There are two solutions for given system of equations: (5, 35) and (-4, 8).
What does "system of equations" and its solution means ?A system of equations is a grouping of two or more equations with numerous variables that are treated as a whole. The solution to a system of equations is the set of variable values that satisfies all of the equations in the system at the same time.
Typical approaches for resolving equation systems include:
Substitution MethodElimination MethodMatrix MethodGraphical MethodGiven system of equations is,
[tex]y=x^2+2x[/tex]..................(1)
[tex]y=3x+20[/tex]..................(2)
Solving equations algebraically,
Equating the formulas for 'y' in both equations:
[tex]x^2 + 2x = 3x + 20[/tex]
Rearranging the equation :
[tex]x^2 - x - 20 = 0[/tex]
Here, we got a quadratic equation,Solving for values of x,
[tex](x - 5)(x + 4) = 0[/tex]
[tex]x - 5 = 0 \\x=5\\or\\x + 4 = 0\\x=(-4)[/tex]
For values of 'y', putting values of x in equation (1),
for x = 5,
[tex]y = 5^2 + 2(5)=25 + 10 = 35[/tex]
Thus, (5, 35) is one of the solution.
for x= -4,
[tex]y = (-4)^2 + 2(-4)=16 - 8 = 8[/tex]
Thus, (-4, 8) is other solution.
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A rectangular pyramid is shown in the figure.
A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.
What is the surface area of the pyramid?
The surface area of the pyramid is 113 cm².
What is rectangular pyramid?A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.
The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.
To find the surface area of the pyramid, we need to find the area of each face and then add them up.
Area of the base:
The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:
Area of base = length × width = 7 cm × 5 cm = 35 cm²
Area of the four triangular faces:
Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:
Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²
Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²
There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:
Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face
= 2 × 19 cm² + 2 × 20 cm²
= 78 cm²
Total surface area:
Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:
Total surface area = area of base + total area of four triangular faces
= 35 cm² + 78 cm²
= 113 cm²
Therefore, the surface area of the pyramid is 113 cm²
.
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3. In a sports centre, the ages of 100 people were recorded as follows: Age Under 20 years 20 to 29 years 30 t0 39 years 40 to 59 years 60 years and over Number of people 30 15 12 14 29 Fri, 24 Mar 2023 Angle (i) complete the table above to show the angle for each categ rounded off to the nearest degree. (ii) construct a pie chart using the circle below.
100 people = 360° of circle
For n people, the degree for the circle is (n×360)÷100
30 people = (30×360)÷100 = 108°
15 people = 54°
12 people = 43.2° ≅ 43°
14 people = 50.4° ≅ 50°
29 people = 104.4° ≅ 104°
What is the perimeter of the triangle?
Answer:
40 units
Step-by-step explanation:
a = 8
b = 15
To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]8^{2} +15^{2} =x^{2}[/tex]
64 + 225 = c^2
289 = c^2
c = 17
a + b + c = perimeter
8 + 15 + 17 = 40
Answer:
40 units
Step-by-step explanation:
You want the perimeter of the triangle shown in the graph.
DimensionsYou can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.
The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:
c² = a² +b²
c² = 8² +15² = 64 +225 = 289
c = √289 = 17
The long side of the triangle is 17 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides:
P = 8 + 15 + 17 = 40
The perimeter is 40 units.
__
Additional comment
A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.
The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)
60°
y
Find the value of y.
A. y = 2
B.
4√√3
3
y = 4
C.
D. y = 4√3
8
30°
The value of y is 4, so the answer is option A: y = 4.
What is trigonometric ratios ?
Trigonometric ratios are mathematical relationships between the angles and sides of a right triangle. There are three primary trigonometric ratios: sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.
Using the given diagram, we can use the trigonometric ratios to find the value of y.
First, we can find the length of the side opposite the 30-degree angle by using the sine ratio:
sin(30°) = opposite/hypotenuse
sin(30°) = y/8
y/8 = 1/2
y = 8/2
y = 4
Therefore, the value of y is 4, so the answer is option A: y = 4.
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please help fill in these..
Answer:
Vertex: (-2, -1)
Axis of Symmetry: x = -2
Y-intercept: (0, 3)
Min/Max: Min
Domain: All Real
Range: y ≥ -1
Step-by-step explanation:
Given the graph:
Vertex is the intersection of the axis of symmetry and the max/min value.Axis of Symmetry is the line that equally divides an object into two halves.Y-intercept is when the line crosses the y-axis and can be found when x is equal to zero.Min is the lowest value and max is the highest value.Domain is all of the x-values that work in the function.Range is all of the y-values that work in the function.Answer:
So, the answers to the question is:
Vertex: (-2, -1)
Axis of Symmetry: x = -2
Y-intercept: (0, 3)
Min/Max: Min
Domain: All Real
Range: y ≥ -1
On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
Answer:
B.
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
the description is very confusing and lacks any hint about the behavior of the curve before the change.
but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.
I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.
now they pay the driver. $0.25 per mile.
this has to come out of their profit.
so, the Y (profit) values all go down by 0.25.
therefore, the y-intercept is going down too.
that eliminates C. and D.
for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).
so, the line must be in a form
y = ax + b
with "b" <> 0.
and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).
because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.
and that eliminates A, leaving B. as the right answer.
PLEASE HELP !!
(Do not guess please and thank you )
Step-by-step explanation:
A = π r²
r = 3 inches
A = 3.14 × (3)²
A = 3.14 × 9
A = 28.29 square inches
You have a bag with 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble. What is the probability of drawing a red marble out of the bag?
Answer:
40%
Step-by-step explanation:
We Know
You have a bag with 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble.
4 + 3 + 2 + 1 = 10 marbles total
What is the probability of drawing a red marble out of the bag?
We Take
(4 ÷ 10) x 100 = 40%
So, 40% of drawing a red marble out of the bag.
Peanuts sell for Php 10.00 per gram. Cashews sell for Php 8.00 per gram. How many grams of cashews should be mixed with 12 g of peanuts to obtain a mixture that sells for Php 9.00 per gram?
PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]
Answer:
Phn10x12
Step-by-step explanation:
PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]
12. The length of a rectangle is 6 meters longer than the width. If the total area of the rectangle is 16m², find the dimensions of the rectangle.
Answer: Let's say that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is 6 meters longer than the width, which means that the length is (x + 6) meters.
The formula for the area of a rectangle is:
Area = Length x Width
We are given that the total area of the rectangle is 16m². Substituting the expressions for length and width, we get:
(x + 6) x = 16
Expanding the product and rearranging, we get a quadratic equation:
x² + 6x - 16 = 0
We can solve this equation by factoring or by using the quadratic formula. Factoring, we get:
(x + 8) (x - 2) = 0
This equation is satisfied when either x + 8 = 0 or x - 2 = 0. Therefore, the possible values for the width are x = -8 or x = 2. However, since the width of a rectangle cannot be negative, we reject the solution x = -8.
Therefore, the width of the rectangle is x = 2 meters. The length is 6 meters longer than the width, so the length is (2 + 6) = 8 meters.
Therefore, the dimensions of the rectangle are 2 meters by 8 meters.
Step-by-step explanation:
whats the answer to 102-38x14 divided by 7+162= help plss
Answer:
-2.5
Step-by-step explanation:
follow BIMDAS.
like my answer if you find it helpful
What are the variables in expression x + 8 - y?
Answer:
x and y are the variables.
Step-by-step explanation:
What is the average of these numbers?
45 46 50 52 51 59 55 51 42 44
51 55 60 62 52 54 47 74 52 52
59 52 65 45 58 59 59 52 54 65
If you are performing a right-tailed z-statistic test with a sample size n = 100 and a 0.01 significance level, what is the critical value?
If your calculated value of the z-statistic is z = 2.88, what is your conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis)?
1. The critical value, according to the z-table, is roughly 2.33. 2. There is enough data to support the alternative hypothesis and reject the null hypothesis.
What is null hypothesis?A null hypothesis is a claim that assumes there is no meaningful difference between two or more variables in a population or that any difference that is detected is the result of chance in statistical hypothesis testing. Typically, it is indicated by H0. A statement that rejects the null hypothesis and assumes that the variables being compared have a substantial difference is known as an alternative hypothesis, or Ha. In contrast to the null hypothesis, which the researcher is attempting to refute, the alternative hypothesis is what the researcher is attempting to prove.
1. We can use a z-table or a calculator to determine the critical value for a right-tailed z-statistic test with a sample size of 100 and a significance level of 0.01. The z-score that equates to the 0.99 probability level, which is the complement of the 0.01 significance level, is the critical value. The crucial value, according to the z-table, is roughly 2.33.
2. We compare the estimated z-statistic value, z = 2.88, to the crucial value, 2.33. The estimated value of z falls in the rejection zone of the null hypothesis because it exceeds the crucial value. As a result, we find that there is enough data to support the alternative hypothesis and reject the null hypothesis.
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Landon and Maria are meeting at the library to work on their history project. Maria walks 9 blocks east and 3 blocks north to get to the library from her house. Landon walks 5 blocks south and 7 blocks west to get to the library from his house. The map below shows the location of the library and Landon's and Maria's houses. To the nearest block, how far is Landon's house from Maria's house if Maria could walk in a straight line?
To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.
What is Pythagoras theorem?A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.
This can be written in mathematical notation as:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.
In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:
Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks
Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks
Now we can use the Pythagorean theorem to find the distance between their houses:
Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks
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Find the logarithm of this
The logarithm of the expression [tex]5^{(-3log_{5} 2 )} * 2^{(log_{2}3)}[/tex] is log(3/8).
What is logarithm?Mathematical functions called logarithms let us change the scale at which numbers are expressed. They specifically aid in the transformation of numbers stated in exponential form into numbers expressed in standard form. The exponent to which the base must be raised in order to obtain a given number is given by the logarithm of the number to the specified base. For instance, since 23 = 8, the logarithm base 2 of 8 is 3. Natural logarithms, which are logarithms to the base e (about 2.718), and common logarithms, which are logarithms to the base 10, are the two types of logarithms that are most frequently used.
The given logarithmic expression is:
[tex]5^{(-3log_{5} 2 )} * 2^{(log_{2}3)}[/tex]
Using the properties of logarithm we have:
[tex]5^{(-3log_{5} 2 )} 2^{(log_{2}3)}\\= (5^{(log_{5}2)})^{(-3)} * 3\\= 2^{(-3)} * 3\\= 3/8[/tex]
Hence, the logarithm of the expression [tex]5^{(-3log_{5} 2 )} * 2^{(log_{2}3)}[/tex] is log(3/8).
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The supply and demand for a product are related to price by the following equations, where y is the price, in dollars, and x is the number of units, in thousands. Find the equilibrium point for this product.
y=300+40x
y=9300-50x
helpp..
Answer: At equilibrium, the supply and demand are equal, so we can set the two equations equal to each other:
300 + 40x = 9300 - 50x
Simplifying and solving for x:
90x = 9000
x = 100
Now that we know x, we can use either equation to find y:
y = 300 + 40(100) = 4300
So the equilibrium point is when x = 100 and y = 4300.
Step-by-step explanation:
What is the volume of a cube with a length of 11 meters? Volume V = $³ V = /w/z V = Bh V=²h Cube Rectangular prism Triangular prism Cylinder OA) 33 m³ B) 121 m³ C) 1,221 m² D) 1,331 m³ or V = Bh
Answer:
The volume of a cube with a length of 11 meters is 33 m³.
A container in the shape of a rectangular prism has a height of 2 feet. Its length is four
times its width. The volume of the container is 200 cubic feet. Find the length and width of
the container.
Answer: length = 20 feet and width = 5 feet
Step-by-step explanation: Volume is equal to volume = height * width * length. The questions tells us the total volume is 200 cubic feet and that the lenght is equal to length = 4w. Set up the equation 4w * w * 2 = 200 cubic feet. Multiply to get 8w^2 = 200 and solve for w.
Could someone help me find the answers and show me how they got it it’s a review for a quiz I have to take for tomorrow
Area of composite shape = 12 + 9
= 21 cm²
How to solve
Area of composite shapes:
13) Figure 1:
Figure1 is a rectangle.
l = 4 cm & w = 2 cm
Area of figure1 = l * w
= 4 * 2
= 8 cm²
Figure2:
Figure2 is a parallelogram
base = b = 4 cm
h = 4 cm
Area of figure2 = b * h
= 4 * 4
= 16 cm²
Area of composite shape = 8 + 16
= 24 cm²
14) Figure1:
Figure 1 is a trapezium. a & b are parallel sides and h is the height
a = 4 cm ; b = 6 cm; h = 4 -2 = 2 cm
Figure2:
Figure2 is a rectangle. l = 6 cm ; w = 2 cm
Area of figure2 = 6*2
= 12 cm²
Area of composite shape = 10 + 12
= 22 cm²
15) Figure 1 & figure 2:
Figure 1 and figure 2 are congruent triangles
base = b = 3 cm & h= 4 cm
= b *h
= 3 * 4
= 12 cm²
Figure3:
Figure 3 is a square.
side = 3 cm
Area of figure3 = side *side
= 3 * 3
= 9 cm²
Area of composite shape = 12 + 9
= 21 cm²
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Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity
The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).
Explanation:The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.
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4)
Northbrook Middle School surveyed 325 students to learn more about their after-schoo
activities. They found that 90 students are in a club and play a sport. 140 total students
play a sport and 200 total students are in a club. Construct a two-way relative freques
table summarizing the data.
Plays a Sport
In a Club
Not In a Club
Total
Doesn't Play a
Sport
Total
Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).
What is frequency?Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.
90 students are in a club and play a sport.
140 total students play a sport.
Therefore, 140 - 90 = 50 students play a sport but are not in a club.
The total number of students who play a sport is 140 + 50 = 190.
200 total students are in a club.
Therefore, 200 - 90 = 110 students are in a club but do not play a sport.
The total number of students who do not play a sport is 325 - 190 = 135.
The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.
This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.
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solve for r if $425.83=400(1+r)^5 ? (show explanation please)
Answer: 0.0295
Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.
Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:
$1+r=\sqrt[5]{1.064575}$.
Subtracting 1 from both sides gives $r\approx 0.0295$.
Therefore, your answer would be 0.0295.
Create a Truth Table for
A ⋀ ~B
By answering the presented question, we may conclude that Finally, the expressions fourth column represents the value of the expression A ⋀ ~B for each possible combination of truth values of A and B.
how can we create truth table?To create a truth table for A ⋀ ~B, we first need to list all possible combinations of truth values for A and B, and then calculate the value of the expression A ⋀ ~B for each combination.
A B ~B A ⋀ ~B
True True False False
True False True True
False True False False
False False True False
In the above truth table, the first column lists all possible truth values of A, and the second column lists all possible truth values of B. The third column represents the negation of B, which is denoted as ~B. Finally, the fourth column represents the value of the expression A ⋀ ~B for each possible combination of truth values of A and B.
Therefore, the truth table for A ⋀ ~B is:
A B A ⋀ ~B
True True False
True False True
False True False
False False False
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The expression 12x +8 is equivalent to the expression a(bc+c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4). Which statement best explains whether the students answer is correct or incorrect
The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
What is expression?Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.
This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.
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Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).
Which statement best explains whether the student's answer is correct or incorrect?
OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).
C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).
OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).
How is this solved? how does this even work
Part a: The Weight corresponding to the given z score: z = -1 is 2.4 kilograms.
Part b: The Weight corresponding to the given z score: z = 1.34 is 3.921 kilograms.
Define about the z score:The relationship between a value and a group of values' mean is described by the Z score or standard score. It gauges how far a data point deviates from the mean.
the procedure of standardising or normalising a raw score to get a standard score. The most popular name for the standard scores is Z Scores.
Given that for the normal distribution.
mean weight of the new born babies μ = 3.05 kilogramsstandard deviation σ = 0.65 kilogramsLet the weight for the given z scores be x.Weight corresponding to the given z score-
Part A: z = -1
Z score :
z = (x - μ)/σ
-1 = (x - 3.05)/0.65
x - 3.05 = -0.65
x = -0.65 + 3.05
x = 2.4
Thus, the Weight corresponding to the given z score: z = -1 is 2.4 kilograms.
Part b: z = 1.34
z = (x - μ)/σ
1.34 = (x - 3.05)/0.65
x - 3.05 = 1.34*0.65
x = 0.871 + 3.05
x = 3.921
Thus, the Weight corresponding to the given z score: z = 1.34 is 3.921 kilograms.
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PLEAE HELP ME!!! I need this quickly!
Find the exact value of the expressions cos(alpha + beta) sin(alpha + beta) and tan(alpha + beta) under the following conditions. sin(alpha) = 24/25 a lies in quadrant I, and sin(beta) = 15/17 B lies in quadrant II.
We can use the trigonometric identities to find the exact values of the expressions.
First, we can find cos(alpha) and cos(beta) using the Pythagorean identity:
cos(alpha) = sqrt(1 - sin^2(alpha)) = sqrt(1 - (24/25)^2) = 7/25
cos(beta) = -sqrt(1 - sin^2(beta)) = -sqrt(1 - (15/17)^2) = -8/17 (since beta is in quadrant II, where cosine is negative)
Next, we can use the sum formulas for sine and cosine to find sin(alpha + beta) and cos(alpha + beta):
sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) = (24/25)(-8/17) + (7/25)(15/17) = -117/425
cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta) = (7/25)(-8/17) - (24/25)(15/17) = -24/85
Finally, we can use the quotient identity for tangent to find tan(alpha + beta):
tan(alpha + beta) = sin(alpha + beta) / cos(alpha + beta) = (-117/425) / (-24/85) = 39/85
Therefore, cos(alpha + beta) sin(alpha + beta) = (-24/85)(-117/425) = 936/7225, and tan(alpha + beta) = 39/85.
An insurance company reported that 70% of all automobile damage claims were made by people under the age of 25. If 5 automobile damage claims were selected at random, determine the probability that exactly 4 of them were made by someone under the age of 25.
I need the method more than the answer, as detailed as possible, please.
There is a 0.00567 percent chance that 4 out of the 5 auto damage claims were submitted by individuals under the age of 25.
what is a binomial theorem?An expression that has been raised to any finite power can be expanded using the binomial theorem. A binomial theorem is a potent expansionary technique with uses in probability, algebra, and other fields.
A binomial expression is an algebraic expression with two terms that are not the same. For instance, a+b, a3+b3, etc.
Let n = N, x, y, R, then the binomial theorem holds.
(x + y)n = nΣr=0 where, nCr xn - r yr
what is a probability?The likelihood of an event happening is gauged by probability. Several things are impossible to completely predict in advance. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. A crucial subject for pupils in class 10, probability explains all the fundamental ideas of the subject. A sample space has an overall probability of 1 for all events.
This is a binomial probability problem, where each automobile damage claim is a Bernoulli trial with a probability of success (a claim made by someone under the age of 25) of p=0.70. We want to find the probability of getting exactly 4 successes out of 5 trials.
The probability of getting exactly k successes out of n trials in a binomial experiment with probability of success p is given by the binomial probability formula:
P(k successes out of n trials) = (n choose k) * [tex]p^k[/tex] * [tex](1-p)^(n-k)[/tex]
where (n choose k) = n! / (k! * (n-k)!) is the number of ways to choose k items out of n items.
In this case, we have n=5 and p=0.70. So, the probability of getting exactly 4 successes out of 5 trials is:
P(4 out of 5 claims made by someone under 25) = (5 choose 4) * [tex]0.70^4[/tex] *[tex](1-0.70)^(5-4)[/tex]
P(4 out of 5 claims made by someone under 25) = 5 * [tex]0.70^4[/tex] *[tex]0.30^1[/tex]
P(4 out of 5 claims made by someone under 25) = 0.00567 (rounded to 5 decimal places)
Therefore, the probability that exactly 4 of the 5 automobile damage claims were made by people under the age of 25 is approximately 0.00567.
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What is the solution to the equation 3/5x-4-3√7x+8?
A x = -6
B x=-1
C x = 1
D x = 2
The solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
To solve the equation 3/5x - 4 - 3√7x + 8 = 0:
First, simplify the expression by combining like terms:
3/5x - 3√7x + 4 = 0 + 8
3/5x - 3√7x + 4 = 8
Next, move the constant term to the right side:
3/5x - 3√7x = 8 - 4
3/5x - 3√7x = 4
Factor out x from the left side:
x(3/5 - 3√7) = 4
Divide both sides by (3/5 - 3√7):
x = 4 / (3/5 - 3√7)
To simplify the expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (3/5 + 3√7):
x = 4(3/5 + 3√7) / [(3/5 - 3√7)(3/5 + 3√7)]
x = 12/5 + 12√7/5 / (9/25 - 63/25)
x = 12/5 + 12√7/5 / (-54/25)
x = -10√7/9
Therefore, the solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.
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What is M in triangle properties
I hope this helps you.