Answer:
$115.36
Step-by-step explanation:
Given data
P=$103
r=1.9%
t= 6 years
The expression for the amount is given as
[tex]V = P e ^{r t}[/tex]
substitute
[tex]V = 103*e^{0.019 *6}[/tex]
[tex]V = 103*e^{0.114}\\\\V = 103*1.120\\\\V = 115.36\\\\[/tex]
Hence the final amount is $115.36
mathematicians find an easier way to solve quadratic equations, how do they do it?
Answer:
His secret is in generalizing two roots together instead of keeping them as separate values.
Mark brainiest
London went shopping for a new video game because of a sale. The store was offering a 20% discount. If the price on the tag was $50, what would be the price after the discount but before tax, to the nearest dollar and cent?
The price of a new video game, before tax in the shop that London visited is $10.00
How to determine the price of a new video gameThe question is a percentage problem, percent is a fraction of hundred and the calculations will be using 100
In the store that London visited, they were offering a 20% discount
= 20 percent
= 20 / 100
= 0.2
discount factor = 1 - 0.2 = 0.8
the discount factor will be used to multiply by the price of the video game to get a new price
selling price of the new video game before tax = $50 * 0.2 = $10
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for the function f(x)= 1-2x/5x-1, find f^-1(x)
'Therefore , the solution of the given problem of function comes out to be f⁻¹(x) = 1 + x / 5x+2 .
What exactly does the word function mean?Mathematics is the study of number, their variations, the geographical tissue, architecture, and both both actual and fictitious locations. A equation is a depiction of the relationship here between number of inputs and the corresponding outputs for each one. A function is just a collection of input that, when put together, provide one variable distinct output with each input. Every function is assigned a city, county, or scope, sometimes known as a realm.
Here,
Given:
=> f(x) = (1 -2x)/(5x-1)
To find f⁻¹(x)
So,
=> y = (1 -2x)/(5x-1)
=> x = (1 -2y)/(5y-1)
=> y = 1 + x / 5x+2
=> f⁻¹(x) = 1 + x / 5x+2
Therefore , the solution of the given problem of function comes out to be f⁻¹(x) = 1 + x / 5x+2 .
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15.
Marco is making blueberry muffins. The ratio between flour and blueberries for the recipe being used is shown in the table below.
Cups of Cups of
Flour Blueberries
1-2
24
A.Ocup
2
8
How many cups of blueberries will Marco need if he has 2 cups of flour to use?
B.
cup
D
1
2
3
4
1
c. 11 cups
6 cups
The magic ratio for muffins in 2:2:1:1.
What is the appropriate liquid-to-flour ratio while baking muffins?The magic muffin ratio is 2:2:1:1. This equates to 2 parts flour, 2 parts liquid, 1 part fat, and 1 part eggs. The most crucial aspect is to remember to utilize the same unit of weight for each component!
Rinse frozen blueberries many times in cold water until the water turns lighter in color to prevent your batter and baked items from developing a purple-blue tint. Then, blot them dry with a paper towel and gently fold them into the batter. The goal of this procedure is to maintain fast breads light and delicate by limiting the quantity of gluten produced during the mixing process. To do this, the dry components are mixed in a one bowl, the wet ingredients are combined in a separate bowl, and then the two mixtures are combined together.
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What is the area of the trapezoid shown? Express your answer in simplest exact form. [asy] unitsize(1.5cm); pair a=(0,0); pair b=(1,sqrt(3)); pair c=(3,sqrt(3)); pair d=(4,0); draw(a--b--c--d--a); label("2",(a+b)/2,NW); label("2",(b+c)/2,N); label("2",(c+d)/2,NE); label("~$60^\circ$",a,NE); label("$60^\circ$~",d,NW); [/asy]
The area of the trapezium shown is 284.31 in²
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The area is calculated for a two dimensional shape. It shows the amount of space occupied for that shape.
The area of a trapezium is given by:
Area = (1/2)(sum of parallel sides) * height
For the trapezium shown, the parallel sides have a measure of 17 inches and 31 inches respectively. The height is 11.7 inches, hence:
Area = (1/2)(17 + 31.6)(11.7) = 284.31 in²
The area is 284.31 in²
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Determine the partial fraction expansion for the rational function below: s/(s – 7)(s^2 - 49) S/(s - 7) (s2 - 49) Determine the partial fraction expansion for the rational function below. -25-56/ (5+3) (s^2+ 16) - 2s - 56 / (s +3)(s^2 + 16)
The partial fraction expansion for the rational function
S/ (s - 7) (s^2 - 49) = -25-56/ (5+3) (s^2+ 16) - 2s - 56 / (s +3) (s^2 + 16)
can be found by decomposing it into the sum of simpler fractions.
One way to do this is to use the method of long division and then match the coefficients of the resulting polynomials. The process is as follows:
Divide S by (s - 7) to get a quotient of S1 and a remainder of R1.
Divide R1 by (s^2 - 49) to get a quotient of S2 and a remainder of R2.
Write the expansion as S1 + S2 + R2/(s - 7)(s^2 - 49)
Alternatively, we can use the method of partial fraction decomposition by inspection.
To do this, you will write the rational function as the sum of simpler fractions with the same denominator.
S/ (s - 7) (s^2 - 49) = A/(s-7) + B/ (s^2 - 49) + (C*s + D)/(s^2 - 49)
where A, B, C, and D are unknowns that you will find by matching coefficients.
S = (A(s^2-49) + B(s-7) + C*s + D) / (s-7) (s^2-49)
You can use this equation to solve for A, B, C, and D by matching coefficients.
-25-56/ (5+3) (s^2+ 16) - 2s - 56 / (s +3) (s^2 + 16) = A/(s-7) + B/(s^2 - 49) + (C*s + D)/ (s^2 - 49)
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a cone has a diameter of 3 inches . the cone holds 12 inches of water what is the height of the cne
5.1 inches is the correct answer. o.o :P C: 0'0 your welcome sir/ma'am also i dont want this deleted because i did the work for this so pls dont delete it ok? plssssss donttttt deleteeeeeee ittttttt plssssss dont deleteeee iitttt ty c;
Please solve the question and show work.
Answer:
all i could do was simplify it
Step-by-step explanation:
What is the image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin?
The image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin is (4, -4).
What is dilation at origin?
On the coordinate plane, figures can be magnified. The centre of dilation is frequently the origin. The coordinates of the points in the preimage can be multiplied by the scale factor to get the points in the image if you are distorting a figure that is centered at the origin.
We have to find the image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin.
To find the image after dilation multiply both coordinates (12, -12) by 1/3 which is the same as dividing by 3.
⇒ (12, -12)*1/3 = (4, -4)
Hence, the image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin is (4, -4).
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find the y-intercept, the equation of the axisof symmetry, and the x-coordinate of vertex for the graph of f(x)= x^2-3x+5. use this information to graph the function.
The y-intercept of the graph of f(x) = x^2 - 3x + 5 is (0, 5).
The equation of the axis of symmetry is x = (3/2).
The x-coordinate of the vertex is (3/2), and the y-coordinate of the vertex is (5 - (9/4)) = (-1/4).
So the vertex of the graph of f(x) = x^2 - 3x + 5 is (-1/4, (3/2)).
To graph the function, you can start by plotting the vertex, then use the axis of symmetry to reflect the parabola across the line x = (3/2). The y-intercept is the highest point of the parabola if it opens upwards, and the lowest if opens downwards. This can be used to confirm the direction of the parabola.
A quadratic function's U-shaped curve is seen on a parabola graph. A right circular cone and a plane surface intersect to generate one of the conic sections known as a parabola in mathematics. It has a U-shaped symmetry in the plane. The conventional form of a parabola is a graph whose equation takes the form f(x) = ax2+bx+c. A parabola's vertex is its most extreme point, and the vertical line that runs through it forms its axis of symmetry.
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Which system of equations can be graphed to find the solution(s) to x2 = 2x + 3?A.y=x2+2x+3/y=2x+3B.y=x2-3/y=2x+3C.y=x2-2x-3/y=2x+3D.y=x2/y=2x+3
The correct choice is:
y= x^2 and y= 2x+3
Given equation,
x^2=2x+3
this can be used for factorization by taking all the factors in one side of the equation
x^2-2x-3=0
or, x^2-3x+x-3=0
or, x(x-3)+x(x-1)=0
or, (x-3)(x-1)=0
Therefore,
x=-1 or x= 3
The result indicates,
when we plot the equation x^2=2x+3 in graph, as a function of y=x^2-3x+x-3, the x axis will be intersected on x=-1 and x=3
Now, if we consider
y=2x+3 and y=x^2
it gives x^2-2x-3=0 all over again, when combined.
The solution to,
x^2=2x+3 is the intersection point of the graph of straight line alongside the graph for the quadratic equation curve.
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The correct answer is y= [tex]x^{2}[/tex] and y= 2x+3 that can be graphed to find the solution(s) to [tex]x^{2}[/tex]= 2x + 3 .
The Given equation was ,
[tex]x^{2}[/tex]= 2x + 3 .
this can be used for factorization by taking all the factors in one side of the equation
[tex]x^{2}[/tex] - 2x - 3 =0
or, [tex]x^{2}[/tex]-3x+x-3=0
x(x-3)+x(x-1)=0
(x-3)(x-1)=0
∴x=-1 or x= 3
The result indicates,
when we plot the equation [tex]x^{2}[/tex]=2x+3 in graph, as a function of y=[tex]x^{2}[/tex]-3x+x-3, the x axis will be intersected on x=-1 and x=3
Now, if we consider
y=2x+3 and y=x^2
it gives [tex]x^{2}[/tex]-2x-3=0 all over again, when combined.
The solution to,
[tex]x^{2}[/tex]=2x+3 is the intersection point of the graph of straight line alongside the graph for the quadratic equation curve.
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For a recipe to make lemonade , every 6 cups of water requires one and a half cups of sugar. if you are using 24 cups of water, how many cups of sugar would you need
The number of cups of sugar that you will need to make lemonade would be = 2 cups of sugar.
What is a recipe?A recipe is defined as the list of condiments that are used for the preparation of a food and it's guidelines.
In the recipe to make lemonade,
6 cups of water = 1/2 cup of sugar
24 cups of water = X cup of sugar.
Make X the subject of formula;
X cup of sugar = 24 × 1/2 ÷ 6
= 12/6 = 2 cups of sugar.
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What pixel value means?
Pixel value refers to the numerical value assigned to a single pixel in an image.
What is pixel value?It is usually a measure of the brightness of the pixel, with higher numbers indicating brighter pixels and lower numbers indicating darker pixels.
The range of values can vary depending on the image type, but typically, 8-bit images use a range of 0 (black) to 255 (white). Pixel values are used for a variety of tasks in digital image processing, such as analyzing the colors of an image or isolating objects in a scene.
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design a waterskiing ramp. show how you can use direct variation to plan the heights of the vertical supports.
In designing the waterskiing ramp using direct variation the vertical supports, y will be related to the horizontal distance, x by a constant k, as in the relation
k = y/x
What is a constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional.
When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.
In the problem, the distances between the vertical supports is x while the height of the support is y. To have a direct proportionality this relationship between x and y must be a constant say k.
Hence we say k = y / x
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24:73 in its simplest form
The school's track is 1/4 mile long. If Janice can compete each lap in 1/10 of on hour, what is Janice's running speed? Include units of measure.
Answer: To find Janice's running speed, we need to determine how many miles she runs per hour.
We know that the track is 1/4 mile long and Janice can complete each lap in 1/10 of an hour. To find the total number of miles Janice runs in an hour, we can multiply the length of the track by the number of laps she completes in an hour.
Length of the track * number of laps = total miles
1/4 mile * (1/10 hour)^-1 = total miles
On the second equation, we are using the inverse of the time, to get the number of laps completed in an hour
The speed is distance over time, so we need to express the distance in miles and the time in hours.
So Janice's running speed is 4 miles/hour.
Step-by-step explanation:
3X + 1 i need help with this asp
Answer:
In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers. The elements of a generating set of this semigroup are related to the sequence of numbers involved in the still open Collatz conjecture or the "3x + 1 problem".
Step-by-step explanation:
Etimate how that there are 1. 4 \cdot 10^81. 4⋅10
8
1, point, 4, dot, 10, tart upercript, 8, end upercript pet fih and 9. 4 \cdot 10^69. 4⋅10
6
9, point, 4, dot, 10, tart upercript, 6, end upercript pet reptile in the United State. How many fih and reptile pet are in the United State all together?
Expre your anwer in cientific notation
There are 1.449 × 10⁸ pet fish and pet reptiles all together in the United States.
Total number of pet fish in the United states = 1.4 × 10⁸
Total number of pet reptiles in the United States = 4.9 × 10⁶
So the total number of pet fish and pet reptiles = (1.4 × 10⁸) + (4.9 × 10⁶)
= 1.449 × 10⁸
The final answer is in scientific notation. Scientific notation is the way of writing number that are too big or too small and inconvenient to write in decimal form. They are expressed in the multiple of 10 with a suitable power on 10.
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hELP QUICK PLEASEE!!! 30 points!
The solution to the following linear equation problem can be seen in the graph showing how the width and diameter of one face are linearly related.
What exactly is a linear equation?In a linear model, one level is the maximum amount of levels that may be used. Any equation that has a theoretical extension of at least two is said to be nonlinear. There is a straight line on a map with a simple equation. A nonlinear equation's curve is depicted on the graph.
Here,
one face's perimeter and side lengths are linearly related.
line-drawing formula.
The formula y = mx + b can be used to describe a regular model.
If m is the rising rate and b is in reality the y intercept, then x and y are variables.
The graph shows a linear relationship between the length and perimeter of one face.
Therefore, the graph showing how the perimeter or edge length of one face are linearly connected is the solution to the provided linear equation problem.
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Question content area topPart 1 Two hikers are 22 miles apart and walking toward each other. They meet in 5 hours. Find the rate of each hiker if one hiker walks 2.2 mph faster than the other.
Answer: if one hiker walks faster than the other, their rate would be 9.68mph or 9.7mph if u round up and the rate of the other hiker that is walking slower is 4.4mph.
Step-by-step explanation:
For the hiker walking 2.2mph
I did: 22 x 2.2 = 48.4/5 = 9.68
Rate = 9.68mph
For the other hiker
I did: 22/5= 4.4
rate = 4.4mph
Estimate the level of DVD sales (measured in million dollars) for movies, by using the amount of annual revenue (measured in million dollars) generated by the box office gross. We randomly selected a sample of 43 movies for the same year.
Excel (for α = 0.05) printed out: r^2 = 0.5123, SY.X = 12.2279, tcritical = 2.0195, hin = 0.026249, b0 = 4.8445, b1 = 0.1631. Assume normality and homoscedasticity are satisfied.
Source df Sum of Squares Mean Squares F Stat P-value F Crit
Regression 1 6439.6133 ? ? N/A 4.0785
Error ? ? ?
Total 42 12570.025
a) Interpret the meaning for the coefficient of determination and also the standard error of prediction, for this problem.
b) At the 0.05 level of significance, is there evidence of a linear relationship between the revenues of DVD sales and the box-office gross?
c) Construct the 95% confidence interval of the actual mean revenue of DVD sales for all the movies that generated 100 million dollars box-office gross.
d) Construct the 95% prediction interval for the actual revenue of DVD sales for a movie that generated 100 million dollars box-office gross.
please show all work and calculations
The average deviation of predicted DVD sales from the actual is 12.2279 million dollars. F-critical value is 4.0785>4.0785 we can reject the null hypothesis. The 95% confidence interval is (17.1536, 25.1554). The 95% prediction interval for the given value of x is (-3.8623, 46.1713).
Estimate the level of DVD sales for movies, by using the amount of annual revenue generated by the box office gross
We randomly selected a sample of 43 movies for the same year.
Excel α = 0.05, r^2 = 0.5123
=51.23%
51.23% of the DVD sales variation is explained by annual revenue.
SY.X = 12.2279.
Therefore, the average deviation of predicted DVD sales from the actual is 12.2279 million dollars.
b. The hypothesis being tested is:
Null Hypothesis, H0: β1 = 0
Alternative Hypothesis, H1: β1 ≠ 0
The test statistic, F = (6439.6133/1)/((12570.025 - 6439.6133)/(42 - 1)) = 43.07
The F-critical value is 4.0785.
Since 43.07 > 4.0785, we can reject the null hypothesis.
Therefore, we can conclude that there is a linear relationship between the revenues of DVD sales and the box-office gross.
c. y = bo + b1*x
y = 4.8445 + 0.1631*x
Put x = 100
y = 4.8445 + 0.1631*100 = 21.1545
The 95% confidence interval for the given value of x is:
= y ± t*s*[tex]\sqrt{0.026249}[/tex]
= 21.1545 ± 2.020*12.2279*[tex]\sqrt{0.026249}[/tex]
= (17.1536, 25.1554)
d. The 95% prediction interval for the given value of x is:
= y ± t×s×[tex]\sqrt{}[/tex]1 + hin [The t-value is calculated using =TINV(0.05,42-1) in Excel]
= 21.1545 ± 2.020*12.2279*[tex]\sqrt{1 + 0.026249}[/tex]
= (-3.8623, 46.1713)
Therefore, the value is (-3.8623, 46.1713).
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Is a scale factor of 2 double?
If the original shape is scaled by a factor of 2, the resultant shape is twice as large as the original shape.
How do you find the scale factor of 2 figures?The scale factor is calculated using the following fundamental formula: Scale factor = Dimension of the new shape Dimension of the old shape. The formula for calculating the scale factor is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is magnified.Consider being told that the smaller square's side length is 2 inches and that the ratio of the smaller to the larger square is 1: 2. So, 1 inch on the smaller square is equivalent to 2 inches on the larger square, just in case you forgot. A lesser value will result from multiplying by the scale factor, which is 1/2. A number having more than two elements is referred to as a prime number if it has no more than two factors.To learn more about factor refer to:
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If the original shape is scaled by a factor of 2, the resultant shape is twice as large as the original shape.
How do you find the scale factor of 2 figures?The scale factor is calculated using the following fundamental formula: Scale factor = Dimension of the new shape Dimension of the old shape. The formula for calculating the scale factor is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is magnified.
Consider being told that the smaller square's side length is 2 inches and that the ratio of the smaller to the larger square is 1: 2. So, 1 inch on the smaller square is equivalent to 2 inches on the larger square, just in case you forgot. A lesser value will result from multiplying by the scale factor, which is 1/2. A number having more than two elements is referred to as a prime number if it has no more than two factors.
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A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 10 granola bars and each large box has 24 granola bars. The camp bought a total of 10 boxes that have 184 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Answer:
Step-by-step explanation:
s = # of small boxes
l = # of large boxes
s + l = 10
10s + 24l = 184
Why is geometry so hard?
Due to the lack of spatial thinking instruction in most math classes, geometry is hard. They should acquire geometrical ideas easily instead.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
Everyone finds it difficult to dive into the issue of proofs. Children must realize that this issue affects everyone, even the mathematically skilled. Because they have trouble seeing how 3D, and 2D, forms, angles, and lines connect from various viewpoints, most youngsters struggle with geometry issues. Even kids who are really good at solving sum problems in math might be utterly stumped by this.
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Due to the lack of spatial thinking instruction in most math classes, geometry is hard. They should acquire geometrical ideas easily instead.
What are some reasons that children think geometry is hard?Visual Ability: While some kids think in terms of forms and proportions, others think visually. Children must comprehend geometry in order to visualize, or else they may not be able to see things in a larger context.
Numbers & Measurements: Children will learn about the link between shapes and sizes as numbers and measures come to life in shapes and sizes. Children will be able to comprehend the measurements and connections of lines, angles, surfaces, and solids using numbers and measures.
3D Thinking: Since these ideas originated in geometry, children cannot possibly comprehend 2 and 3 dimensions without having a working knowledge of geometry! The only way to visualize X, Y, and Z axis, triangles, and pyramids are with the aid of geometry.
Spatial Understanding: If it weren't for geometry, kids could have trouble comprehending the notion of spatial comprehension. Children will learn to appreciate the wonders of the world by studying concepts relating to space, location, size, and shape of objects.
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A person places $358 in an investment account earning an annual rate of 7.3%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 10 years.
The amount of money, to the nearest cent, in the account after 10 years is found as $742.87.
Explain the term compounded continuously?The interest gained on an investment is computed and reinvested back through into account for just an infinite number of periods, which results in a continuously compounded return. Both principal amount and interest accrued during the specified periods are used to calculate the interest, which is then reinvested back through into cash balance.The formula for the continuous compound is:
V = Pe^{rt}
In which:
V is the value of the account in t years, P is the principal initially invested: $358e is the base of a natural logarithm: 2.72r is the rate of interest: 7.3%t is the time of compounding: 10 yearsV= 358*2.72*{0.073*10}
V = 358*2.07
V = 742.87
Thus, the amount of money, to the nearest cent, in the account after 10 years is found as $742.87.
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Solve the inequality and write the solution in set-builder notation. r - 8 <= 7
So on solving the provided question, we can say that inequality equation will be as follows r - 8 <= 7 r<=15 or r >= -15
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
here the question, is
r - 8 <= 7
r<=15
or r >= -15
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If you solve this first I’ll make you brainliest and of course take your time good luck.
Answer: 28x^4y^7
Step-by-step explanation: Add exponents of common base
Answer:
28x⁴y⁷
Step-by-step explanation:
First multiply the numbers;
Then combine the exponents;
Then combine the exponents again;
Then you have the answer :)
I need help finding the answer for number 17!!
Answer:
39°
Step-by-step explanation:
[tex]angle \: 1 + 2 = 180(co \: interior \: angles \: \:in \: parallel \: lies \: are \: add \: up \: t \: equal \: 180) \\ [/tex]
13x + 24 + 5x -6 = 180
18x+ 18 =180
18x +18 -18 =180-18
18x = 162
18 18
x = 9
Therefore,
m<2 = 5x- 6
= 5(9) -6
= 45-6
= 39°
A bag contains 8 red marbles, 9 yellow marbles, and
7 green marbles. How many additional red marbles
must be added to the 24 marbles already in the bag so
that the probability of randomly drawing a red marble
is 3/5?
A. 11
B. 16
C. 20
D. 24
E. 32
Answer:
x = 16
Step-by-step explanation:
[tex]\frac{8+x}{24+x}=\frac{3}{5}\\ \\ 5(8+x)=3(24+x)\\\\40+5x=72+3x\\\\5x=32+3x\\\\2x=32\\\\x=16[/tex]
What is the first number of ordered pairs?
The first number in an ordered pair (x,y) is the x-coordinate, also called the "abscissa". It represents the horizontal position of the point on a coordinate plane. The second number in an ordered pair is the y-coordinate, also called the "ordinate". It represents the vertical position of the point on a coordinate plane.