The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Using the sine rule, the measurement of the angle of opposite the side measuring 11 inches can be done. Therefore, the measure can be written as,
8/ Sin(30°) = 11/ Sin(θ)
Sin(θ) = [11 × Sin(30°)]/8
Sin(θ) = 0.6875
θ = Sin⁻¹ (0.6875)
θ = 43.4325° ≈ 43°
Hence, The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.
Learn more about Sine Rule:
https://brainly.com/question/17289163
#SPJ1
Part 1: Come up with and describe two scenarios: one that models a direct variation situation and one that models an inverse variation situation. Do not state explicitly which scenario is which, but provide at least four data pairs for each situation. Your classmates will have to determine which of the scenarios is a direct variation and which is an inverse variation, and the value of k for each.
Answer:
1. I went to a store four days in a row and only bought chocolate bars each day. All chocolate bars were the same and cost the same. On the first day, I bought 2 chocolate bars for $2.38. On the second day I bought 1 chocolate bar for $1.19. On the third day, I bought 10 chocolate bars for $11.90. On the fourth day, I bough 4 chocolate bars for $4.76.
2. A sink is full. It contains 20 gallons of water. The stopper is removed and water starts draining out. One minute after the stopper is removed, the volume of water in the sink is 18 gallons. Two minutes after the stopper is removed, the volume of water in the sink is 16 gallons. Four minutes after the stopper is removed, the volume of water in the sink is 12 gallons. Ten minutes after the stopper is removed, the sink is empty.
Which inequality does the graph
represent?
y
−2 O 2 x
2
−2
Answer:
Step-by-step explanation:
period of f(x)=cos(x)+2
Answer:
The period is 2π
Explanation:
The period is 2 times pi because 2 is the standalone-term multiplied by pi to get the period.
A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second. the function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t. what is the max height the pumpkins will reach and what time will it reach that height?
The maximum height of the pumpkin is 3 feet
We have given that,
A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second.
The function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t.
We have to determine the maximum height.
What is the maxima?
At the point of maxima f'(x)=0
first, find the maxima
Therefore differentiate the given function with respect to t we get,
[tex]h'(t)=-32t+96[/tex]
h'(t)=0
Then we get,
[tex]0=-32t+96\\-32t=-96\\t=\frac{-96}{-32} \\t=3[/tex]
Therefore the maximum height of the pumpkin is 3 feet.
To learn more about the maxima visit:
https://brainly.com/question/13995084
#SPJ1
The Algebra Club has decided to rent a convention center for their annual Algebra Gala. The cost for the rental will be split evenly among the attendees, which means that the price per person varies inversely with the number of people attending.
If 25 people attend, the cost will be $30 per person.
How many people would need to attend to get the cost under $20 per person?
A) 28
B) 38
C) 48
D) 58
Part b
what is the area of the target that earns at least 30 points on a throw?
select the correct from the drop-down menu.
the area is ____ square inches.
a) 16
b) 49
c) 121
d) 144
Tyger buys his car for $6900 he spends some Time repairing it and improving it. He sells it for $9200. What is his percentage profit?
If Tyler sold his car for $9200, then the approximate percentage profit for this product is 33.3%.
How to calculate the percentage?Final price - initial price
$9200 - $6900 = 2300Calculate the percentage $2300 is equivalent to by using the information you already have.
6900 = 1002300 = xx= 100 x 2300/ 6900x= 33.3%33.3% is the profit percentage.
Learn more about percentage in: https://brainly.com/question/1691136
#SPJ1
Fill out the chart please!
The dot plot and the box plot shown both represent Manuel’s data. Determine which visual display is more useful for answering each of the questions listed in the table, and explain your reasons.
1. Mean of the data: 8
2. Median: 8
3. IQR = 4
4. Members that use the facility 10 days a month is: 2.
See reasons below.
What is the Mean, Median, and Interquartile Range of a Data?Mean = sum of all values ÷ number of data values (easily solved using a dot plot
Median = middle value (easily found using a box plot).
Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).
1. Mean of the data: use the dot plot.
Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8
2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.
Median = 8
3. IQR = Q3 - Q1 = 10 - 6
IQR = 4
4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.
Learn more about the mean, median, and interquartile range on:
https://brainly.com/question/9821103
#SPJ1
What is the missing probability from the line?
Give your answer as a decimal.
The missing probability from the line in the diagram attached is 0.5.
What is a missing probability from the number line?The number line is a graduated straight line system showing the value of each real number from (-∞, +∞).
The probability of a number line in the diagram below is halfway (middle) between the impossible event and a certain event.
Thus,
Probability from the line = 1/2Probability from the line = 0.5 (decimal)Learn more about missing probability here:
https://brainly.com/question/17165819
#SPJ1
The volume of a rectangular prism is 400 cm3 . If the length is 16 cm and the width is 5cm, what is its height?
Answer:
H = 5
Step-by-step explanation:
rectangular prism:
V = L x W x H
400 cm3 = 16 x 5 x H
400 cm3 = 80 x H
400/80 = 5
h = 5 cm
95% sure this is correct! :)
Answer:
5 cm
Step-by-step explanation:
Formula used :
Volume of the rectangular prism = Length × Width × Height
=========================================================
Given :
⇒ Volume = 400 cm³
⇒ Length = 16 cm
⇒ Width = 5 cm
===========================================================
Solving :
⇒ 400 cm³ = 16 cm × 5 cm × Height
⇒ Height = 400 cm³ / 80 cm²
⇒ Height = 5 cm
Alex wants to cover his wall
with a circular clock that has a
diameter of 16 in. How much
space will the clock cover on
his wall?
Answer: A = π r2
r=8 and 8 squared is 64 and 64×3.14=200.96 or rounded to the nearest whole number it would be 201
Step-by-step explanation: brainliest please?
The first term in an arithmetic sequence is -3. If the sequence has a common difference of 8, what is the 30th term in the sequence?
Will give brainliest to right answer :))
Answer:
229
Step-by-step explanation:
(my work for the problem is in the photo I attached)
(I also wrote this step-by-step in the photo because I can explain things better as I do them)
This will be a little bit confusing without me writing out the numbers, so mainly this is if you can't read my handwriting
-3 + 8 = 5 ; 5 + 8 = 13
(1st term) (2nd term) (3rd term)
Instead of adding 8 repeatedly (repeated addition), we can use multiplication.
To get the 3rd term in this sequence, we had to add 8 twice, which could also be done by multiplying 8 twice (8 x 2)
13 + 8 = 21
(4th term)
to get the 4th term, we added 8 three times (or, 8 x 3)
So, if we are looking for the 30th term in a sequence, we will have to add 8, 29 times (8 x 29) to our original term.
8 x 29 = 232
-3 + 232 = 229
This means that the 30th term of the sequence will be 229.
Brad took 5 kicks and made 4 goals: 4/5
Sydney will take 10 shots and she wants to make an equivalent fraction of the goals. How many goals must She make?
4/5 x ?/? = ?/10
Answer: 8/10
Step-by-step explanation: so you have to multiply 5 times x u till you get 10 so you’ll multiply it 2 times and since you multiplied the left 5 times two you have to multiply the 4 by 2 also to keep everything equal so the final answer is 8/10
4X+8<28
ayudenme por favor
Answer:
x < 5.
Step-by-step explanation:
Creo que esto es correcto. :')
which of the following equations will produce the graph shown below?
A circle can be characterized by its center's location and its radius' length. The correct option is A.
What is an equation of a circle?A circle can be characterized by its center's location and its radius' length. Let the center of the considered circle be at (h,k) coordinate and the radius of the circle be 'r' units. Then, the equation of that circle would be:
(x-h)² + (y-k)² = r²
The given graph is the graph of a circle that has its origin at (0,0) and has a radius of 4 units, therefore, the equation will be,
(x-0)² + (y-0)² = 4²
x² + y² = 16
Multiply both the sides of the equation by 2,
2x² + 2y² = 32
Hence, the correct option is A.
Learn more about the Equation of a circle:
https://brainly.com/question/10165274
#SPJ1
A school sold all but 5 of ta school sold all but 5 of their old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally have
Answer:
20
Step-by-step explanation:
The proceeds from the sale can be described by an equation involving the original number of computers.
__
setupLet n represent the number of computers the school originally had. Then n-5 is "all but 5" and is the number sold. Each is sold for ₹1200, and the value of the sale is ₹18000. This can be expressed by the equation ...
(n -5)×1200 = 18000
__
solutionThis 2-step linear equation can be solved by dividing by the coefficient, and adding the opposite of the constant.
n -5 = 18000/1200 = 15 . . . . . divide by 1200
n = 15 +5 = 20 . . . . . . . . . . add the opposite of -5
The school originally had 20 computers.
what is 15/56 in simplest form
Answer:
15/56
Step-by-step explanation:
15 and 56 have a GCF of 1.
What is the area of the shape
The area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively, option (a) is correct.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners. Two pairs of congruent sides, and it has one pair of opposite congruent angles.
We know the area of the kite = pq/2
Where p and q are the length of the diagonals
p = 10+10 = 20 ft
q = 7+11 = 18 ft
Area = (20×18)/2
Area = 180 square feet
Thus, the area of the shape is 180 square feet if the length of the diagonals are 20 and 18 ft respectively option (a) is correct.
Learn more about the quadrilateral here:
brainly.com/question/6321910
#SPJ1
The archway of the main entrance of a university is modeled by the quadratic equation y = -x2 6x. the university is hanging a banner at the main entrance at an angle defined by the equation 4y = 21 − x. at what points should the banner be attached to the archway?
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The archway of the main entrance of a university is modeled by the quadratic equation
y = -x² + 6x ....1
The university is hanging a banner at the main entrance at an angle defined by the equation
4y = 21 − x ....2
Then the banner attached to the archway will be
From equations 1 and 2, we have
4(-x² + 6x) = 21 - x
-4x² + 24x = 21 - x
4x² - 25x + 21 = 0
4x² - 21x - 4x + 21 = 0
x(4x - 21) - 1(4x - 21) = 0
(4x - 21)(x - 1) = 0
x = 5.25, 1
Then the value of y will be
When x = 5.25, then we have
y = -(5.25)² + 6(5.25)
y = 3.938
When x = 1, then we have
y = -(1)² + 6(1)
y = 5
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
The graph is given below.
More about the parabola link is given below.
https://brainly.com/question/8495504
#SPJ1
The mean percent of childhood asthma prevalence in 43 cities is 2.16%. A random sample of 31 of these cities is selected. What is the
probability that the mean childhood asthma prevalence for the sample is greater than 2.6% ? Interpret this probability. Assume that o=1.36%.
The probability is:
Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.
What is Probability ?
Probability is the measure of likelihood of an event.
For a Normal Distribution ,
the z-score formula is given by
[tex]\rm Z = \dfrac{X - \mu }{\sigma}[/tex]
Here [tex]\rm \mu\\[/tex] is the mean and [tex]\rm \sigma\\[/tex] is the standard deviation .
It is the measure of the deviation of the data from its central tendency.
Each z-score has a probability value.
It is given in the question that
Mean of 2.16% = [tex]\rm \mu\\[/tex] = 2.16
Standard deviation of 1.36% means that [tex]\rm \sigma\\[/tex] = 1.36
For Sample of 31 the value of standard deviation is [tex]\rm s = \dfrac{\sigma}{\sqrt{n}}[/tex]
s = 1.36/√31
s = 0.2442
Substituting the values
Z = (2.6 -2.16)/0.2442
Z =1.8
the p value from the graph of z and p , 0.9643
To determine value of probability more than X is 1 - 0.9643= 0.0357
the
Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.
To know more about Probability
https://brainly.com/question/11234923
#SPJ1
Pls helpDetermine the area, in square units, of rectangle ABCD.
Enter the area of rectangle ABCD.
The area of the rectangle, as shown in the image given is calculated as: 48 square units.
What is the Area of a Rectangle?The area of a rectangle = length × width.
Find the length and width of the rectangle:
Length (BC) = 8 unitsWidth (AB) = 6 unitsArea of rectangle ABCD = 8 × 6 = 48 square units.
Learn more about area of a rectangle on:
https://brainly.com/question/25292087
#SPJ1
Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9).
A= units^2
Check the picture below. so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}[/tex]
[tex](\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the diagonal of the rectangular solid with the given measures. (Part of the answer is provided for you.)
l = 18, w = 10, h = 2
Answer:
Step-by-step explanation:
Length=18
Width/Breadth =10
Height=2
The formula for a diagonal face of a cuboid is=√(l²+ b²)
Face diagonal=√(18²+10²)
= 20.59 to 2.d.p
The formula for the body diagonal of a cuboid is=√(l² + b² + h²)
Body diagonal=√(18² + 10² + 2²)
=20.69 to 2.d.p
find the distance between the two points in simplest radical form.
(3,-8) and (8,4)
Answer:
13
Step-by-step explanation:
The way to find the distance between two points on the coordinate plane is to use the distance formula, which is basically a way of applying the Pythagorean Theorem.
The distance formula is [tex]\sqrt{(x_{1}- x_{2} )^2 + (y_{1}- y_{2})^2}[/tex]. Let's say the coordinate (3, -8) is (x1, y1) and the coordinate (8, 4) is (x2, y2). We can plug these values into the formula:
[tex]\sqrt{(3- 8 )^2 + (-8 - 4)^2}\\\sqrt{(-5)^{2} + (-12)^{2}} \\\sqrt{25+144} \\\sqrt{169} \\13[/tex]
So, the distance between the two points is 13.
TRUE OR FALSE
1. Standard units gives a consistent and accurate of the volume of a container.
TRUE OR FALSE ?
Answer:
True
Step-by-step explanation:
Cant really provide step by step per se.
Q). Express each of the following recurring decimal as a rational numbers . 1) 0.5 2) 0.13 3) 0.341
The following recurring decimal as a rational number are 1/2, 13/100 and 341 / 1000
What is rational number?A rational number is a number that is expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator such as;
3/4. where,
Numerator = 3Denominator = 4Therefore,
0.5
= 5/10
= 1/2
0.13
= 13/100
0.341
= 341 / 1000
Learn more about rational number:
https://brainly.com/question/12088221
#SPJ1
Regress smoker on cubic polynomials of age, using a linear probability model. What is the p-value for testing the hypothesis that the probability model is linear in age? (two decimal places)
The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
What is probit regression?A probit model is a type of regression in statistics where the dependant variable can only take two values.
We have:
Regress smoker on cubic polynomials of age
If we use linear probability model.
Here the data are missing, but we can say about the estimate that:
Only the estimate intercept is statistically significant at the 5% level is wrong,
Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
Learn more about the probit regression here:
brainly.com/question/23389011
#SPJ4
If a baseball player hits 10 home runs in the first 45 game, at the same rate how many home runs can he expect to hit during the 162 game season
Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the player hits 10 home runs in 45 games, hence the proportion is:
p = 10/45.
Then, in 162 games, the amount is:
HR = 10/45 x 162 = 36.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Fiona recorded the mean math exam grade for six random samples of students from the entire seventh-grade class. Sample Sample Mean Grade 1 65 2 92 3 78 4 45 5 95 6 70 Why is a valid prediction for the mean of the population not possible using these samples?
The reason why Fiona cannot make a valid prediction based on the mean of the population is that the variation of Fiona’s samples is too large.
Why can't Fiona use the means she recorded?Mean is quite sensitive to outliers so it is best used when the variation between variables is not too much.
In Fiona's case, there variation is quite high with high variable of 95 compared to a low value of 45.
Find out more on effect of outliers at https://brainly.com/question/16815987.
#SPJ1
Answer: just confirming/
Step-by-step explanation:
The question is in the picture.
Answer:
x² - 22x + y² + 18y + 58 = 0
Step-by-step explanation:
Using the equation of a circle :
(x - h)² + (y - k)² = r²
Solving :
Substitute 11, -9, 12 in place of h, k and r respectively.
(x - 11)² + (y + 9)² = (12)²x² - 22x + 121 + y² + 18y + 81 = 144x² - 22x + y² + 18y + 202 = 144x² - 22x + y² + 18y + 58 = 0