Applying the formula for the area of triangle using sine, we have:
sin A = 1/3 (A ≈ 19.5°).
How to Find the Area of a Triangle Using Sine Rule?Given that a triangle has the following parameters:
Area of triangle ABC = 21 square units
Side b = 14 units
Side c = 9 units
Thus, applying the area of a triangle using the sine rule, we have the following formula:
Area = 1/2 * b * c * sin A
Plug in the values:
21 = 1/2 * 14 * 9 * sin A
2 * 21 = 126 * sin A
42 = 126 * sin A
42/126 = sin A
sin A = 1/3
A = sin^(-1)(1/3)
A ≈ 19.5°
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The graph shows the distribution of the amount of chicken (in ounces) that adults eat in one sitting. The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
A graph titled Chicken Consumption has amount (ounces) on the x-axis, going from 3.2 to 12.8 in increments of 1.2. The highest point of the curve is at 8.
What percentage of adults eat more than 10.4 ounces of chicken in one sitting?
A. 2.5%
B. 47.5%
C. 95%
D. 97.5%
The percentage of adults who eat more than 10.4 ounces of chicken in one sitting is 2.5%. The correct option is A.
We know that the distribution is approximately normal with a mean of 8 ounces and a standard deviation of 1.2 ounces. We want to find the percentage of adults that eat more than 10.4 ounces of chicken in one sitting.
To solve this problem, we can use the standard normal distribution table or a calculator with the normal distribution function.
Using the calculator, we can standardize the value 10.4 using the formula:
[tex]z = \dfrac{(x - \mu)} { \sigma}[/tex]
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, we have:
[tex]z = \dfrac{(10.4 - 8) }{1.2} = 2[/tex]
We can then use the calculator to find the percentage of the distribution that lies above the z-score of 2. This is approximately 2.5%.
Therefore, the answer is A. 2.5%.
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Suppose that the functions f and g are defined as follows.
Find f.g and f+ g. Then, give their domains using interval notation.
The composition of f. g derived from the equations in the attached image is: [tex]\frac{1}{10}(2x + 1)[/tex] and f+g as √(4x-1))/(5x²+3)
How to solve compositionComposition is a mathematical operation that combines two functions to form a new function. From our question, we are given two functions f(x) and g(x).
One of their composition can be represented by f(g(x)).f(g(x)) means function out of g(x) will serve as input x for function f(x). In a more simpler words, f(g(x)) is the function obtained by taking the output of g(x) and using it as the input for f(x).
Using the question given as an example,
For f.g:
Firstly, we have to compute the composition of f and g.
This can be expressed as:
f(g(x))f(g(x)) = f(√(4x-1))= 1/[5(√(4x-1))² + 3]= 1/[5(4x-1) + 3]
= 1/(20x + 10)
= [tex]\frac{1}{10}(2x + 1)[/tex]
For f+g:
To find f+g, we will just add the two functions together as below:
f+g = 1/(5x²+3) + √(4x-1)= (√(4x-1) + (5x²+3)
= √(4x-1))/(5x²+3)
So the answers are;
f.g: = [tex]\frac{1}{10}(2x + 1)[/tex]
f+g = √(4x-1))/(5x²+3)
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Think of a number puzzle
The equation is: (2x + 8) / 4 - 3 = x - 7
The solution is x = 12
How to solve the puzzleLet x be the number you thought of at the beginning. Following the steps:
Multiply by 2: 2x
Add 8: 2x + 8
Divide by 4: (2x + 8) / 4
Subtract 3: (2x + 8) / 4 - 3
The final answer is seven less than the number you thought of at the beginning: (2x + 8) / 4 - 3 = x - 7
The equation is: (2x + 8) / 4 - 3 = x - 7
2. (2x + 8) / 4 - 3 = x - 7
(1/2)x + 2 - 3 = x - 7
(1/2)x - 1 = x - 7
Now add 1 to both sides:
(1/2)x = x - 6
Subtract (1/2)x from both sides:
-1/2x = -6
Now multiply both sides by -2:
x = 12
3. Properties used to solve the puzzle
Addition Property of Equality
Multiplication Property of Equality
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what is the perimeter of a rectangle with corners at (-5, 1) ,
(2, 1) , and (2, -3) ?
Answer:
22
Step-by-step explanation:
length is given by (3--1=4)
width is given by (2--5=7)
perimeter is given by:
P=2l + 2w
P=2(4)+2(7)
P=8+14
P=22
Apiece of Wire 80cm long is cut into the two parts and bent each part to Form a square the tota area of the two squaresquare is 250 Find perimiter of each Square side length of each Square
The perimeter of the square with side of 5 cm is 20 cm.
The perimeter of the square with side length of 15 cm is 60 cm.
What is the area of each square?The area of each square is calculated as follows;
Let the dimension of first square = x
Let the dimension of second square = y
x² + y² = 250 ---- (1)
4(x + y) = 80 ----- (2)
x + y = 80/4
x + y = 20
x = 20 - y
Substitute x in equation (1)
(20 - y)² + y² = 250
400 - 40y + y² + y² = 250
2y² - 40y + 150 = 0
y² - 20y + 75 = 0
solve for y, using formula method;
y = 15 or 5
Solve for x;
x = 20 -15 = 5 or
x = 20 - 5 = 15
The perimeter of first = 4x = 4 x 5 = 20 cm
The perimeter of the second = 4y = 4 x 15 = 60 cm
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Johan wants to make some small cakes.
He finds a recipe that says he needs 360 grams of flour to make 15 small cakes.
Johan has 0.85 kg of flour.
Johan works out how much flour he would need to make 38 small cakes, using the
information given in the recipe.
Does Johan have enough flour, according to the recipe, to make 38 small cakes?
Show your working clearly.
The amount of flour that will be needed for 38 cakes is 912 grams therefore Johan does not have enough amount of flour
What is word problem?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
360 grams is needed for 15 small cakes
therefore for 1 small cake, 369/15 = 24grams will be needed
therefore for 38 small cakes = 38× 24 = 912 grams of flour will be needed.
Johan has 0.85 kg of flours which is equivalent to 0.85 × 1000grams = 850 grams of flour.
Since 912 grams will be needed for 38 small cakes , it shows that Johan does not have enough amount of flour for 38 small cakes.
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find the misding values in the ratio table then write the equivalent ratios forks 16 8 spoons 10, 30
The missing number in the ratios of numbers are 16:10 8:20 and 0:30
How to determine the missing numbers?Ratios are quantitative relationships between two numbers that describe how many times one value can contain another
the given parameters are
Forks 16 8 ----
Spoons 10 --- 30
The numbers are written in ascending order of magnitude
Using AP,
for forks: a = 16, 2nd term = 8
common difference = 8-16 - -8
For spoons a = 10, 3rd term = a + 2d = 30
30 = 10 + 2d
30 -10 = 2d
d= 20/2 = 10
Therefore the 2nd term = 10+10=20
The table reappears as follows
Forks 16 8 0
Spoons 10 20 30
Therefore the equivalent ratios are 16:10 8:20 and 0:30
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Find the solutions to y = –8x for x = 2, 4, and 8.
A. (–16, 2), (–32, 4), (–64,8)
B. (16, 2), (32, 4), (64,8)
C. (2, 16), (4, 32), (8, 64)
D. (2, –16), (4, –32), (8, –64)
The solutions to y = –8x for x = 2, 4, and 8 are (2, –16), (4, –32), (8, –64), hence, option D is correct.
We are given the equation y = -8x and asked to find the solutions for x = 2, 4, and 8. To find the solutions, we substitute the given values of x into the given linear equation and solve for y.
For x = 2, we have,
y = -8x
y = -8(2)
y = -16
Therefore, the solution for x = 2 is (2, -16).
For x = 4, we have,
y = -8x
y = -8(4)
y = -32
Therefore, the solution for x = 4 is (4, -32).
For x = 8, we have,
y = -8x
y = -8(8)
y = -64
Therefore, the solution for x = 8 is (8, -64).
Putting these solutions together, we get {(2,-16), (4,-32), (8,-64)}. Hence, the correct answer is option D.
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A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $46,400 per month. A television ad costs $1000, a radio ad costs $200, and a newspaper ad costs $600. The department wants to run 64 ads per month, and have as many television ads as radio and newspaper ads combined. How many of each type of ad can the department run each month?
The number of each type of ad that the department can run each month are:
TV Ads = 32
Radio Ads = 12
News Ads = 20
How to solve Simultaneous equation word problems?x = number of tv ads
y = number of radio ads
z = number of news ads
Two formulas are indicated.
x + y + z = 64
1000x + 200y + 600z = 46400
they want as many tv ads as radio and news ads combined.
equation for that is x = y + z
since x = y + z, replace x with y + z in both equations to get;
y + z + y + z = 64
1000 * (y + z) + 200 * y + 600 * z = 46400
combine like terms and simplify to get:
2y + 2z = 64
1000y + 1000z + 200y + 600z = 46400
combine like terms again to get:
2y + 2z = 64
1200y + 1600z = 46400
Solving simultaneously gives:
y = 12
z = 20
Thus:
x = 12 + 20
x = 32
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On a recent math test, the mean score was 75 and the standard deviation 5. What is the 25th percentile for the math scores
The 25th percentile for the math scores is 71.65.
How to determine the 25th percentile for the math scores?In Mathematics and Geometry, the z-score of a given sample size or data set can be calculated by using this formula:
Z-score, z = (x - μ)/σ
Where:
σ represents the standard deviation.x represents the sample score.μ represents the mean score.Note: 25th percentile for the math scores is the same as the first quartile for the math scores.
Based on the z-score table A, 25th percentile (0.25) is equal to a z-score of -0.67;
0.2514 = -0.67
By substituting the parameters, we have:
Z-score, z = (x - μ)/σ
-0.67 = (x - 75)/5
x = 75 - 3.35
x = 71.65
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What is the volume of a hemisphere with a radius of 9.8 in, rounded to the nearest tenth of a cubic inch?
The volume of the hemisphere is approximately 1970.2 cubic inches.
Given that:
Radius, r = 9.8 inches
The formula for the volume of a hemisphere is given as:
V = (2/3) x π x r³
V = (2/3) x π x (9.8 in)³
V = (2/3) x 3.14 x 941.192
V = 1970.2 cubic inches
Therefore, the volume of the hemisphere is approximately 1970.2 cubic inches.
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Segment AB is perpendicular to the circle centered at O. The length of AB is 2.5 units and the length of CB is 1.5 units. Find the exact length of the radius of this circle.
The exact length of the radius of this circle is 2.69 units.
Given that, the length of AB is 2.5 units and the length of CB is 1.5 units.
Since AB is perpendicular to the circle, the triangle ABC is a right triangle. By the Pythagorean theorem, the radius of the circle can be found by solving:
r² = (2.5)² + (1.5)²
r² = 7.25
r = √7.25
r = 2.69 units
Therefore, the exact length of the radius of this circle is 2.69 units.
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Jared's class took a survey to see how many students owned a trampoline. Of the 24 students in the class, 14 students said they owned a trampoline. If you chose a student at random from Jared's class, what is the probability that the student does not own a trampoline?
The probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.
The probability that the student does not own a trampoline is equal to the number of students who do not own a trampoline divided by the total number of students in the class.
The number of students who do not own a trampoline is equal to the total number of students in the class minus the number of students who own a trampoline:
24 - 14 = 10
Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is:
P(not owning a trampoline) = 10/24
Simplifying the fraction,
P(not owning a trampoline) = 5/12
Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.
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A right triangle has side lengths 6 centimeters and 8 centimeters. Is it possible for there to be more than one right triangle with whole-number side lengths that includes the given side lengths? Explain.
The given side lengths, 6 cm and 8 cm, satisfy the Pythagorean theorem because $6^2 + 8^2 = 100 = 10^2$, which means that the triangle is a right triangle.
To determine if there is more than one right triangle with whole-number side lengths that includes these given side lengths, we need to check if there exist other pairs of whole numbers that satisfy the Pythagorean theorem and include 6 cm and 8 cm as two of their sides.
Let's call the third side of the right triangle x. Then we have:
62+82=x26^2 + 8^2 = x^262+82=x2
which simplifies to:
36+64=x236 + 64 = x^236+64=x2
100=x2100 = x^2100=x2
x=100=10x = \sqrt{100} = 10x=100
=10
So the only other possible triangle with whole-number side lengths that includes the given side lengths has side lengths of 6 cm, 8 cm, and 10 cm.
Therefore, there is only one other right triangle with whole-number side lengths that includes the given side lengths, and it is unique.
Last week's and this week's low temperatures are shown in the table below.
Low Temperatures for 5 Days This Week and Last Week
Low Temperatures
This Week (°F)
Low Temperatures
Last Week (°F)
4
10
13 9
6
5
9
6
8 5
Which measures of center or variability are greater than 5 degrees? Select three choices.
O the mean of this week's temperatures
O the mean of last week's temperatures
the range of this week's temperatures
the mean absolute deviation of this week's temperatures
the mean absolute deviation of last week's temperatures
The measures of center or variability are greater than 5 degrees
The the mean of this week's temperatures the mean of last week's temperaturesthe range of this week's temperaturesHow to measure for variablilyThis Week's Mean: (4 + 13 + 6 + 9 + 8) / 5 = 40 / 5 = 8
Last Week's Mean: (10 + 9 + 5 + 6 + 5) / 5 = 35 / 5 = 7
Then the ranges
This Week's Range: (13 - 4) = 9
Last Week's Range: (10 - 5) = 5
The MAD for both weeks
|(4 - 8)| + |(13 - 8)| + |(6 - 8)| + |(9 - 8)| + |(8 - 8)|
= 4 + 5 + 2 + 1 + 0 = 12
This Week's MAD: 12 / 5 = 2.4
|(10 - 7)| + |(9 - 7)| + |(5 - 7)| + |(6 - 7)| + |(5 - 7)| = 3 + 2 + 2 + 1 + 2 = 10
Last Week's MAD: 10 / 5 = 2
Hence the measures of center or variability are greater than 5 degrees are:
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A single die is rolled twice. The 36 equally-likely outcomes are shown to the right.
Find the probability of getting two numbers whose sum exceeds .
The probability that the sum exceeds 5 is P ( A ) = 0.6111
Given data ,
To find the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice, we need to count the number of outcomes where the sum of the two numbers is greater than 5, and then divide that by the total number of equally-likely outcomes.
The outcomes where the sum exceeds 5 are:
(2, 4), (2, 5), (2, 6)
(3, 3), (3, 4), (3, 5), (3, 6)
(4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 22 outcomes where the sum exceeds 5 out of a total of 36 equally-likely outcomes.
So, the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice is:
P(sum > 5) = 22 / 36 ≈ 0.6111 or approximately 61.11 %
Hence , the probability is P ( A ) = 0.6111
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The complete question is attached below :
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right.Find the probability of getting two numbers whose sum exceeds 5
Pls help, this is for geometry
I'm not 100 percent sure so please only rate after you see if it's right.
ANSWER: $1090
STEP 1:
The volume of one brick is given by multiplying its length, width, and height:
V = (7 1/4) in x 3 in x (2 1/4) in
V = (29/4) in x 3 in x (9/4) in
V = 2187/16 cubic inches
STEP 2:
The cost of one brick is given by multiplying the volume by the cost per cubic inch:
C = (2187/16 cubic inches) x $0.05/in^3
C = $1.09/brick
STEP 3: To find the cost of 1000 bricks, we simply multiply the cost of one brick by 1000:
Cost of 1000 bricks = 1000 x $1.09/brick
Cost of 1000 bricks = $1090
Therefore, the cost of 1000 bricks is $1090, rounded to the nearest cent.
Which statement could be made based on the diagram below?
A) m∠3 + m∠6 = 90
B) ∠3 = ∠6
C) ∠3 = ∠5
D) m∠4 + m∠5 = 180
Answer:
A) angle 3 plus angle 6 = 90°
Step-by-step explanation:
just think about it : to the left of m at the intersection with n is 90°. so, to the right it must be 90° too.
because one side of a line represents always 180° for all angles around a single point.
What is 0.007 divided by 0.498 to nearest tenth
Answer:
0.0
Step-by-step explanation:
To find 0.007 divided by 0.498, we can perform the following calculation:
0.007 / 0.498 ≈ 0.0141
Rounding this to the nearest tenth gives:
0.0141 ≈ 0.0
Therefore, the result, rounded to the nearest tenth, is 0.0.
pls help me and explain as well because I rlly don’t understand this
Step-by-step explanation:
A linear function is a function where we have a constant rate of change.
The equation of a linear function is
[tex]y = mx + b[/tex]
where m is the slope (change in y/change in x)
and b is the y intercept.
Note: Sometimes our variables will different names, but
Slope is just change in dependent variable/change in independent variable.
A linear function has a constant slope throughout.
In this problem,
t is the independent variable
W is the dependent variable
So our point will. be
(t,W)
where t is number of weeks after planted
and W is weight
So the slope would be
Change in W/Change in t.
We know at 3 weeks, the pumpkin weighed 141
So this point is
(3,141)
We know 7 weeks, later, the pumpkin weighed 372 so
(10,372)
A. The weight the pumpkin gain each week is our slope so
[tex] \frac{372 - 141}{7} [/tex]
[tex] \frac{231}{7} = 33[/tex]
So the pumpkin gained 33 pounds each week.
Part 2: Is in slope intercept form,
and we know the slope,33,
[tex]w = 33t + b[/tex]
We don't know what b is.
Let plug in a coordinate pair, and solve for b.
Let's use (3,141)
[tex]141 = 33(3) + b[/tex]
[tex]141 = 99 + b[/tex]
[tex]42 = b[/tex]
So our equation is
[tex]w = 33t + 42[/tex]
Hope this helps
The weight that the pumpkin gained per week can be found to be 33 pounds.
The equation to show the relationship between pumpkin weight and elapsed time is W = 33 t + 42
How to find the weight gained ?The weight gained by the pumpkin per week can be found by the formula :
= (Weight gained after 7 more weeks - Weight after 3 weeks ) / 7 weeks
= ( 372 - 141 ) / 4
= 33 pounds
This means the original weight of the pumpkin was:
= 141 - ( 33 x 3 weeks )
= 42 pounds
The equation to show the relationship between pumpkin growth and weeks is therefore:
W = Growth per week x Number of weeks + original weight
W = 33 x + 42
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5(10v-8w+4) as a distributive property
Using distributive property, the solution to the given expression is: 50v - 40w + 20
How to use distributive property?The Distributive Property is a term which is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.
For example:
4(3 + 5)
According to the distributive property, you first have to multiply out the bracket to get:
4*3 + 4*5 = 12 + 20
= 32
Thus:
5(10v - 8w + 4) = (5 * 10v) - (5 * 8w) + (5 * 4)
= 50v - 40w + 20
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HELP ASSAP 20 POinTSSSSSSSSSSSSSS
Step-by-step explanation:
use the formula V=1/3hπr².
V=1/3×3 π 2×2
V=1/3×12π
V=4πcm3
Which angles are congruent to each other? Select all that apply.
Answer:
1,2, and 4
Step-by-step explanation:
vertical angles theorem, which says that the vertical angles that are formed when two lines intersect are congruent.
What is the probability the he will choose a red marble
The probability that Tom will choose a red marble from the bag is 1/9.
Given that,
Tom is choosing at random from a bag of colored marbles.
Odds in favor = number of success : number of failures
Odds of getting a red marble = 1 : 8
This means that there ratio of red marbles to other marbles = 1 : 8
Number of red marbles = 1
Total number of marbles = 1 + 8 = 9
Probability of choosing a red marble = 1/9
Hence the required probability is 1/9.
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This table shows the percent increase in the consumer price index (CPI) over five three-month periods. A Bar Graph was made to represent this information graphically.
What is wrong with this Bar Graph?
A. The vertical axis is divided into unequal intervals.
B. The vertical axis is too small for this data.
C. The bars are not of the same width.
D. The heights of the bars do not represent the correct percent increase.
Answer:
D
Step-by-step explanation:
What is 3/11 simplified
Danielle is saving to buy a bedroom set that cost $2,976. If she saves for 24 weeks, how much will she need to save each week?
Answer:
$124 per week
Step-by-step explanation:
To fins how much she needs to save each week, divide the total cost by the amount of time. In this problem, divide $2,976 by 24 weeks to find the amount she needs to save.
$2976/24=$124 per week
Amelie travelled to her friend's house and her journey is shown on the distance-time graph below. She travelled the final 4 hours of her journey at a constant speed of 60 km/h. Work out the value of d. Distance travelled (km) 270- 0 3 Time (hours) -
The total distance traveled by Amelia to her friend's house is d = 510 miles
Given data ,
Let the distance traveled by Amelia to her friend's house be d
Now , the speed of the final 4 hours of her journey = 60 km/hr
So , the distance traveled in the final 4 hours = 4 x 60 = 240 km
And , the initial distance traveled = 270 km
So , from the graph
The total distance d = 270 + 240
d = 510 miles
Hence , the distance traveled by Amelia = 510 miles
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The population of a particular country was 23 million in 1981; in 1987, it was 32 million. The
exponential growth function A =23ekt describes the population of this country t years after 1981. Use
the fact that 6 years after 1981 the population increased by 9 million to find k to three decimal places.
K's value is around 0.055 to three decimal places.
Let's first use the given information to set up two equations:
A(0) = 23 (the initial population in millions)
A(6) = 32 (the population 6 years later in millions)
Substituting these values into the exponential growth function A = 23e^(kt), we get:
[tex]23 = 23e^(k0) = > e^{(k0)} = 1\\32 = 23e^{k*6}[/tex]
Dividing the second equation by the first, we get:
[tex]32/23 = e^{6k}[/tex]
Taking the natural logarithm of both sides, we get:
ln(32/23) = 6k
Solving for k, we get:
k = ln(32/23)/6
k ≈ 0.055
Rounding to three decimal places, we get k ≈ 0.055.
Therefore, the value of k to three decimal places is approximately 0.055.
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If you were to graph 9x + 5y > 1 , where would you shade according to the slope of the line? The shading would occur above the solid line of the slope The shading would occur below the solid line of the slope. The shading would occur below the dashed line of the slope. The shading would occur above the dashed line of the slope.
The requried shading would occur above the solid line of the slope.
To graph the inequality 9x + 5y > 1, we first need to graph the equation 9x + 5y = 1, which is the equation of the line that separates the two regions determined by the inequality.
To graph this line, we can solve for y in terms of x:
9x + 5y = 1
y = (-9/5)x + 1/5
This is the equation of a line with slope -9/5 and y-intercept 1/5. We can plot this line on a coordinated plane. Since the slope of the line is negative, the shading should occur above the line, which means the correct answer is: The shading would occur above the solid line of the slope.
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