct costs (cost price) of commodities from sales (selling prices) of the commodities.
Profit = Selling Price - Cost Price
Example:
A trader buys some dresses for #2,500 in May and agrees to pay for it in three months’ time. He sells off all the dresses in August for #4,500. The profit for the month is #2,000.
The formula for percentage profit is \(\frac{profit * 100}{cost price}\)
The formula for gross profit is Revenue – Cost of Sold Items
Profit Margin = \(\frac{Total Income}{Net Sales}\) * 100
While Gross Profit Margin can be calculated as \(\frac{Gross Profit}{Net Sales}\) * 100
Any of these formulas can be used to calculate profit-related questions.
what is 7,750 divided by 155?
Answer:
50
Step-by-step explanation:
7,750÷155=50
To the nearest hundredth, how many kilometers are equal to 5 miles?I’ll mark brainliest!
Answer:
8.04
Step-by-step explanation:
Harold has five more cakes than jake has. write an expression that shows how many cakes Harold has in relation to Jake
Answer: J (The cakes that Jake has) +5 = H (the cakes that Harold has), or J + 5 = H
Step-by-step explanation:
Harold has 5 more cakes than Jake.
To write this as an expression, we must make a variable for Harold and Jake's cakes.
Let's put H and J respectively for the two.
Now, we must show that Harold, or H, has 5 more cakes than Jake.
We can show that by putting +5 next to Jake's variable.
This shows that Harold has 5 more cakes than Jake.
Now, we know that Jake's cakes plus 5 equal Harold's cakes, so we can easily write the expression as J+5=H.
Stella is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, spins a spinner with three equal-sized sections labeled Walk, Run, Stop, and spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday?
Answer:
60 outcomes-----------------------
To calculate the total number of possible outcomes we need to multiply the number of options for each component (die, first spinner, second spinner).
For the first component we have 4 options, for the second component- 3 options and for the third component- 5 options.
Therefore, the total number of possible outcomes is:
4 × 3 × 5 = 60 different possible outcomesIn New York the mean salary for high school teachers in 2017 was 97010 with a standard deviation of 9540. Only Alaska’s mean salary was higher. Assume new York’s state salaries follow a normal distribution. (A) what percent of new York’s high school teachers earn between 83,000 and 88,000? (B) what percent of New York teachers earn between 88,000 and 103,000?
(C) what percent of new York’s state high school teachers earn less than 73,000?
a. 20.31% of New York's high school teachers earn between 83,000 and 88,000
b. 18.49% of New York teachers earn between 88,000 and 103,000
c. 1.19% of New York’s state high school teachers earn less than 73,000
Given,
The salary for high school teachers in 2017 = 97010
Standard deviation = 9540
Consider salaries as normal distribution.
Here,
Mean, μ = 97010, Standard deviation, σ = 9540
a. Percentage of New York's high school teachers earn between 83,000 and 88,000
The proportion is the p-value of Z when X = 88,000 subtracted by the p-value of Z when X = 83,000.
That is,
X = 88,000
Z = (X - μ) / σ = (88,000 - 97010) / 9540 = -9010/9540 = -0.944
The p value of z score - 0.944 is 0.3452
Next,
X = 83,000
Z = (X - μ) / σ = (83,000 - 97010) / 9540 = -14010/9540 = -1.468
The p value of z score - 1.468 is 0.1421
Then,
0.3452 - 0.1421 = 0.2031 = 20.31%
That is,
20.31% of New York's high school teachers earn between 83,000 and 88,000
b. Percentage of New York teachers earn between 88,000 and 103,000
The proportion is the p-value of Z when X = 103,000 subtracted by the p-value of Z when X = 88,000
X = 103,000
Z = (X - μ) / σ = (103,000 - 97010) / 9540 = 5990/9540 = 0.6279
The p value of z score 0.6279 is 0.5301
Next,
X = 88,000
Z = (X - μ) / σ = (88,000 - 97010) / 9540 = -9010/9540 = -0.944
The p value of z score - 0.944 is 0.3452
Then,
0.5301 - 0.3452 = 0.1849 = 18.49%
That is,
18.49% of New York teachers earn between 88,000 and 103,000
c. Percentage of new York’s state high school teachers earn less than 73,000
The proportion is the p-value of Z when X = 73000
X = 73,000
Z = (X - μ) / σ = (73,000 - 97010) / 9540 = -24010/9540 = -2.516
The p value of z score - 2.516 is 0.0119
That is,
1.19% of New York’s state high school teachers earn less than 73,000
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I am confused on this problem and need help on how to write this equation in slope intercept form
We want to write the equation:
\(y+6=-\frac{8}{5}(x-9)\)In slope-intercept form.
The slope-intercept form is given by the equation:
\(y=mx+b\)Where m is the slope, and b is the slope-intercept with y-axis.
Now, we could start by multiplying the number outside the bracket per all the terms inside of it. This is,
\(y+6=-\frac{8}{5}x+\frac{72}{5}\)Now, we could solve the equation for y as follows:
\(\begin{gathered} y=-\frac{8}{5}x+\frac{72}{5}-6 \\ \\ y=-\frac{8}{5}x+\frac{42}{5} \end{gathered}\)And that's the slope-intercept form of the equation.
Seventy-five 6th- grade students chose to watch a movie on the last day of school. This is 25% of the 6th-grade class. How many total students are in the 6th grade?
what does 7,124 ÷ 26 equal too explain with what you know
Answer:
274
Step-by-step explanation:
i used a calculator. You can try long division
Answer:
274
Step-by-step explanation:
7,124 ÷ 26 =274
0 2 7 4
2 6 7 1 2 4
0
7 1
5 2
1 9 2
1 8 2
1 0 4
1 0 4
0
A culture started with 5000 bacteria after three hours it grew 6500 bacteria predict how many bacteria will be present after 13 hours round your answer to the nearest whole number
Answer:
15595 bacteria will be present after 13 hours.
Step-by-step explanation:
Continuous population growth:
The continuous population growth model, for the population after t hours, is given by:
\(P(t) = P(0)e^{rt}\)
In which P(0) is the initial population and r is the growth rate.
Started with 5000 bacteria
This means that \(P(0) = 5000\)
So
\(P(t) = 5000e^{rt}\)
After three hours it grew 6500 bacteria:
This means that \(P(3) = 6500\). We use this to find r.
\(P(t) = 5000e^{rt}\)
\(6500 = 5000e^{3r}\)
\(e^{3r} = \frac{65}{50}\)
\(\ln{e^{3r}} = \ln{\frac{65}{50}}\)
\(3r = \ln{\frac{65}{50}}\)
\(r = \frac{\ln{\frac{65}{50}}}{3}\)
\(r = 0.0875\)
So
\(P(t) = 5000e^{0.0875t}\)
How many bacteria will be present after 13 hours?
This is P(13). So
\(P(13) = 5000e^{0.0875*13} = 15594.8\)
Rounding to the nearest whole number
15595 bacteria will be present after 13 hours.
HELP PLZ WILL GIFT EXTRA POINTS PLZ
Answer:
42.85 units
Step-by-step explanation:
Since the circle is linked to the equilateral triangle, then the diameter of the circle is 12. Therefore r = 6.Then, the perimeter of the resulting figure is:P = 6 * pi + 12 +12 = 42.85 Units.
A publisher has the exclusive right to publish a book expected by the public. It is expected to sell “x” collections of books per month at a price of “p” dollars each collection, where p=600-5x. Considering that the publisher has fixed monthly costs of $8,000 and a variable cost per collection of $75.
a) Graph the utility function that each month can have (also apply the tabulation), indicating how much this maximum monthly utility amounts to. Finally, ¿what are the intersection points of this function with the "x" axis?
Answer:
Variable selling costs per unit. $ 5. Allocated fixed selling costs per unit ... P + FC = Q x (SP – VC).
Step-by-step explanation:
Variable selling costs per unit. $ 5. Allocated fixed selling costs per unit ... P + FC = Q x (SP – VC).
What are the coordinates of the image of the point (-4,-5) after reflecting over the y-axis
If a trader Gaines 15% interest by selling an article for 1560.00 what is the cost price for the article
$1356.52 is the cost price of the article.
To find the cost price of the article, we can utilize the concept of calculating the original amount based on a percentage increase.
Let's assume the cost price of the article is "x" dollars.
The trader gained a 15% interest, which means the selling price is 115% of the cost price. In other words, the selling price is 115% of "x".
To calculate the selling price, we can set up the following equation:
115% of x = 1560
To convert the percentage to a decimal, we divide it by 100:
1.15 * x = 1560
Now we can solve for x by dividing both sides of the equation by 1.15:
x = 1560 / 1.15
Using a calculator, we find:
x ≈ 1356.52
Therefore, the approximate cost price of the article is $1356.52.
This means that the trader purchased the article for around $1356.52 and then sold it for $1560.00, resulting in a 15% gain.
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The mean age of 5 people in a room is 37 years.
A person enters the room.
The mean age is now 34.
What is the age of the person who entered the room?
please help me this is hard for me
The age of the person who entered the room is 19
How to determine what is the age of the person who entered the room?The given parameters are:
The mean age of 5 people in a room = 37 years.The mean age of now = 34 years.Mean is calculated as:
Mean = Sum/Count
For the five people, we have
Sum/5 = 37
Multiply by 5
Sum = 185
For the five people, we have
Sum/6 = 34
Multiply by 6
Sum = 204
Let the last person be x
So, we have
x + 185 = 204
Subtract 185
x = 19
Hence, the age of the person who entered the room is 19
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