Each week, Colt saves 2 times the amount he saved the previous week. He saves $5 the first week, and (2¹)($5), or $10, the second week. How much does he save the fourth week? Write and simplify an expression with exponents to determine your answer.
On solving the provided question, we can say that the expression will be
an = a + (n-1)d => 20.75 = 5 + (n-1)1.75 => n = 10
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
Given that
a=5
d = 1.75
an = 20.75
the expression will be
an = a + (n-1)d
20.75 = 5 + (n-1)1.75
15.75 = (n- 1) 1.75
n-1 = 15.75/1.75
n- 1 = 9
n = 10
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HELP ASAP QUESTION 2!
Answer:
number 2 or B
Step-by-step explanation:
Height of vase?
Pre Calculus
The height of the hyperbolic vase is 5.12 * 2 = 10.24 inches.
What is a hyperbola?
A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows. These two sections are known as connected components or branches. A plane and both halves of a double cone connect to form a hyperbola, which is an open curve with two branches. The hyperbola will be symmetrical regardless of whether the plane is perpendicular to the cone's axis or not.
The eccentricity formula for a hyperbola is
[tex]e = \sqrt{1+\frac{b^2}{a^2} }[/tex]
e = 2.5
Given width at the narrowest point is 4 inches.
So the value of a from the below figure is
a = ±2
So we can find b from the above eccentricity formula
2.5 = [tex]\sqrt{1+\frac{b^2}{2^2} }[/tex]
6.25 = 1 + b²/4
b²/4 = 5.25
b² = 21
b = ±4.6
So the equation of the hyperbola is
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
[tex]\frac{x^2}{4} - \frac{y^2}{21} = 1[/tex]
Now we are asked to find the height of the vase
The width at the top is 6 inches.
So take x = 3
Then we can find y from the above equation
[tex]\frac{3^2}{4} - \frac{y^2}{21} = 1[/tex]
y² = 26.25
y = 5.12 inches
Therefore the height of the hyperbolic vase is 5.12 * 2 = 10.24 inches.
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What is the inverse of the function f(x) = 2x + 1?
h(x) = 1/2x – 1/2
h(x) = 1/2x + 1/2
h(x) = 1/2x – 2
h(x) =1/2 x + 2
Answer:
h(x) = [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
let y = f(x) and rearrange making x the subject , that is
y = 2x + 1 ( subtract 1 from both sides )
y - 1 = 2x ( divide both sides by 2 )
[tex]\frac{y-1}{2}[/tex] = x
change y back to x with x the inverse function h(x)
h(x) = [tex]\frac{x-1}{2}[/tex] = [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]
If Emmanuel and benji ride a zebra, which is moving at 10 miles per hour, for a half hour, how far will they have traveled?
Answer: 5 miles
if they go 10 miles in one hour, they would only go 5 miles in one half-hour.
Step-by-step explanation:
10 miles in 60 min, so you half that for the miles and minutes
half of 10 is 5 and half of 60 is 30
Sam invested $10,000. Part of it was invested into a fund that paid 5% annual interest, and the rest was invested into opening a business, which made a loss of 2%. At the end of the year, he made $300 profit. How much did he
invest into the business?
A line passes through the point (8, 9) and has a slope of -3/4 Write an equation in slope-intercept form for this line.
Answer:
y = - [tex]\frac{3}{4}[/tex] x + 15
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = - [tex]\frac{3}{4}[/tex] , then
y = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation
to find c substitute (8, 9 ) into the partial equation
9 = - [tex]\frac{3}{4}[/tex] (8) + c = - 6 + c ( add 6 to both sides )
15 = c
y = - [tex]\frac{3}{4}[/tex] x + 15 ← equation of line
Simplify
X^2
X-1
3x^2
X+4
Answer:
(x+4)/(3x-3)
Step-by-step explanation:
You want to simplify the compound fraction ((x²/(x-1))/((3x²/(x+4)).
Division of fractionsAs with numerical fractions division by a fraction is the same as multiplication by its inverse. Common factors in the numerator and denominator cancel.
[tex]\dfrac{\left(\dfrac{x^2}{x-1}\right)}{\left(\dfrac{3x^2}{x+4}\right)}=\dfrac{x^2}{x-1}\times\dfrac{x+4}{3x^2}=\dfrac{x+4}{3(x-1)}=\boxed{\dfrac{x+4}{3x-3}}[/tex]
Please help for 40 points!
The radius of a circle is 6 cm. Find its circumference in terms of π.
Answer: 18.84
Step-by-step explanation: just multiply 3.14 by the radius
The giving table shows several points on the graph of a linear function work exercises 83–92 in order to see connections between the slope formula the distance formula the midpoint formula and the linear functions
The slope of the line with the first two points (0, 1) and (-7, -3) is equal to 4.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following slope and data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (-7, -3).Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-3 - (-7))/(1 - 0)
Slope, m = 4/1
Slope, m = 4.
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the intensity of radiation at a distance x meters from a source is modeled by the function r given by r(x)=k/x^2, where k is a positive constant.Which the followig gives the average intensity of radioation between 10 meters and 50 meters from source? a. k/900
b. -k/50 + k/10
c. 1/40 (-k/50 + k/10)
d. 1/2 (k/100 + k/2500)
Step-by-step explanation:
The average intensity of radiation between 10 meters and 50 meters from the source can be found using the following formula:
Average Intensity = (1 / (50 - 10)) * (Integral of r(x) from x=10 to x=50)
Using the formula for r(x), the integral of r(x) between 10 and 50 can be found as:
Integral of r(x) = -k * ln(x) evaluated at x = 50 and x = 10
Therefore, the average intensity of radiation between 10 and 50 meters from the source is given by:
Average Intensity = (1 / (50 - 10)) * (-k * (ln(50) - ln(10)))
This simplifies to:
Average Intensity = (1 / 40) * (-k * ln(5))
This is equivalent to choice c.
Average Intensity = 1/40 (-k/50 + k/10).
In a examination the total mark is 900 .if a boy obtains 630 marks what percentage is this
5. Mona always brings fabric samples with her when she holds client meetings. She likes to use them to help clients understand how her designs will look and
how different fabrics will go together. What is another reason that Mona MOST LIKELY brings along fabric samples?
They allow the client to see and feel the texture of the fabric.
They allow the client to see how stain resistant the fabric is.
They allow her to reupholster furniture on the spot.
They allow the client to imagine the paint color that will be used.
Mona always brings fabric samples with her when she holds client meetings. She likes to use them to help clients understand how her designs will look and
how different fabrics will go together.
Another reason that Mona MOST LIKELY brings along fabric samples is a) They allow the client to see and feel the texture of the fabric.
The importance of product samplesFrom the illustration above Mona brings product samples when she meets in a business meeting with her customers.
This is a step to provide a clearer picture to potential customers so they can see Mona's products in more detail.
So the most appropriate choice is option A, namely Mona's reason is also to provide potential consumers with experience and knowledge about the texture of the fabrics sold by Mona.
This can also help to improve the quality of business relationships.
Providing samples of new products will further enhance the business relationship between us and customers. Impress them with what we have given them. Give them something special on birthdays or other special days for them, that way your business bond and them will get stronger and closer.
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1) Which math component are taught in the curriculum, problem solving, procedural fluency, missed mathematical concepts, etc.?
2) What are some specific types of mathematical instruction that are promoted?
3) Are there any specific procedures used to teach basic mathematical instruction?
Answer:
1) The math curriculum typically includes components such as number sense, arithmetic operations, algebra, geometry, data analysis and probability, among others. Problem solving and procedural fluency are emphasized as important skills to develop. Students may also receive instruction on missed mathematical concepts from previous grades to ensure they have a strong foundation for future learning.
2) Some specific types of mathematical instruction that are promoted include hands-on and concrete learning experiences, use of real-world problems, direct instruction, cooperative learning, and using technology to enhance learning. Additionally, promoting a growth mindset and a positive attitude towards mathematics is also emphasized.
3) Some specific procedures used to teach basic mathematical instruction include direct instruction, visual aids such as graphs and diagrams, manipulatives and hands-on activities, scaffolding, and systematic review and practice. Teachers may also use questioning techniques to encourage students to think critically and develop their problem-solving skills.
Step-by-step explanation:
Which graph represents the function f(x) = -x-21-1?
-5-4-3-2
8.14
Y
& 1-
O
5 x -6-4-3-2-11
O
2 3 4 5
A graph which represents the function f(x) = -|x - 2| - 1 include the following:
What is an absolute value function?In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and it typically measures the distance of a point on the x-axis to the x-origin (0) of a cartesian coordinate (graph).
Next, we would use an online graphing calculator to plot the given absolute value function f(x) = -|x - 2| - 1 as shown in the graph attached below.
By observing critically the graph (see attachment), the two ordered pairs (points) that fit on its axes include the following:
Ordered pair = (2, -1).
Ordered pair = (0, -3).
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Principal amount: $1,000
Interest rate: 10%
Time: 12 months
The Simple Interest on Principal amount: $1,000 is $100.
What is Simple Interest?Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied.
Given:
Principal amount: $1,000
Interest rate: 10%
Time: 12 months
So, the Simple Interest
= P x R x T/100
= 1000 x 10 x 1 / 100
= 10000/100
= $100
and, Amount = P + I
Amount = $1100
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Name a median for ABC.
In the triangle ABC the line segment bisecting AC is the median, i.e. BD.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
The triangle ABC is given.
In Δ ABC, the line segment AC is bisected, so -
AD = CD
The line segment from a vertex to the middle of the other side is what is meant by a median. When the vertex is an angle in an equilateral triangle or the non-congruent angle of an isosceles triangle, it is also an angle bisector.
Since line segment BD bisects AC.
Therefore, the median is BD.
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can anyone help with this?
Answer:
Step-by-step explanation:
why do you need help if you already did it?
The biology teacher has 59 tests to grade.
She grades 40 of the tests. Let t equal the number of tests she has left to grade. Choose the equation that will solve the problem.
OPTIONS-
t/40 = 59
40t = 59
t-40 = 59
t + 40 = 59
Answer:
t + 40 = 59
Step-by-step explanation:
We know
She has 59 tests to grade. So, it will be the total of the equation.
She already grades 40 on the tests.
t is the number of tests she has left to grade.
So, the equation is
t + 40 = 59
ALGEBRA Express the given function
The function h as a composition of two functions f and g are;
[tex]f(x)=\sqrt[7]{x} \\\\ g(x)=x^6-4[/tex]
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Functions are formed by composing two or more functions in a way that one's output is another's input are called composite functions. They are also called function of functions.
From the information given we can deduce that the functions are:
[tex](f\circ g)(x)=\sqrt[7]{x^6-4}[/tex]
The simplification of the function gives the individual function as;
[tex]f(x)=\sqrt[7]{x} \\\\ g(x)=x^6-4[/tex]
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20. in this problem we assume that fish are caught at a constant rate h independent of the size of the fish population. then y satisfies dy dt
the solution of the given derivative will be y = k/2(1±√(1-4h/rk))
What is derivative?
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.
dy/dt = 0
-r/k y²+ry-h=0
y = k/2(1±√(1-4h/rk))
Hence the solution of the given derivative will be y = k/2(1±√(1-4h/rk))
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Please help me i need to doo thissss
YO HELP PLEASE PLEASE
A rectangle has a length pf 18 yards less than 4 times its width. if the area of the rectangle is 630 yards, find the length of the rectangle
Answer:
The width of the rectangle is approximately 8.904 yards, and the length of the rectangle is 24.71 yards.
Step-by-step explanation:
Let x be the width of the rectangle, then the length of the rectangle is 4x - 18.
The area of the rectangle is x * (4x - 18) = 630, so we can solve for x:
x * (4x - 18) = 630
Expanding and rearranging the equation:
4x^2 - 18x - 630 = 0
Using the quadratic formula, we can find the solutions for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
where a = 4, b = -18, and c = -630.
x = (18 ± √(18^2 - 4 * 4 * -630)) / (2 * 4)
x = (18 ± √(18^2 + 2520)) / 8
x = (18 ± √(324 + 2520)) / 8
x = (18 ± √2844) / 8
x = (18 ± 53.23) / 8
Since width can't be negative, x must be positive, so:
x = (18 + 53.23) / 8
x = 71.23 / 8
x = 8.904
The length of the rectangle is 4 * 8.904 - 18 = 24.71 yards.
Which sentence is a translation of this equation?
x3 – 14 = 68
Answer:
x cube minus fourteen is equal to sixty-eight
coach wanted to determine whether the mean sprint speed of his team differed from the national athletics mean speed of 12 seconds. he therefore obtained the speed of members of his team shown below:8,12, 9,7,8,10,9,11,13.5,8.5,10.5,9.5,11.5,12.5,9.5,10.5. write/develop the hypothesis for a two-tailed test and calculate the standard error of the mean for the team .what is your conclusion based on the developed hypothesis in A
It can reject the null hypothesis at a significance level of 0.05 and conclude that the mean sprint speed of the team is significantly different from the national athletics mean speed of 12 seconds.
What is the formula for the standard error of the mean?The formula for the standard error of the mean is:
SE = s / √(n)
where s is the sample standard deviation and n is the sample size.
The null hypothesis for a two-tailed test would be:
H0: The mean sprint speed of the team is equal to 12 seconds.
The alternative hypothesis would be:
Ha: The mean sprint speed of the team is not equal to 12 seconds.
To test this hypothesis, we need to calculate the standard error of the mean for the team.
Using the data provided, we can calculate the sample mean, sample standard deviation, and sample size as follows:
x = (8+12+9+7+8+10+9+11+13.5+8.5+10.5+9.5+11.5+12.5+9.5+10.5) / 16 = 10
s = √(1/(n-1) × ((8-10)² + (12-10)² + ... + (10.5-10)²)) = 1.717
n = 16
Therefore, the standard error of the mean is:
SE = 1.717 / √(16) = 0.429
To test the hypothesis, we can calculate the t-statistic using the formula:
t = (x - μ) / (SE)
where μ is the hypothesized population mean.
Plugging in the values, we get:
t = (10.0625 - 12) / 0.429 = -4.389
Using a t-table with 15 degrees of freedom (n-1), we can find that the probability of obtaining a t-value of -4.389 or more extreme is less than 0.01.
This means that we can reject the null hypothesis at a significance level of 0.05, and conclude that the mean sprint speed of the team is significantly different from the national athletics mean speed of 12 seconds.
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40 gm of magnesium sulfate is diluted in 1000 ml LR. After an initial loading dose, the nurse is to infuse a maintenance dose of 2 gm/hour. At how ml/hr should the IV pump be set? **Rounding rule: IV pump with specific med – round to the 10th place.
_______mL/hr
The IV pump should be set at 25ml/hr.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that 40 gm of magnesium sulfate is diluted in 1000 ml LR. After an initial loading dose, the nurse is to infuse a maintenance dose of 2 gm/hour.
Now, 40 gm of magnesium is diluted in 1000 ml.
So, 1 gm of magnesium will be present in (1000/40) ml = 25 ml.
Now, for 2 gm/hr, the pump should be set at 25 ml/hr.
Therefore, the IV pump should be set at 25ml/hr.
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at a baseball game, 250 fans were randomly surveyed about their favorite food to eat while attending a sporting event. The responses are shown in the table. Nachos 58, hamburgers 85 and chicken strips 33. Based on the survey, if the stadium is preparing for 5000 fans, how many hamburgers, nachos, and chicken strips should they have on hand?
The number of food items they need to have on hand is:
Nachos = 1165
Hamburgers = 1700
Chicken strips = 50
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of fans surveyed = 250
Nachos= 58,
Hamburgers = 85
Chicken strips = 33
The percentage of each item.
Nachos= 58/250 x 100 = 23.2%
Hamburgers = 85/250 x 100 = 34%
Chicken strips = 33/250 x 100 = 13.2%
Now,
If,
Number of fans surveyed = 5000
Nachos = 23.2% of 5000 = 23.3/100 x 5000 = 1165
Hamburgers = 34% of 5000 = 34/100 x 5000 = 1700
Chicken strips = 13.2% of 5000 = 13.2/100 x 5000 = 50
Thus,,
Nachos = 1165
Hamburgers = 1700
Chicken strips = 50
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i need help with problem b
The p-value from the data is 0.5289
What is the p-valueTo test whether the average score improvement of the GRE prep company's students is different than 100, we can use a two-sided t-test.
First, we need to set up our null and alternative hypotheses:
Null hypothesis (H0): The true mean score improvement of the GRE prep company's students is equal to 100.
Alternative hypothesis (Ha): The true mean score improvement of the GRE prep company's students is different than 100.
We will use a significance level of α = 0.05, which means we will reject the null hypothesis if the p-value is less than 0.05.
Next, we can calculate the sample mean and sample standard deviation of the data:
Sample mean (x) = 98.16
Sample standard deviation (s) = 8.88
We have a small sample size (n = 10) and the population standard deviation is unknown, so we will use a t-test. The t-statistic for a two-sided test is given by:
t = (x - μ) / (s / sqrt(n))
where μ is the hypothesized population mean (in this case, 100).
Substituting the values, we get:
t = (98.16 - 100) / (8.88 / sqrt(10)) = -0.655
Using a t-table with 9 degrees of freedom (n-1), we find that the two-tailed p-value for t = -0.842 is 0.5289.
Since the p-value (0.5289) is greater than the significance level (0.05), we fail to reject the null hypothesis. We do not have sufficient evidence to conclude that the true mean score improvement of the GRE prep company's students is different than 100.
Therefore, based on the given data, we cannot reject the claim of the GRE prep company that the average score improvement of their students is equal to 100.
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subtract (5x^(2)+3x-9)-(7x^(2)-6x+14)
add (8x^(2)-11x+6)+ (-5x^(2)+9x-7)
subtract (14y^(2)-4y+3)-(9y^(2)+3y-2)
*SHOW WORK PLEASE*!!!
The solution to the subtraction and addition of the given expressions are;
- 2x² + 9x - 23
3x² - 2x - 1
5y² - 7y + 5
How to subtract expressions?(5x² + 3x - 9) - (7x² - 6x + 14)
= 5x² + 3x - 9 - 7x² + 6x - 14
= - 2x² + 9x - 23
(8x² - 11x + 6) + (-5x² + 9x - 7)
open parenthesis
= 8x² - 11x + 6 - 5x² + 9x - 7
= 3x² - 2x - 1
(14y² - 4y + 3) - (9y² + 3y - 2)
= 14y² - 4y + 3 - 9y² - 3y + 2
combine like terms
= 14y² - 9y² - 4y - 3y + 3 + 2
= 5y² - 7y + 5
Hence, the solution to the expressions are - 2x² + 9x - 23; 3x² - 2x - 1; 5y² - 7y + 5.
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