The probability of a bone density score greater than 0.18 is given as follows:
0.4286 = 42.86%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 0, \sigma = 1[/tex]
The probability of a score greater than 0.18 is one subtracted by the p-value of Z when X = 0.18, hence:
Z = (0.18 - 0)/1
Z = 0.18
Z = 0.18 has a p-value of 0.5714.
Hence:
1 - 0.5714 = 0.4286 = 42.86%.
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Higher Order Thinking Tanika has 7 toothpicks. She uses them all to create two polygons. Draw two polygons that Tanika could have created. Write the names of your shapes.
Therefore , the solution of the given problem of polygon comes out to be
hexagon and pentagon.
What is polygon?In Euclidean mathematics, a simple quadrilateral of two sets of equal distances is referred to as a parallelogram. In a specific kind of quadrilateral known as a parallelogram, both set of opposite sides are straight and equal. There are four types of parallelograms, 3 of which are each mutually exclusive. Rhombuses, parallelograms, squares, but also rectangles are the four distinct shapes.
Here,
Here are two examples of shapes Tanika could make with seven toothpicks:
=> First polygon:
This is a hexagon without a triangular. It has seven edges and six sides.
=> Second polygon:
This pentagon has two line segments that stretch from its vertices on either side. It also has 7 edges and 7 sides.
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Numbers such as 1, 2, 3,. . . Are also called the _____ numbers
The numbers 1, 2, 3, and so on are called natural numbers
The numbers 1, 2, 3 and so on are commonly known as natural numbers. They are the most basic and fundamental type of numbers used in mathematics. Natural numbers are positive integers that are used for counting and measuring quantities.
They are called "natural" because they are the numbers that naturally occur when we count objects in the real world. The set of natural numbers is denoted by the symbol N and it is an infinite set that starts from 1 and continues infinitely. Natural numbers form the basis for other types of numbers, such as whole numbers, integers, rational numbers, and real numbers, and they are used in a wide range of mathematical applications.
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Mia wants to make a canvas tent as shown. How much canvas is needed to make the tent in inches squared?
Answer:
429
Step-by-step explanation:
The width of a rectangle is 4 units less than the length. The area of the rectangle is 32 square units. What is the length, in units, of the rectangle?
Answer:
Let L be the length of the rectangle.
According to the problem, the width of the rectangle is 4 units less than the length, so the width is L - 4.
The area of the rectangle is given as 32 square units, so we can set up the equation:
A = L(L - 4) = 32
Expanding the left side of the equation, we get:
L^2 - 4L = 32
Rearranging and factoring, we get:
L^2 - 4L - 32 = 0
We can solve for L by using the quadratic formula:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -4, and c = -32.
L = (-(-4) ± sqrt((-4)^2 - 4(1)(-32))) / 2(1)
L = (4 ± sqrt(16 + 128)) / 2
L = (4 ± sqrt(144)) / 2
L = (4 ± 12) / 2
L = 8 or L = -4
Since the length must be a positive value, we take L = 8.
Therefore, the length of the rectangle is 8 units.
The width and length of the rectangle will be 4 units and 8 units, respectively.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The width of a square shape is 4 units less than the length. The region of the square shape is 32 square units. Then the equations are given below.
[tex]W = L - 4[/tex] ...1
[tex]L \times W = 32[/tex] ...2
From equations 1 and 2, then we have
[tex]L \times (L - 4) = 32[/tex]
[tex]L^2 - 4L = 32[/tex]
[tex]L^2 - 4L - 32 = 0[/tex]
[tex]L^2 - 8L + 4L - 32 = 0[/tex]
[tex]L(L - 8) + 4(L - 8) = 0[/tex]
[tex](L - 8)(L + 4) = 0[/tex]
[tex]L = 8, -4[/tex]
Then the width of the rectangle is given as,
[tex]W = 8 - 4[/tex]
[tex]W = 4 \ units[/tex]
The width and length of the rectangular shape will be 4 units and 8 units, separately.
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pls help me with this
Answer:
5.3
Step-by-step explanation:
The Answer is 5.3 because the number line shows 10 lines between the 5/10 and 6/10 this makes each line worth 0.1 each. Since point A is on the third line the answer would be 5.3 Hope this helps.
I
At an ice cream
stand, there are 4
different types of ice
cream, 3 different
cones, and 3 choices
of toppings.
How many different ways
can an ice cream cone be
ordered?
Answer: 36
Step-by-step explanation: To determine the number of ways an ice cream cone can be ordered; we must apply the multiplication principle of counting.
Given there are 3 different cone types, 3 choices of toppings, and 4 different types of ice cream, we can construct an equation to identify the maximum number of ways an ice cream cone can be ordered:
4 (types of ice cream) × 3 (types of cones) × 3 (choices of toppings) = 36 ways
Therefore, there are 36 different ways an ice cream cone can be ordered.
The number of different ways an ice cream cone can be ordered is 36.
What is the Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Given that, at an ice cream stand, there are 4 different types of ice cream, 3 different cones, and 3 choices of toppings.
We know that, nPr=n!/(n-r)!
Here, ⁴P₁׳P₁׳P₁
= 4!(4-1)! × 3!/(3-1)! × 3!/(3-1)!
= 4×3!/3! × 3×2!/2! × 3×2!/2!
= 4×3×3
= 36
Therefore, in 36 different ways cone can be ordered.
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Paula's Pizza Parlor uses the following ingredients to make pizza.
Number of Pizzas Sauce (oz) Cheese (oz)
2 18 12
5
At this rate, how much sauce and cheese will Paula use to make 5 pizzas?
Paula will use 30 oz of sauce and 45 oz of cheese to make 5 pizzas.
Paula will use 35 oz of sauce and 24 oz of cheese to make 5 pizzas.
Paula will use 45 oz of sauce and 30 oz of cheese to make 5 pizzas.
Paula will use 90 oz of sauce and 60 oz of cheese to make 5 pizzas.
Answer:
Paula will use 45 oz of sauce and 30 oz of cheese to make 5 pizzas
How to find quantity of ingredients for 5 pizzas?
To find this, you can use the proportion of ingredients used for 2 pizzas and scale it up to 5 pizzas.
For 2 pizzas, Paula uses 18 oz of sauce and 12 oz of cheese.
The proportion of sauce to cheese used is 18/12
To make 5 pizzas, you can use this proportion to find how much sauce and cheese is needed:
2 pizzas = 18 sauce
5 pizzas = 5 / 2 x 18 = 45 sauces.
For cheese required, Paula will use:
2 pizzas = 12 cheese
5 pizzas = 5 / 2 x 12 = 30 cheese.
So the total is 45 oz of sauce and 30 oz of cheese.
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Step-by-step explanation:
Answer:
Paula will use 45 oz of sauce and 30 oz of cheese to make 5 pizzas
Step-by-step explanation:
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
The answer is C.
Step-by-step explanation:
Write a system of equations for this-
Cora ran 3 miles last week and will run 7 miles per week from now on. Hana ran 9 miles last week and will run 4 miles per week from now on
The solution to the system of equations is C = 3 and H = 9.
Let C = Cora's miles last week and H = Hana's miles last week
The equation for Cora's miles is C + 7x = 3, and the equation for Hana's miles is H + 4x = 9, where x is the number of weeks.
The solution to this system of equations is C = 3, and H = 9. This can be determined by solving each equation separately and then checking that the answers satisfy both equations.
For Cora's equation, subtract 7x from both sides to get C = 3 - 7x. Solving for x gives x = (3 - C) / 7. Plugging this into Hana's equation gives H + 4((3 - C) / 7) = 9. Simplifying this equation gives H = 9 - 12 + 4C.
Checking the answers, C = 3 - 7(0) = 3, and H = 9 - 12 + 4(3) = 9. Both equations are satisfied by C = 3 and H = 9, so this is the solution to the system of equations.
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Data about annual maximum temperature \( { }^{\circ} \) Celcius of Muscat city for the last ten years since 2011 was collected by a group of STAT2101 students. A summary of the measure of central tendency isA summary of the measure of central tendency is: Based on the given data, what is the distribution of the maximum temperature in Muscat city? Select one: a. The maximum temperature is Another distribution. b. The maximum temperature is No distribution. c. The maximum temperature is Positively Skewed. d. The maximum temperature is Mutually Exclusive.
The distribution of the maximum temperature in Muscat city based on the given data is positively skewed. The correct option is c.
The distribution of the maximum temperature in Muscat city based on the given data is positively skewed. When a dataset's mean is higher than the median, this is known as a positively skewed distribution. It indicates that there are more lower values than upper values in the dataset.The mean, median, and mode are examples of measures of central tendency. A summary of the measure of central tendency of the annual maximum temperature in Muscat city for the last ten years since 2011 is required as it gives a clear overview of the dataset's central tendency, this is an important statistical summary.
The mean, median, and mode are the three most popular measures of central tendency. The mean is the average of all the data points in a dataset. It's calculated by adding up all the values in the dataset and then dividing by the number of data points.The median is the middle number in a dataset when it's sorted from lowest to highest. If there are two middle numbers, the median is the average of the two.Therefore, the distribution of the maximum temperature in Muscat city based on the given data is positively skewed, as there are more lower values than upper values in the dataset.
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the sum of the areas of two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)?
This statement is knοwn as the Pythagοrean Theοrem, and it states that the square οf the hypοtenuse οf a right triangle is equal tο the sum οf the squares οf the οther twο sides.
What is the area?The area is the amοunt οf twο-dimensiοnal space that is enclοsed within a given bοundary οr shape. It is measured in square units, such as square inches, square feet, οr square meters. The area is an impοrtant cοncept in mathematics and is used tο calculate the size οf physical οbjects as well as tο measure figures οn a twο-dimensiοnal surface. Knοwing hοw tο calculate area is an essential skill in a variety οf fields, including architecture, engineering, and landscaping.
This relatiοnship was first discοvered by the ancient Greek philοsοpher Pythagοras οf Samοs, whο nοticed that this equatiοn always held true in right-angled triangles. The equatiοn is expressed as, where a and b are the sides οf the triangle and c is the hypοtenuse.
Fοr example, Lets take an example οf twο legs 3 and 4, and the hypοtenuse be 5,
Lets see if the hypοtenuse² = leg a² + leg b²
⇒ 5² = 4² + 3²
⇒ 25 = 16 + 9
⇒ 25 = 25.
Thus, This statement is knοwn as the Pythagοrean Theοrem, and it states that the square οf the hypοtenuse οf a right triangle is equal tο the sum οf the squares οf the οther twο sides.
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The complete question is:
Is it correct that the sum of the areas of two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)?
Question 1
Use the figure below to answer your the following question.
2 feet
The figure above is a cube. What is the total surface area of the cube?
A. 6 square feet
B. 20 square feet
C. 8 square feet
D. 24 square feet
Question 2
A campsite provides a locking rectangular box with the dimensions shown below to secure food from bears.
3 feet
5 feet
2 feet
What is the surface area of the box?
A. 30 square feet
B. 62 square feet
C. 31 square feet
D. 72 square feet
Question 3
Gina is painting the rectangular tool chest shown in the diagram below.
24 in.
12 in.
10 in.
If Gina paints only the outside of the tool chest what is the total surface area in square inches (in.²) she will paint
A. 368
B. 648
C. 1296
D. 2880
Question 5
A triangular prism is pictured below.
6cm
5cm
6.5cm
6.5cm
16cm
What is the surface area of the prism?
A. 240 cm²
B. 318 cm²
C. 270 cm²
D. 348 cm²
Answer 1:
D. 24 sq feet
The formula to find surface area of a cube is [tex]a=6a^{2}[/tex]
Substitute 2 for a, [tex]2^{2} = 4[/tex]
6 x 4 = 24, so 24 sq feet
Answer 2:
B. 62 sq feet
The formula to find surface area of a rectangular prism is [tex]a = 2(wl+wh+hl)[/tex]
Substitute 3 for w, 5 for l, 2 for h and multiply
a = 62 sq feet
Answer 3:
C. 1296 sq inches
The formula to find surface area of a rectangular prism is [tex]a = 2(wl+wh+hl)[/tex]
Substitute 24 for w, 12 for l, 10 for h and multiply
a = 1296 sq inches
in a certain state, 60% of all adults have high blood pressure, 45% have high cholesterol and 20% have both high blood pressure and high cholesterol. what is the probability that a randomly selected adult from the state has high blood pressure but not high cholesterol?
The probability that a randomly selected adult from the state has high blood pressure but not high cholesterol is 0.40 or 40%.
To find the probability that a randomly selected adult from the state has high blood pressure but not high cholesterol, we need to subtract the probability of having both high blood pressure and high cholesterol from the probability of having high blood pressure.
Using set notation, let A be the event of having high blood pressure and B be the event of having high cholesterol. Then, the probability of having both high blood pressure and high cholesterol can be written as
P(A ∩ B)= 0.20
The probability of having high blood pressure can be written as
P(A) = 0.60
Therefore, the probability of having high blood pressure but not high cholesterol is:
P(A) - P(A ∩ B) = 0.60 - 0.20 = 0.40
Thus, the probability that a randomly selected adult from the state has high blood pressure but not high cholesterol is 0.40 or 40%.
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please help with this
The original coordinates of triangle NLM include the following:
N (-2 , -1)
L (2 , -3)
M (4,0)
What is a reflection?In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
Since triangle NL'M' was reflected over the x-axis, the original coordinates of triangle NLM can be calculated as follows;
(x, y) → (-x, y)
(-x, y) → (x, y)
N'(-2, 1) → N (-2 , -1)
L'(2, 3) → L (2 , -3)
M' (4, 0) → M (4,0)
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I can't figure out these questions. I know the answer because I'm using a textbook with answers in the back, but I don't understand *how* to get the answers. (I put 20 points for each question, please help!)
1. The difference of two polynomials is (3d² - 7d + 4).
One polynominal is (-8d² - 5d + 1).
a) What is the other polynomial? Explain how you found it.
b) How many different answers can you find?
I know that for the answer there are only two polynomials, (-5d² - 12d + 5) and (-11d² - 2d - 3), and I know how to get the first polynomial but the -11 one is confusing for me. I don't understand how to get it
2. Write a polynomial for the perimeter of each shape. Simplify the polynomial. Determine each perimeter when a = 3 cm.
Please help!!!
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
A bike trail is 5 1/10 miles long. Jade rides 1/4 of trail before stopping for a water break. How many miles does Jade ride before stopping? Show your work.
Jade travelled 51/40 miles before stopping
What are fractions?Fractions are simply defined as the part of a whole variable or also the part of a whole number that is given.
In mathematics, fractions take different forms, such as;
Mixed fractionsComplex fractionsProper fractionsImproper fractionsSimple fractionsFrom the information given, we have that;
The bike trail is about 5 1/10 miles long
Represent as an improper fraction, we get;
5 1/10 = 51/10 miles long
If Jade travelled 1/4 of the bike trail, then, we have;
1/4 × 51/10
Divide the values
51/40
1 11/40 of the trail.
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Jade rode about 1.275 miles before stopping.
How many miles does Jade ride before stopping?A mile means unit for measuring distance. We have 1,760 yards in a mile which is the same as 5,280 feet or 63,360 inches.
To find out how many miles Jade rode before stopping, we need to multiply the length of the bike trail by the fraction of the trail that Jade rode before stopping.
The length of the bike trail is 5 1/10 miles which is converted to 51/10 miles.
Jade rode 1/4 of the trail before stopping, which we can also express as 5/20.
The number of miles Jade rode before stopping is calculated as:
= (51/10) x (5/20)
= 1.275 miles.
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A person who is $5\frac{1}{2}$
feet tall casts a $3\frac{1}{2}$
-foot-long shadow. A nearby flagpole casts a 28-foot-long shadow. What is the height (in feet) of the flagpole?
The height of the flagpole is [tex]$\frac{28}{3\frac{1}{2}}\times 5\frac{1}{2}=50$[/tex]feet.
[tex]$\frac{28}{3\frac{1}{2}}\times 5\frac{1}{2}$[/tex]
[tex]$\frac{28\times 5\frac{1}{2}}{3\frac{1}{2}}$[/tex]
[tex]$\frac{140+7}{7}$[/tex]
[tex]$\frac{147}{7}$[/tex]
[tex]$50.71\approx50$[/tex] feet
The person and the flagpole are in the same environment, so if the person's height is 5 and a half feet and their shadow is 3 and a half feet, then the flagpole's shadow should be in the same ratio. By calculating the ratio between the flagpole's shadow and the person's height, we can determine the height of the flagpole. The ratio between the flagpole's shadow (28 feet) and the person's height (5 and a half feet) is 28 divided by 3 and a half. Multiplying this ratio by the person's height will give us the flagpole's height. The flagpole's height is approximately fifty feet.
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help please!!!!!!!!!!!
The equation of the perpendicular bisector of the line is y = 2x +16
What is slope?Slope of a line is defined as the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.01 It can also be expressed as a quotient ("rise")
1) the slope (m) = (change in y)/ change in x
m = (6-2)/ 7+3 = 4/10 = 2/5
b) the slope of the perpendicular is given by m₁*m₂ = -1
m₂ = -1/m₁
m₂ = -1 ÷2/5 = -5/2
c) the mid point of the ordered pair is (y₁+y₂)/2 and (x₁+x₂)/2
[(7+3)/2, (6-2)/2]
[10/2 , 4/2 ]
(5,2)
d) equation of the perpendicular is given by
m = (y - y₁)/ (x - x₁)
m( (x - x₁) = (y - y₁)
By substitution we have
2/5(x +3) = y-2
2x + 6 = y - 10
Making y the subject we have
Therefore, y = 2x +16
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Ms adams shares out 48 pencils between niamh and jack in the ratio 4:8
Niamh gets 16 pencils and Jack gets 32 pencils.
The ratio of 4:8 can be simplified to 1:2 by dividing both sides by 4. This means that for every one pencil Niamh gets, Jack gets two pencils.
To find out how many pencils each child gets, we need to divide the total number of pencils by the total number of parts in the ratio, which is 1 + 2 = 3.
So, each part of the ratio represents 48/3 = 16 pencils.
Therefore, Niamh gets 1 part, which is 16 pencils, and Jack gets 2 parts, which is 2 x 16 = 32 pencils.
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The given question is incomplete, the complete question is:
Ms. Adams shares out 48 pencils between Niamh and jack in the ratio 4:8, How many pencil does each child get ?
What is the area of a sector with a central angle of 60° and a radius of 16.7 ft?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
ft²
Answer:
Step-by-step explanation:
2
Answer:
145.95
Step-by-step explanation:
I took the test and got it right
PLEASE HELP!!!! PLEASE PLEASE PLEASE!!!!
The volume of the cylinder is approximately 753.98 cubic centimeters.and the volume of the cone is approximately 600.98 cubic centimeters.
The solutions of the question are given as following :-
1.To find the radius of a cone with height 19 cm and width (diameter) 12 cm, we can use the Pythagorean theorem to relate the height, radius, and slant height of the cone. The slant height is the distance from the vertex of the cone to any point on the circular base, and it is related to the height and radius by the equation:
slant height² = height² + radius²
We know the height is 19 cm, and the diameter (width) is 12 cm, so the radius is half of the diameter, or 6 cm. We can now substitute these values into the equation for the slant height:
slant height²= 19²+ 6²
slant height² = 361 + 36
slant height² = 397
slant height ≈ 19.92 cm
Therefore, the radius of the cone is approximately:
radius = √(slant height² - height²)
radius = √(397 - 19²)
radius ≈ 5.65 cm (rounded to two decimal places)
2.Volume = (1/3) * π * radius²* height
Substituting the given values, we get:
Volume = (1/3) * π * (5.65 cm)²* 19 cm
Volume ≈ 600.98 cubic centimeters
Therefore, the volume of the cone is approximately 600.98 cubic centimeters.
3.To find the volume of the cylinder with height 15 cm and radius (width/2) 4 cm, we can use the formula for the volume of a cylinder:
Volume = π * radius² * height
Substituting the given values, we get:
Volume = π * (4 cm)² * 15 cm
Volume = π * 16 cm² * 15 cm
Volume ≈ 753.98 cubic centimeters
Therefore, the volume of the cylinder is approximately 753.98 cubic centimeters.
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The quantities
�
xx and
�
yy are proportional.
�
xx
�
yy
9
99
4.5
4.54, point, 5
14
1414
7
77
30
3030
15
1515
Find the constant of proportionality
(
�
)
(r)left parenthesis, r, right parenthesis in the equation
�
=
�
�
y=rxy, equals, r, x.
�
=
The constant of proportionality (r) in the table of values of x and y has a value of 0.5.
Calculating the constant of proportionalityTo find the constant of proportionality (r) in the equation y = rx, we need to determine the ratio of y to x for each pair of quantities given in the table.
If x and y are proportional, then this ratio should be the same for all pairs of quantities.
Using the table, we have:
y/x = 4.5/9 = 0.5
y/x = 7/14 = 0.5
y/x = 15/30 = 0.5
Since the ratio of y to x is the same for all pairs of quantities, we can conclude that x and y are indeed proportional, and the constant of proportionality (r) is 0.5.
Therefore, the equation that represents the relationship between x and y is:
y = 0.5x
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Complete question
Rewrite the following properly and solve:
The quantitiesx and y are proportional.
x y
9 4.5
14 7
30 15
Find the constant of proportionality (r) in the equation
y = rx
Lake A has a volume of 21,150,427,000 cubic meters. Lake B has a volume that is 2.5 times the volume of Lake A. What is the approximate volume of Lake B? Write your answer as the product of a single digit and a power of 10.
Therefore , the solution of the given problem of volume comes out to be Lake B's volume is roughly as follows is 5.28760675 cubic metres.
Volume : What is it?The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Cubic measurements are represented by the symbols litre and in3. However, you can calculate an object's measurements using its bulk. In most cases, the item's weight is transformed into mass units like kilogrammes and kilos.
Here,
=> Lake B's capacity is 2.5 times greater than Lake A's.
=> Lake B's volume is 2.5 times that of Lake A.
=> Lake B's volume is 2.5 x 21,150,427,000.
=> Lake B has a volume of 52,876,067,500.
By moving the decimal point until there is only one non-zero digit left of the decimal point, we can represent this number as the sum of a single integer and a power of 10. We need to multiply by 1010 to account for the fact that we shifted it 10 positions to the left.
Therefore, Lake B's volume is roughly as follows:
=> 5.28760675 cubic metres
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please help me again
Answer:
75
Step-by-step explanation:
[tex]10x^2 - 3x - 6, x=3\\[/tex]
substitute all values of x.
[tex]10(3)^2 -3(3)-6[/tex]
then simplify the equation.
[tex]90-9-6[/tex]
=[tex]75[/tex]
Hope this helps!
Brainliest is much appreciated!
Answer:
75
Step-by-step explanation:
10(3)^2-3x3(or 9)-6
Warm-up:
1. -g + 2(3 + g) = -4(g +1)
The solution for g is -2
How to solve the linear equation?[tex]-g+2\left(3+g\right)=-4\left(g+1\right)[/tex]
expand [tex]-g+2\left(3+g\right)[/tex]
= [tex]g+6[/tex]
expand [tex]-4(g+1)[/tex]
[tex]-4g-4[/tex]
[tex]g+6=-4g-4[/tex]
collect like terms:
[tex]5g=-10[/tex]
Divide both side by 5:
[tex]\frac{5g}{5} =\frac{-10}{5}[/tex]
=[tex]g = -2[/tex]
Therefore, the solution for g is -2.
What is linear equation?A linear equation is an algebraic equation in which the highest power of the variable is 1. It can be written in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
The slope is the rate of change of the line, which represents how steeply it rises or falls, and the y-intercept is the point where the line intersects the y-axis.
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What is the surface area of this cone?
Answer:
211.55
Step-by-step explanation:
Answer: 215.83mm
Step-by-step explanation: to get the surface area of a cone, you need to plug in the radius (r) and the height (h) to this problem: A=Pi*r(r+{h to the power of 2+r to the power of 2} squared) so the actual problem would be A=Pi*3.7(3.7+{14.4 to the power of 2+ 3.7 to the power of 2} squared)=215.83mm
The half-life of carbon-14 is 5,730 years. Suppose a fossil is found with 30 percent as much of its carbon-14 as compared to a living sample. How old is the fossil?
Step-by-step explanation:
Find the number of half lives to get to .3 (which is 30%) then multiply by 5730 years per half life:
.3 = (1/2)^n <====solve for 'n'
log .3 / log (1/2) = n = 1.737 half lives
1.737 X 5730 = ~ 9953 years old
Travis tossed a coin off a bridge into the stream below. The path of the coin can be modeled by the equation where t is the time in seconds and h is the height in feet. How long will it take the coin to reach the stream?
The coin will reach the stream in 5.61 seconds.
How to determine how long it will take the coin to reach the stream?
Since the height of the coin, after t seconds, is given by the equation:
h = -16t² + 72t + 100
The stream is the ground level. Thus, the coin reaches the stream when h(t) = 0.
So we can equate the equation to zero and solve for t:
-16t² + 72t + 100 = 0
Using the quadratic formula:
t = −b ± √(b² − 4ac) 2a
where a = -16, b = 72 and c = 100
t = −72 ± [√(72² − 4(-16)(100))] /2(-16)
t = −72 ± [√11584]/(-32)
t = (-72 ± 107.63)/(-32)
t = (-72 + 107.63)/(-32) or (-72 - 107.63)/(-32)
t = -1.11 or 5.61
Since t cannot be negative. Thus, t = 5.61 seconds
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Complete Question
Travis tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t² + 72t + 100. How long will it take the coin to reach the stream?
PLEASE HELP ME WITH THIS PROBLEM !!!
Answer: 24
Step-by-step explanation: 2x2x2 is the volume since 2x2x2 is 8. so the surface area of one side would be 2x2. 4x6= 24. Since there are 6 sides, the answer is 24.
It’s argent
How much would you have to deposit now to be able to withdraw $2,400 at the end of each year for 10 years from an account that earns 4% compounded annually?
Answer:
The amount that would need to be deposited now to withdraw $2,400 at the end of each year for 10 years from an account that earns 4% compounded annually is $60,058.50.
Step-by-step explanation:
To determine how much would need to be deposited now to withdraw $2,400 at the end of each year for 10 years from an account that earns 4% compounded annually, we can use the present value formula for an annuity:
PMT x [(1 - (1 + r/n)^(-nt)) / (r/n)] = PV
Where:
PMT = the periodic payment
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the total number of years
PV = the present value (the amount to be deposited now)
In this case, we have:
PMT = $2,400
r = 4% = 0.04 (decimal)
n = 1 (compounded annually)
t = 10 years
Plugging these values into the formula, we get:
PV = $2,400 x [(1 - (1 + 0.04/1)^(-1*10)) / (0.04/1)]
PV = $2,400 x [(1 - 0.5537) / 0.04]
PV = $60,058.50
Therefore, the amount that would need to be deposited now to withdraw $2,400 at the end of each year for 10 years from an account that earns 4% compounded annually is $60,058.50.
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