The value of a when b=4 and c=4 is 72.70. Rounded to two decimal places, the answer is 72.70.
The variable a is jointly proportional to the cube of b and the square of c. This means that the relationship between a, b, and c can be expressed as: a = k * b^3 * c^2, where k is a constant of proportionality.
When a=433, b=5, and c=7, we can plug these values into the equation to find the value of k:
433 = k * 5^3 * 7^2
433 = k * 125 * 49
433 = k * 6125
k = 433/6125
k = 0.07069
Now, we can use this value of k to find the value of a when b=4 and c=4:
a = k * b^3 * c^2
a = 0.07069 * 4^3 * 4^2
a = 0.07069 * 64 * 16
a = 72.70
Therefore, the value of a when b=4 and c=4 is 72.70. Rounded to two decimal places is 72.70.
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What is the common ratio of this geometric sequence
Answer:
what about you read well and stop cheating
Send help due today!
question 1
A coat is on sale for 33% off the original price. What percent of the original price would you have to pay to buy the coat?
question 2
If Juan bought a video game and paid 8% sales tax on his purchase, what percent of the purchase price of the game did he pay as the total bill?
You would have to pay 67% of the original price to buy the coat and Juan paid 1. 08% of the purchase price as the total bill.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
If the coat is on sale for 33% off the original price, then the price you would have to pay is equal to 100% - 33% = 67% of the original price.
So, you would have to pay 67% of the original price to buy the coat.
If Juan paid 8% sales tax on his purchase, then the total bill would be the original price plus 8% of the original price.
Let's say the purchase price of the video game is x.
Then, the sales tax would be 8% of x, which is 0.08x.
So, the total bill that Juan paid is x + 0.08x = 1.08x.
Therefore, Juan paid 1. 08% of the purchase price as the total bill.
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The volume of a cone is 196π cubic feet. Its radius is 7 feet. Find the height
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=196\pi \\ r=7 \end{cases}\implies 196\pi =\cfrac{\pi (7)^2 h}{3}\implies 196\pi =\cfrac{49\pi h}{3} \\\\\\ \cfrac{3}{49\pi }\cdot 196\pi =h\implies 12=h[/tex]
geometric probability
The probability that the point will be in the square is given by P = 63.70 %
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that the point will be in the square be P
Now , the radius of the circle r = 1 inch
So , the area of the circle = πr²
The area of circle = 3.14 inches²
Now , the diagonal of the square = 2 inches
So , the area of the square = 2 inches²
And , probability that the point will be in the square P = ( area of the square / area of circle ) x 100
On simplifying , we get
The probability that the point will be in the square P = 2 / 3.14
The probability that the point will be in the square P = 0.6370
The probability that the point will be in the square P = 63.70 %
Hence , the probability is 63.70 %
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The U.S. Federal Reserve System publishes data on family income based on its Survey of Consumer Finances. When the head of the household has a university degree, the mean pre-tax family income is $ 85,700. Suppose that 70% of the pre-tax family incomes when the head of the household has a university degree are between $76,300 and $95,100 and that these incomes are normally distributed. What is the standard deviation of pre-tax family incomes when the head of the household has a university degree?
According to the question the standard deviation is approximately $9,400.
What is standard deviation?Standard deviation is a measure of variability or dispersion in a data set. It is a measure of how much the individual data points within a set deviate from the mean. The standard deviation is calculated by taking the square root of the variance and is expressed as the same unit of measurement as the data set.
The standard deviation of pre-tax family incomes when the head of the household has a university degree can be computed using the empirical rule. According to the empirical rule, approximately 68% of the data lies within one standard deviation of the mean, 95% of the data lies within two standard deviations of the mean, and 99.7% of the data lies within three standard deviations of the mean.
Given that 70% of the pre-tax family incomes when the head of the household has a university degree are between $76,300 and $95,100,
we can calculate that the standard deviation is approximately ($95,100 - $76,300) / 2.66 ≈ $9,400.
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State all x-values that are excluded from the solution set of the rational equation, then solve the equation for x. (2)/(x+2)=(3)/(x-2)-(7)/((x+2)(x-2))
The x-values that are excluded from the solution set of the rational equation are those that would make the denominator of any of the fractions equal to zero. These are the values x = -2 and x = 2, since they would make the denominators (x+2) and (x-2) equal to zero.
To solve the equation for x, we can first find a common denominator for all the fractions and then combine them into one fraction:
(2)/(x+2)=(3)/(x-2)-(7)/((x+2)(x-2))
Multiply both sides of the equation by the common denominator (x+2)(x-2) to eliminate the fractions
:2(x+2)(x-2) = 3(x+2)(x-2) - 7
Distribute the terms:
2x^2 - 8 = 3x^2 - 12x + 12 - 7
Combine like terms and rearrange the equation:
x^2 - 12x + 13 = 0
Use the quadratic formula to find the values of x:
x = (-b ± √(b^2 - 4ac))/(2a) = (-(-12) ± √((-12)^2 - 4(1)(13)))/(2(1)) = (12 ± √(144 - 52))/(2) = (12 ± √92)/(2) = (12 ± 2√23)/(2) = 6 ± √23
Therefore, the solutions for x are 6 + √23 and 6 - √23.
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Did I get these Zeros right while factoring?
Answer:
You forgot the +- part when taking the square roots
Step-by-step explanation:
5 x^2 = -2
x^2 = -2/5
x = +- sqrt ( -2/5) <==== note sqrt(-2/5) NOT sqrt (-2) / 5
x = ± i sqrt(2/5)
x^2 = 8
x = ±sqrt 8
x = ±2 sqrt (2)
You are going to paint one side of a building. The wall is 105 feet long and 35 feet high. One gallon of paint covers 317 square feet with a single coat of paint. Find how many gallons should be purchased to apply one coat of paint to the side of the building.
Amount of paint that should be purchased to apply one coat of paint to the side of the building is 12 gallons.
What is area?Area is the amount of space occupied by a two-dimensional shape. That is, it is a quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is the square unit, commonly expressed in square inches, square feet, and so on.
Given,
length of the wall = 105 feet
height of the wall = 35 feet
Area of the wall
= length × height
= 105 × 35
= 3675 square feet
One gallon paints 317 square feet
Number of gallons to paint 3675 square feet
= 3675/317
= 11.59 ≈ 12
Hence, 12 gallons should be purchased to apply one coat of paint to the side of building.
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I really need the answers to these math equations
A correct 2-column proof include the following: B. table B.
What is a supplementary angle?In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Since line segment r is parallel to line segment s, the 2-column proof to justify that angle b and angle h are supplementary angles should be written as follows;
Statement Reasons_________________
r║s Given
∠b ≅ ∠c Vertical angles
∠c and ∠e are supplementary Same-side interior angles
∠e ≅ ∠h Vertical angles
∠b and ∠h are supplementary Substitution
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540 is what percent of 8460
Answer:
6.3829787234%
Step-by-step explanation:
If someone could help me out on this!
The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;
(f- g)(x) = -2x² - 9x + 9
(g-f)(x) = 2x² + 9x - 9
(f + g)(x) = 4 x² - x + 5
What is a function?A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.
here, we have,
The general mathematical representation of a function is y = f(x).
f(x)=x²- 5x+7
g(x)=3x² + 4x - 2
so, we get,
(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)
(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2
(f- g)(x) = -2x² - 9x + 9
(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)
(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7
(g-f)(x) = 2x² + 9x - 9
(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2
(f + g)(x) = 4 x² - x + 5
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Are the polygons similar? If they are, write a similarity statement. The figures are not drawn to scale.
The two polygons are similar using the SAS criteria.
What are polygons?A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end. A polygon's line segments are therefore referred to as its sides or edges. The vertex or corners made by two line segments are where an angle is created. A triangle with three sides is an illustration of a polygon. A circle is a planar figure as well, but since it is curved and lacks sides and angles, it is not regarded as a polygon. Hence, we may argue that while all two-dimensional forms are polygons, not all two-dimensional figures are polygons.
For the given polygons we find the scale factor to determine whether the two figures are similar.
The scale factor is given as:
SF = length of original/ length of new image
SF = 4 / 6
SF = 2/3
For the second segment:
SF = 6/9
SF = 2/3
The ratios of the segment are same. Also the angle between the corresponding segments is 86 degrees.
Hence, the two polygons are similar using the SAS criteria.
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Help me please I need help with my math assignment it’s hard for my three brain cells :D
Answer:
if we follow the rule using y=mx+c, we would use rise and run so the distance is 3 up and 4 run.
7 total distance i guess.....i hope this helps.
What is the smallest positive integer that is a multiple of 2 , of 6 , and of 9 ?
The smallest positive integer that is a multiple of 2, 6, and 9 is 18.
To find the smallest positive integer that is a multiple of 2, 6, and 9, we need to find the smallest common multiple of these three numbers. We can do this by finding the prime factorization of each number and taking the highest power of each prime factor.
The prime factorization of 2 is 2, the prime factorization of 6 is 2 x 3, and the prime factorization of 9 is [tex]3 * 3[/tex]. To find the smallest common multiple, we take the highest power of each prime factor, which gives us [tex]2 * 3 * 3 = 18[/tex]. Therefore, 18 is the smallest positive integer that is a multiple of 2, 6, and 9.
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Researchers at the Mayo Clinic have studied the effect of sound levels on patient healing and have found a significant association (louder hospital ambient sound level is associated with slower postsurgical healing). Based on the Mayo Clinic's experience, Ardmore Hospital installed a new vinyl flooring that is supposed to reduce the mean sound level (decibels) in the hospital corridors. The sound level is measured at five randomly selected times in the main corridor. New Flooring Old Flooring 42 48 41 51 40 44 37 48 44 52 Calculate the test statistic.
At α =. 05, is the mean sound level reduced?
Since t-value is less than the critical value, at α = 0.05, therefore we can find that the mean sound level is reduced after installing the new vinyl flooring.
The Mayo Clinic conducted a study on the impact of sound levels on patient healing and discovered a significant correlation between hospital ambient sound levels and slower postsurgical healing. In light of this, Ardmore Hospital installed new vinyl flooring with the goal of reducing mean sound levels in the corridors.
To determine whether this installation had the intended effect, a hypothesis test was performed with a null hypothesis that the mean sound level after installation was the same as or higher than the mean sound level with the old flooring, and an alternative hypothesis that the mean sound level after installation was lower.
A one-tailed t-test was used with a significance level of α = 0.05, and the test statistic was calculated using the sample mean, standard deviation, and size for both old and new flooring data. The calculated t-value was compared to the critical value obtained from a t-table or calculator, and since the calculated t-value was less than the critical value, the null hypothesis was rejected.
Therefore, it can be concluded that there is evidence to suggest that the mean sound level after installing the new vinyl flooring is lower than the mean sound level with the old flooring, and at α = 0.05, it can be said that the mean sound level is reduced after installing the new vinyl flooring.
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1/8 divided by 3,680
Answer: 0.00003396739
Step-by-step explanation:
hope this helps
If f(x)=2x+1 and g(x)=x^2 find (f o g)(x)
The value of the expression is f(g(x)) = f(x^2) = 2(x²) + 1 = 2x² + 1.
What is composition of function?A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Hence, a function is essentially applied to the output of another function.
Given that,
f(x)=2x+1 and g(x)=x²
To get the composite function we substitute the value of g(x) in the x-value of the function of f(x).
f(g(x)) = f(x^2) = 2(x²) + 1 = 2x² + 1
Hence, the value of the expression is f(g(x)) = f(x^2) = 2(x²) + 1 = 2x² + 1.
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Which change, if any, is needed to the underlined text?
“Taking up to six months, hikers who plan to complete the entire
journey”
-A journey of up to six months, hikers planning to complete it entirely
-Taking up to six months to complete, hikers who plan the entire journey
-The entire journey takes up to six months to complete, so hikers who plan to
finish it
-No change
No change is needed. The underlined text is grammatically correct and conveys the intended meaning clearly.
What is the meaning of the underlined test?The underlined text "Taking up to six months, hikers who plan to complete the entire journey" means that the journey being referred to may take up to six months to complete, and it is being undertaken by hikers who have planned to complete the entire journey.
The text suggests that the journey is a long and challenging one that requires careful planning and preparation by the hikers.
Therefore, the correct answer is as given above. It could then be concluded that the underlined text does not need to change.
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Jackson made a mistake when solving the inequality
The step that Jackson made an error when solving the inequality was Step 1 because he did not multiply - 10 by 4.
How to describe the error ?When solving the inequality, Jackson had the right idea of multiplying the different sides of the equation by 4 in order to get rid of 4 as a denominator.
However, he was to multiply every figure in the equation by 4. He did not do this with the - 10 on the left side of the equation. This meant that Jackson did not convert that number to - 40 which then led to an incorrect inequality.
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What are the coordinates for the graph and what do I need to do?
not completely sure but i think you times the x and y numbers then draw a graph of the units
Wind turbines harness the power of the wind to generate electricity. One particular wind turbine consists of three 100 -foot-long rotor blades that rotate around the top of a 150 -foot vertical shaft. a. Use a protractor, a straightedge, and the given graph to estimate the height of the blade tip when the blade is at angles of0∘,30∘;45∘,60∘and90∘. The arc on the graph represents a portion of the blade tip's path. Assume the blade rotates counterclockwise and the blade is at an angle of0∘when the blade tip is directly to the right of the top of the vertical shaft. This position has been labeled as0∘on the graph. Horizontal Position of Blade Tip (feet)
angles of 0°, 30°, 45°, 60°, and 90° are 100 feet, 86.6 feet, 71.4 feet, 50 feet, and 0 feet, respectively.
To answer this question, we need to use a protractor, a straightedge, and the given graph to estimate the height of the blade tip when the blade is at angles of 0°, 30°, 45°, 60°, and 90°. The arc on the graph represents a portion of the blade tip's path. Assume the blade rotates counterclockwise and the blade is at an angle of 0° when the blade tip is directly to the right of the top of the vertical shaft. This position has been labeled as 0° on the graph.
Using the protractor, we can measure the angles on the graph, which is marked in 15° increments. For each angle, we can measure the horizontal position of the blade tip from the graph. The heights of the blade tips for 0°, 30°, 45°, 60°, and 90° can be estimated using the Pythagorean theorem.
At 0°, the height of the blade tip is 100 feet (which is equal to the length of the blade). At 30°, the height of the blade tip is 86.6 feet. At 45°, the height of the blade tip is 71.4 feet. At 60°, the height of the blade tip is 50 feet. At 90°, the height of the blade tip is 0 feet.
Therefore, the estimated heights of the blade tip when the blade is at angles of 0°, 30°, 45°, 60°, and 90° are 100 feet, 86.6 feet, 71.4 feet, 50 feet, and 0 feet, respectively.
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Find the area of the parallelogram when the base is 3 side is 5.3 and the height is 5
Area of the parallelogram is 15 cm²
Area of the parallelogram:
Given that;
Base of parallelograms = 3 cm
Side of parallelograms = 5.3
Height of parallelograms = 5 cm
Find:
Area of the parallelogram
Computation:
Area of the parallelogram = l × b
Area of the parallelogram = 3 × 5
Area of the parallelogram = 15 cm²
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The length of a rectangular poster is 9 more inches than three times its width. The area of the poster is 30 square inches. Solve for the dimensions (length and width) of the poster.
The dimensions of the poster are 2 inches by 15 inches.
What is algebra?Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It is used to solve problems and represent mathematical relationships and formulas. In algebra, letters and other symbols are used to represent numbers and quantities, allowing us to express mathematical relationships and patterns in a more general and abstract way. Common topics in algebra include equations, inequalities, functions, and graphing.
What are equations?An equation is a mathematical statement that shows that two expressions are equal. Equations typically include variables, which are placeholders for unknown or changing values, and mathematical operations, such as addition, subtraction, multiplication, and division, that manipulate these values.
In the given question,
Let's use algebra to solve for the dimensions of the poster.
Let w be the width of the poster in inches. Then, according to the problem statement, the length of the poster is 9 more inches than three times its width, or 3w + 9. The area of the poster is given as 30 square inches, so we can set up the equation:
A = lw = (3w + 9)w = 30
Expanding the right-hand side and simplifying, we get:
3w^2 + 9w - 30 = 0
Dividing both sides by 3, we obtain:
w^2 + 3w - 10 = 0
This is a quadratic equation that we can solve using factoring or the quadratic formula. Factoring, we can write:
(w + 5)(w - 2) = 0
This gives us two solutions: w = -5 and w = 2. Since the width of the poster must be a positive number, we can discard the negative solution and conclude that the width of the poster is 2 inches.
To find the length, we can substitute w = 2 into the expression we found earlier for the length:
l = 3w + 9 = 3(2) + 9 = 15
Therefore, the dimensions of the poster are 2 inches by 15 inches.
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Rearrange the parallelogram as a rectangle. Then find the area.
The area of the rectangle is 9 square units
How to determine the area of the rectangleFirst, we need to know the properties of a rectangle. They are;
A rectangle is a quadrilateralThe opposite sides are parallel and equal to each otherEach interior angle is equal to 90 degreesThe sum of all the interior angles is equal to 360 degreesThe diagonals bisect each otherBoth the diagonals have the same lengthFrom the diagram shown, we have that;
Length of the transformed shape(parallelogram to rectangle) = 3 units
Width = 3 units
The formula for the area of a rectangle is expressed as;
Area = lw
Substitute the values
Area = 3(3)
Area = 9 square units
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Question 19, 2.6.101 Part 3 of 7 computer is x dollars. Let f(x)=x-200 and g(x)=0.7x. e functions f and g model in terms of the price of the computer.
Using composition function , the price of the computer after both discounts are applied is 0.7x - 140.
To find the price of the computer after both discounts are applied, we can use composition function . Specifically, we can find the composition of f and g, denoted as f(g(x)) or (f o g)(x). This will give us the price of the computer after both discounts are applied.
To find f(g(x)), we can substitute the expression for g(x) into the function f(x):
f(g(x)) = f(0.7x) = (0.7x) - 200
So the price of the computer after both discounts are applied is (0.7x) - 200.
Alternatively, we could find the composition of g and f, denoted as g(f(x)) or (g o f)(x). This will give us the same result, since the order of the discounts does not matter.
To find g(f(x)), we can substitute the expression for f(x) into the function g(x):
g(f(x)) = g(x-200) = 0.7(x-200) = 0.7x - 140
Either way, we can see that the price of the computer after both discounts are applied is a function of the original price x, and can be represented by the composition of the functions f and g.
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Angie used a twenty-dollar bill to pay for a bottle of water. The cashier gave her back 1 ten-dollar bill, 7 one-dollar bills, 3 quarters, and 2 pennies as change. How much did Angie's bottle of water cost?
$
Answer:
$2.23
Step-by-step explanation:
To find the cost of the bottle of water, we need to subtract the amount of change that Angie received from the twenty-dollar bill that she used to pay. The cashier gave her back $10 in one ten-dollar bill, $7 in seven one-dollar bills, $0.75 in three quarters, and $0.02 in two pennies.
Therefore, the total change that Angie received was: $10 + $7 + $0.75 + $0.02 = $17.77
To find the cost of the bottle of water, we need to subtract this amount from the twenty-dollar bill: $20.00 - $17.77 = $2.23
Therefore, the bottle of water cost $2.23.
The gold bar trapezium has cross-sectional area. Gold has a density of 19. 3 per cm3. Work out the mass of the gold bar. Give your answer in kilograms
The mass of the gold bar of the trapezium shape and a density of 19.3g/cm³ is found to be 8.646 KG.
The volume of the trapezoidal prism will be determined first. V = BL, where B is the area of the trapezoidal face and L is the prism's length, is the formula for the volume of the prism.
We are aware that a trapezoid's area is equal to B = 1/2(6+10). (4)
B = 32 m²
When we enter the formula for volume, V = 32 x 14 V = 448 m³, we know that L is 14 cm.
Divide the mass by the volume to get the density, or D = M/V.
According to values,
19.3 = M/448
M = 8646.4 grams, which is equal to 8.646 grams.
The density is stated to be 19.3 kg/m³. Hence, the gold weighs 8.646 kilos.
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Complete question - The gold bar trapezium has cross-sectional area. Gold has a density of 19. 3 per cm3. Work out the mass of the gold bar. Give your answer in kilograms. The dimension of the trapezium are length = 14cm, parallel sides are 6cm and 10cm nd the height is 4cm.
Adina is starting a band and wants to buy a guitar and amplifier. The cost of the guitar is g(m) = 680 + 10m where m is time in months. The amplifier cost is represented by the function a(m) = 450 - 5m. Adina hopes to have
enough money saved up to buy both items in 4 months. How much will she need?
A. $1,070
B. $290
C. $1,190
D. $1,150
Answer:
b
Step-by-step explanation:
its really easy when u read it multiple of times
Hello user can you help my question. (See picture below)
Step-by-step explanation:
1. R
2. W
3. O
4. RW
5. OW
6 RO
7. RWO
2.
1.UG
2. G
3. MG
4. MU
5. M
6. U
sarah plants 760 vines in rows containing either 20 vines or 25 vines. there are 3 times as many rows containing 25 vines as there are rows containing 20 vines. how many rows contain 25 vines?
Answer:
Let's start by using variables to represent the number of rows containing 20 vines and 25 vines. Let:
x be the number of rows containing 20 vines
3x be the number of rows containing 25 vines (since there are 3 times as many rows containing 25 vines as there are rows containing 20 vines)
We know that Sarah plants a total of 760 vines, and that each row contains either 20 vines or 25 vines. Therefore, we can write an equation based on the total number of vines:
20x + 25(3x) = 760
Simplifying and solving for x:
20x + 75x = 760
95x = 760
x = 8
So there are 8 rows containing 20 vines, and 3 times as many rows containing 25 vines, or 3(8) = 24 rows containing 25 vines.
Therefore, Sarah planted 8 rows with 20 vines and 24 rows with 25 vines.