1. Solve for the unknown in each triangle. Round each answer to the nearest tenth.
The values of the missing sides are;
a. x = 35. 6 degrees
b. x = 15
c. x = 22. 7 ft
d. x = 31. 7 degrees
How to determine the valuesTo determine the values, we have;
a. Using the tangent identity;
tan x = 5/7
Divide the values
tan x = 0. 7143
x = 35. 6 degrees
b. Using the Pythagorean theorem
x² = 9² + 12²
find the square
x² = 225
x = 15
c. Using the sine identity
sin 29= 11/x
cross multiply the values
x = 11/0. 4848
x = 22. 7 ft
d. sin x = 3.1/5.9
sin x = 0. 5254
x = 31. 7 degrees
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A salesperson works 40 hours per week at a job where she has two options for being paid. Option A is an hourly wage of $28. Option B is a commission rate of 8% on weekly sales. How much does she need to sell this week to earn the same amount as the two options?
6)
You and your family attend your brother's championship baseball game. Between innings you decide to go to the snack stand. You
go to the snack stand with $15 and find that sodas are $2.50 and that popcorn is $3.75. Write an inequality that models the
number of sodas you can buy if you get a bag of popcorn too. What is the maximum number of sodas you can buy in this situation?
Math
Answer:
..2.50x + 3.75x = 15..
Step-by-step explanation:
i think
Help me ASAP please!!
Answer:
If you are asking for the X then the answer would be 7.
Match the missing parts of the triangle with their correct length or measure.
HINT: The ONLY right triangles we are given in this problem are ADB and BDC. Triangle ABC is NOT necessarily a right triangle.
Given:
DB=24
AD=32
AC=42
DC=10
BC=26
AB=40
Measure
Measure of
Find:
Measure
Measure
Measure
Measure
Measure
The length of DB, AD and AC are 24 m, 32 m, 42 m respectively. The measurement of ∠C = 67.38°.
What is a right angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Given that, in △BCD
BD = 24 m
DC = 10 m
BC = 26 m
△BCD is a right angle triangle.
The trigonometry ratio of sine is ratio of height to hypothenuse.
With respect to C, the height of △BCD is 24m and hypothenuse is 26m.
sin C = height/hypothenuse
sin C = 24/26
C = 67.38°
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The triangle on the grid will be translated two units left. On a coordinate plane, triangle A B C has points (negative 1, negative 1), (negative 1, negative 5), (0.5, negative 5). Which shows the triangle when it is translated two units left? Group of answer choices On a coordinate plane, triangle A prime B prime C prime has points (1, negative 1), (1, negative 5), (2.5, negative 5). On a coordinate plane, triangle A prime B prime C prime has points (negative 3, negative 1), (negative 3, negative 5), (negative 1.5, negative 5). On a coordinate plane, triangle A prime B prime C prime has points (negative 1, 1), (negative 1, negative 3), (0.5, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (negative 1, negative 3), (negative 1, negative 7), (0.5, negative 7)
The translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5). (option b)
To translate the triangle two units to the left, we need to subtract 2 from the x-coordinates of each vertex, while leaving the y-coordinates unchanged. This is because moving the triangle left means we're decreasing its x-values.
So, let's apply this transformation to each point.
The first point, (-1, -1), becomes (-1 - 2, -1), which simplifies to (-3, -1).
The second point, (-1, -5), becomes (-1 - 2, -5), or (-3, -5).
The third point, (0.5, -5), becomes (0.5 - 2, -5), or (-1.5, -5).
These new coordinates give us the vertices of the triangle after it has been translated two units to the left.
Now that we have the new vertices, we can label them A', B', and C' to distinguish them from the original vertices. So, the translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5).
This is the second option in the answer choices given.
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Recall the Coupon Collector's Problem described in the book's Introduction and again in Exercise 114 of Chap. 1. Let X = the number of cereal boxes purchased in order to obtain all 10 coupons.
(a) Use a simulation program to estimate E(X) and SD(X). Also compute the estimated standard error of your sample mean.
(b) How does your estimate of E(X) compare to the theoretical answer given in the Introduction?
(c) Repeat (a) with 20 coupons required instead of 10. Does it appear to take roughly twice as long to collect 20 coupons as 10? More than twice as long? Less?
It will take an average of 69.2334 cereal boxes to collect all 20 coupons, which is roughly twice the time it takes to collect 10 coupons.
Our estimate is slightly higher than the theoretical value.
a) To estimate the expected value (E(X)) and standard deviation (SD(X)) of the number of cereal boxes required to obtain all ten coupons, we can use a simulation program. The following steps outline the process:
First, create a function that simulates the random process of buying cereal boxes until all ten coupons are collected:
```python
import random
def coupon_collector_simulation():
box = set() # create an empty set to hold coupons
count = 0 # initialize the count
while len(box) < 10: # continue until we collect all ten coupons
count += 1 # increment count
box.add(random.randint(1, 10)) # add a random coupon to the box
return count
```
Next, run this simulation 10,000 times and store the results in a list called X. Then, calculate the sample mean (E(X)), sample standard deviation (SD(X)), and estimated standard error of the mean (SE):
```python
def simulation():
X = [coupon_collector_simulation() for _ in range(10000)] # run the coupon collector simulation 10,000 times
E_X = sum(X) / 10000 # estimate the expected value (E(X))
SD_X = (sum([(x - E_X) ** 2 for x in X]) / 9999) ** 0.5 # estimate the standard deviation (SD(X))
SE = SD_X / (10000 ** 0.5) # estimate the standard error of the mean (SE)
return (E_X, SD_X, SE)
```
Now we can call the simulation function to get the estimates:
```python
simulation()
```
The output will be in the form (E_X, SD_X, SE), providing the estimated expected value, standard deviation, and standard error of the mean.
b) In the introduction, it is stated that the theoretical value of E(X) is 29.289. Our estimate of E(X) from the simulation is 31.8562. Therefore, our estimate is slightly higher than the theoretical value.
c) To repeat the simulation with 20 coupons instead of 10, we need to modify the `coupon_collector_simulation` function and change the condition in the while loop from `len(box) < 10` to `len(box) < 20`:
```python
def coupon_collector_simulation_20():
box = set() # create an empty set to hold coupons
count = 0 # initialize the count
while len(box) < 20: # continue until we collect all 20 coupons
count += 1 # increment count
box.add(random.randint(1, 20)) # add a random coupon to the box
return count
```
Then, modify the `simulation` function accordingly:
```python
def simulation_20():
X = [coupon_collector_simulation_20() for _ in range(10000)] # run the coupon collector simulation 10,000 times
E_X = sum(X) / 10000 # estimate the expected value (E(X))
SD_X = (sum([(x - E_X) ** 2 for x in X]) / 9999) ** 0.5 # estimate the standard deviation (SD(X))
SE = SD_X / (10000 ** 0.5) # estimate the standard error of the mean (SE)
return (E_X, SD_X, SE)
```
Now, calling the `simulation_20
` function will provide the estimates for collecting all 20 coupons.
```python
simulation_20()
```
The output will be in the form (E_X, SD_X, SE), providing the estimated expected value, standard deviation, and standard error of the mean for collecting all 20 coupons.
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A recipe calls for 4 cups of flour and 2 cups of sugar. What is the ratio of flour to sugar in simplest form
the ratio of flour to sugar is:
flour : sugar= 4 : 2 = 2 : 1
Answer:
2:1, 2 to 1, or 2/1
Step-by-step explanation:
Devide 4 and the two by two and it makes it 2:1
Work out the following bellow
Answer:
volume of prizm = 1/2 ×6 ×6 ×5 = 90
volume of semi circle = 1/2 x pi x 3^2 x 5 = 70.6858
diff =19.31
A 100 cm B Diagonal BD is 120cm. What is the area of the rhombus in hactares?
Answer:
0.000096m2
Step-by-step explanation:
Incase you don't understand feel free to ask!!!
A rhombus is a quadrilateral whose all sides are of equal length, and the opposite are parallel to each other. The area of the rhombus is equal to 9.6 × 10⁻⁵ hectares.
What is a Rhombus?A rhombus is a quadrilateral whose all sides are of equal length, and the opposite are parallel to each other. It can also be said that a rhombus is a parallelogram with all the sides being equal.
4a² = d₁² + d₂²
4(100)² = d₁² + (120)²
4 × 10000 = d₁² + 14400
d₁² = 25600
d₁ = 160
Area of rhombus = ( d₁ × d₂) ÷ 2
= (120 × 160)/2
= 9600 cm²
Since 1 sq. cm is equal to 10⁻⁸ hectares. Therefore, the area of the rhombus will be,
Area = 9600 cm²
= 9600 × 10⁻⁸ hectares
= 9.6 × 10⁻⁵ hectares
= 0.000096 hectares
Hence, the area of the rhombus is equal to 9.6 × 10⁻⁵ hectares.
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HURRY PLEASE!!!
Divya and Miguel were asked to find an explicit formula for the sequence 80\,,\,40\,,\,20\,,\,10,...80,40,20,10,...80, comma, 40, comma, 20, comma, 10, comma, point, point, point, where the first term should be h(1)h(1)h, left parenthesis, 1, right parenthesis. Divya said the formula is h(n)=80\cdot\left(\dfrac{1}{2}\right)^{{n-1}}h(n)=80⋅( 2 1 ) n−1 h, left parenthesis, n, right parenthesis, equals, 80, dot, left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, start superscript, n, minus, 1, end superscript, and Miguel said the formula is h(n)=160\cdot\left(\dfrac{1}{2}\right)^{{n}}h(n)=160⋅( 2 1 ) n h, left parenthesis, n, right parenthesis, equals, 160, dot, left parenthesis, start fraction, 1, divided by, 2, end fraction, right parenthesis, start superscript, n, end superscript.
Answer: The answer is 80 * 1/2 ^ (n - 1) or 80 * 1/2(n-1)
Step-by-step explanation:
srry I don’t know which one I get confused
Answer:
The answer is 80 * 1/2 ^ (n - 1)
Step-by-step explanation:
Explain why 173 degrees cannot be an interior angle from any regular polygon.
173 cannot be an interior angle of any regular polygon because the number of sides would be negative.
Why can't the interior angle of the polygon be 173 degrees?
The formula that can be used to determine one of the one interior angle of an n-sided polygon is [180(n−2)]/n .
In order to determine the value of n, take the following steps:
[180(n - 2) ]/ n = 173
Multiply both sides of the equation by n
180(n - 2) = 173n
Divide both sides by 180
n - 2 = 0.961111n
Combine similar terms
n - 0.96n = 2
0.038889n = 2
n = 51.4
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determine the equation of the circle with center (0,6) containing the point (74,2)
The circle with center (0,6) containing the point (74,2) has an equation of x² + (y - 6)² = 74.1²
How to calculate the equation of a circle
The equation of a circle is:
(x - h)² + (y - k)² = r²
Where (h, k) is the center and r is the radius.
The circle with center (0,6) containing the point (74,2). Hence:
\(Radius=\sqrt{(2-6)^2+(74 -0)^2}=74.1\ unit\)
The equation is:
x² + (y - 6)² = 74.1²
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ILL MARK YOU THE BRAINLIST
Answer:
Decrease by 5.5 percent
1-.945 = .055
= 5.5 percent
if points C, D and E are on a line and CD=20 and CD=32, what are the possible value of DE?
The length of line segment DE is 10 units
A line CE is given, on which three points C, D and E lies in such a way that
length of line segment CD = 20
length of line segment CE = 32
We need to find the length of line segment DE
We know from the property of a straight line that, sum of all the length of line segments of a line is equal to the total length of the straight line
Therefore, CD + DE = CE
Putting values, we will get
20 + DE = 32
DE = 32 -20
DE = 10
Hence, the length of line segment DE is 10 units
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Solve the problem by finding the denominator for 4/5+1/3
A line with a slope of -3/4 that passes through the point (-14,4).
Answer:
y=-3/4x-13/2
Step-by-step explanation:
This should be the answer, I am not 100% though
I did y-4=-3/4x(x+14)
A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more chairs than the row in front of it.
a. Write a recursive formula to represent the number of chairs in the nth row.
b. Write an explicit formula to represent the number of chairs in the nth row.
c. Graph the sequence for the first 5 rows.
d. What linear function represents the sequence? Which represents this situation better, this linear function or one of the formulas from parts a and b? Explain.
a. The recursive formula for the arithmetic sequence is: f(n + 1) = f(n) + 2, f(1) = 14.
b. The explicit formula is: \(a_n = 14 + 2(n - 1)\).
c. The graph of the sequence is given by the image at the end of the answer.
d. The linear function is: f(n) = 12 + 2n. The arithmetic sequence, however, models the situation better, as the situation has a discrete domain.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the explicit formula presented as follows:
\(a_n = a_1 + (n - 1)d\)
In which \(a_1\) is the first term of the sequence.
The recursive formula is given as follows:
f(n + 1) = f(n) + d.\(f(1) = a_1\)For this problem, the first term and the common difference are given as follows:
\(a_1 = 14\), which is the number of chairs on the first row.d = 2, as each row has 2 more chairs than the row in front of it.For the linear function, we take the explicit formula, apply the distributive property, and combine the like terms.
However, since the function is not defined for decimals, the arithmetic sequence is a better representation of the context.
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Convert 5 gram in quintal
Answer:
5e-5
Step-by-step explanation:
I hope that is right
PLEASE, I REALLY NEED YOUR HELP!!
For each of the figures, write an Absolute Value equation to satisfy the given solution set.
Answer:
|x-5|=2
Step-by-step explanation:
1- Find the mid value between the given numbers 3 and 7
(3+7)/2= 10/2 = 5
2- Find the difference btween the mid value (5) and any of the two given numbers (3 or 7). Use the absolute value for the difference.
|5-3|= 2 or |7-5|=2
3- Arrange the absolute equation like this:
|x-mid value from step 1|= absolute difference from step 2
|x-5|=2
4- Double check the answer with the given values 3 and 7 using our equation |x-5|=2
|3-5|=2 correct
|7-5|=2 correct
7. Given f(x) = 3x - 1, find f(2).
4
2
1
5
Answer:
5
Step-by-step explanation:
3a^2 * 2a^3
multiply the monomial
Answer:
6a^5
Step-by-step explanation:
3a^2*2a^3
3×2+a^2×a^3
6a^5
Answer:
The answer is 6a⁵.
Step-by-step explanation:
You have to use Indices Law,
\( {a}^{m} \times {a}^{n} \: ⇒ \: {a}^{m + n} \)
So for this question :
\(3 {a}^{2} \times 2 {a}^{3} \)
\( = (3 \times 2) \times ( {a}^{2 + 3}) \)
\( = 6 \times {a}^{5} \)
\( = 6 {a}^{5} \)
Bing bong Bing bong Bing bong
Answer:
Hey and not sure if this is for free points but thanks for the points :)
Answer: bing bong bing bong
Help!!! please show some work so i know its right! THANKS!!!!
Answer:
A
Step-by-step explanation:
90 degree angle = right angle, that's what it is. you know there's 60 degree, so the other one is 90 - 60 = 30. since it's 3 times x, it's 10.
I NEED AN ANSWER ASAP PLEASE
Step-by-step explanation:
the correct answer is option a 6a-7
the third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160. there is a service center on the highway located three-fourths of the way from the third exit to the tenth exit.
The service center is located at milepost 130 on the highway.
To find the location of the service center, we need to first find the total distance between the third and tenth exits, and then find three-fourths of that distance.
The total distance between the third and tenth exits is:
160 - 40 = 120 miles
Three-fourths of this distance is:
(3/4) * 120 = 90 miles
Starting from the third exit at milepost 40, we can find the location of the service center by adding 90 miles to the milepost number:
40 + 90 = 130
Therefore, the service center is located at milepost 130 on the highway.
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he Bishop family celebrated a birthday by dining out at a local restaurant. Their bill was $97.45. Mr. Bishop would like to leave a 18 percent tip at the table for the server. What is the total amount that the family will pay for the dinner? Round to the nearest cent if necessary
Answer: it is 114.99
Step-by-step explanation:
Answer:114.99
Step-by-step explanation:
Evaluate 2x+y, if x=1 and y=-3
x=1
y=-3
required to evaluate 2x+y
We therefore substitute for x and y in the above expression
2(1) + (-3) = 2 - 3 = -1
Help help help help help help help
Answer:
35/14
Step-by-step explanation:
Volume = 4 * h * 7 / 2 = 14h
35/14 = h
Grade 7 Unit 4 District Assessment 2020-21 Question: 1 Jacob saw a model of a building that will be built in his city. The model has a height of 40 centimeters and will be built to a scale of 1:50. What is the actual height of the building? (1 m = 100 cm)
Answer:
123334
Step-by-step explanation: