A linear function to model the relationship between the number of days and the total cost of renting a mid-size car will be y = 40 + 45x
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, the cost is comprised of a fixed $40 administrative fee for the cleaning and maintenance of the car plus a rental cost of $45 per day.
The linear function to model the relationship between the number of days and the total cost of renting a mid-size car will be:
y = 40 + 45(x)
y = 40 + 45x
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The package of tissues has 180 pieces of tissues. We know that 10% of tissues are blue, 25% of the package are pink tissues, and the rest are white. How many pieces were blue and how many were pink tissue in the package?
What is remainder theorem in math?
Remainder Theorem is a method for polynomial division using Euclidean geometry.
What are polynomials?Algebraic expressions called polynomials include constants and indeterminates.
Polynomials can be thought of as a type of mathematics.
Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
A specific kind of expression is a polynomial.
A mathematical statement without the equals symbol (=) is called an expression. Let's examine the definition and usage of polynomials as they are described below.
An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.
Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.
Hence, Remainder Theorem is a method for polynomial division using Euclidean geometry.
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Function or not a function?
Function has one y for one x. if you pass line through x = 7 it cuts graph on different values of y
it is not function
A drama club is building a wooden stage in the shape of a trapezoidal prism. The height of the
stage is 2 feet. Some measurements of the stage are shown here. What is the area of all the
faces of the stage, excluding the bottom? Show your reasoning. If you get stuck, consider
drawing a net of the prism.
Two triangles will be better than one half times five times thirteen. We'll also have a single rectangular piece. It measures 12 by 10. 20 times 2 equals 40. 13 divided by 2 divided by 2 is equal to 4. I am capable of 44 times two times two. 13 is 52 One is equal to 10 x 2 x 1/2. 12 times 10 is 120, and 5 times 13 is 65. Consequently, the area is 297 square feet (40 plus 52 plus 20 plus 65 plus 120).
What is prism?A prism is a solid shape that is bound on all its sides by plane faces. There are two types of faces in a prism. The top and bottom faces are identical and are called bases. A prism is named after the shape of these bases. For example, if a prism has a triangular base it is called a triangular prism.The faces other than the top and bottom of a prism are called its lateral faces. All the lateral faces are also identical to each other and belong to the class of parallelograms. This means that the lateral faces can either be parallelograms, rectangles, or even squares since all of them have their opposite sides parallel to each other. One of the most common examples of a prism is a cuboid. It has a rectangular base and is called a rectangular prism.To learn more about rectangular prism refer to:
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Answer: 297 ft.2
Step-by-step explanation:
Which point is a solution of the system of linear equations? x − 2y = −1 y = −2x + 3 (1, 1) (1, −1) (−1, 1) (−1, −1)
Answer:
A) (1, 1)--------------------------
Given system:
x - 2y = - 1,y = - 2x + 3.Solve by substitution:
x - 2(- 2x + 3) = - 1x + 4x - 6 = - 15x = 6 - 15x = 5x = 1Find y:
y = - 2*1 + 3 = - 2 + 3 = 1The matching choice is A.
What is exponential form examples?
Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right.
In the exponential form, the exponent indicates the number of times the base is used as a factor.
For example, in the case of 16 it can be written as 2 × 2 × 2 × 2 = [tex]2^{4}[/tex], where 2 is the “base” and 4 is the “exponent.
A product in which the factors are identical is called a power of that factor. The number that is repeated is called the base, and the number of times it repeats is called the exponent, power or degree. And the power that is written on the right upper side are called exponents. when multiplying the numbers having same base and different exponents then the base is kept same and the exponents are added.
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Build a function from the following data:
The function represented by the table can be written as:
y = -4x + 3
How to find the function?Here we have a function represented by a table. Notice that for each increase of one unit in the x-value, the y-value decreases by 4.
Then we have a linear function, which can be written in a general form as:
y = a*x +b
Where a isthe slope and b is the y-intercept.
Because of the first pair on the table, (0, 3), we conclude that the y-intercept is 3, then we can rewrite:
y = a*x + 3
Now we can use the second point (1, - 1) and replace the values on the equation above.
-1 = a*1 + 3
-1 = a + 3
-1 - 3 = a
-4 = a
The linear function is:
y = -4x + 3
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You intend to draw a random sample of size n = 580 from a population whose parameter is p = 0.31 What is the mean of the distribution of sample proportions?
μ ˆ p =
What is the standard deviation of the distribution of sample proportions? (Report answer accurate to 2 decimal places.)
σ ˆ p =
The mean of the distribution of sample proportions is 179.8 and the standard deviation is 0.019
What is sampling distribution of proportion?The sample distribution of the proportions is used to measure the proportion with which success is achieved. The chance of an event taking place is the proportion computed by dividing the number of successes by the size of the sample.
Given that, You intend to draw a random sample of size n = 580 from a population whose parameter is p = 0.31, we are asked to find the mean of the distribution of sample proportions and standard deviation of the distribution of sample proportions.
Under the sampling distribution of the proportions, the mean and standard deviation are calculated by :
a) The mean is given as ;
μ = nP
Where, n is the sample size
P is the population proportion
Therefore,
μ = 580(0.31)
μ = 179.8
b) The standard deviation is given as follows :
δ = [tex]\sqrt{\frac{P(1-P)}{n} }[/tex]
δ = [tex]\sqrt{\frac{0.31(1-0.31)}{580} }[/tex]
δ = 0.019
Hence, the mean of the distribution of sample proportions is 179.8 and the standard deviation is 0.019
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What are the 3 root types?
Answer:
Irrational, Rational, and Complex Roots
Step-by-step explanation:
Irrational roots cannot be written as a fraction, for example, √2 is an irrational root because 2 is not a square number
Rational roots can be written as a fraction. For example, √4 is a rational root because it can be either -2 or 2 which are both rational.
Complex/imaginary roots take the form of [tex]a+bi[/tex] where "a" is the real part and "b" is the imaginary part. For example, √(-1) = i which is complex/imaginary.
A rental car company charge $50 per day to rent a car and $0. 15 for every mile driven. Mei Mei want to rent a car, knowing that:
She plan to drive 100 mile. She ha at mot $130 to pend. Write and olve an inequality which can be ued to determine xx, the number of day Mei Mei can afford to rent while taying within her budget
A rental car company charge $50 per day to rent a car and $0. 15 for every mile driven, then the inequality for the number of days will be represented as x ≤ 2.21 days.
Define Inequality :It is referred to as being unfair when two terms are joined by a sign like "not equal to," "more than," or "less than." The inequality illustrates the relationship between variables and numbers in terms of greater than and less than.
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality'. So, a lack of balance results in inequality.
Given that a rental car company charges $50 per day to rent a car and $0.15 for every mile driven.
The equation of inequality will be written as,
C ≥ [tex]0.15m + 50x[/tex]
Here, C is the total cost, m is the number of miles, and x is the number of days.
C ≥ [tex]0.15m + 50x[/tex]
C ≥ ( [tex]0.15*100[/tex] ) + [tex]50x[/tex]
130 ≥ 19.5 + [tex]50x[/tex]
130 - 19.5 ≥ [tex]50x[/tex]
[tex]50x[/tex] ≤ 110.5
x ≤ 110.5 / 50
x ≤ 2.21 days
Therefore,
A rental car company charge $50 per day to rent a car and $0. 15 for every mile driven, then the inequality for the number of days will be represented as x ≤ 2.21 days.
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 7 cubic feet and the volume of each large box is 20 cubic feet. There were 8 more small boxes shipped than large boxes and the total volume of all boxes was 245 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
Using equations, the number of small boxes shipped is 15 while the number of large boxes shipped is 7.
What is an equation?An equation is described as a mathematical statement of the equality of two or more mathematical expressions.
Equations use the equation sign (=) to show that the expressions are equivalent or equal.
The volume of each small box = 7 ft³
The volume of each large box = 20 ft³
The number of small boxes = x + 8
The number of large boxes = x
The total volume of all the boxes = 245 ft³
The total volume of the 8 additional small boxes = 56 ft³ (8 x 7 ft³)
The remaining volume of the boxes after subtracting the volume of the 8 additional small boxes = 189 ft³ (245 - 56)
Equations:7x + 56 + 20x = 245
7x + 20x = 189
27x = 189
x = 7 (189/27)
The number of small boxes shipped, x + 8 = 7 + 8 = 15 boxes
The number of large boxes shipped, x = 7 boxes
Check:
Small boxes = 15 x 7 ft³ = 105 ft³
Large boxes = 7 x 20 ft³ = 140 ft³
Total 22 245 ft³
Thus, the paper company shipped 15 small boxes with 7 large boxes.
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The graph of which inequality is a dashed line? Select all that apply.
y ≥ 15 − 5x
y > 11 + 4x
y ≤ 16 + 2x
y < 12 + 3x
Answer:y ≥ 15 − 5x
Step-by-step explanation:
A study finds that out of every babies born in the world, have some kind of major birth defect. What is the simplest way to assign random numbers to conduct a simulation based on this statistic?
Question content area bottom
Part 1
Select the correct choice below and fill in the answer boxes to complete your choice.
A.
Use one-digit numbers 09; let 0
enter your response here represent babies born with some kind of major birth defect,
enter your response here
enter your response here represent babies born without a major birth defect, and skip
enter your response here9.
B.
Use one-digit numbers 09; let 0
enter your response here represent babies born with some kind of major birth defect and
enter your response here
enter your response here represent babies born without a major birth defect.
C.
Use two-digit numbers 0099; let 00
enter your response here represent babies born with some kind of major birth defect and
enter your response here
enter your response here represent babies born without a major birth defect.
D.
Use two-digit numbers 0099; let 00
enter your response here represent babies born with some kind of major birth defect,
enter your response here
enter your response here represent babies born without a major birth defect, and skip
enter your response here
Answer: A. Use one-digit numbers 0-9; let 0 represent babies born with some kind of major birth defect, and 1-9 represent babies born without a major birth defect and skip 9.
This is the simplest way to assign random numbers to conduct a simulation based on the statistic that 2% of babies born in the world have some kind of major birth defect.
Using one-digit numbers 0-9 and designating 0 as babies born with a major birth defect and 1-9 as babies born without a major birth defect allows for a simple and easy-to-understand simulation, as only 2% of the numbers generated will be 0.
The other options are not the most simple way to conduct a simulation based on this statistic, as they would require more digits and more complex rules for assigning numbers to represent babies with and without major birth defects.
Step-by-step explanation:
What's the quotient in division?
The quotient is the number that is generated when we perform division operations on two numbers, and the result of the division is called the quotient.
There are four main terminologies used in the arithmetic division such as divisor, dividend, quotient, and remainder.
The number is divided by another number to get a different number as an output.
Dividend = Quotient × Divisor + Remainder
If the remainder is equal to 0, then;
Dividend = Quotient × Divisor
Therefore,
Quotient = Dividend ÷ Divisor
Dividend: The number which is required to be divided
Divisor: The number which divides the given dividend
Remainder: The number which is left after the division method. When a number is completely divided then the remainder is zero.
Consider an example 25/5=5-----quotient.
where 25 is the dividend
5 is the divisor.
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40-32 dived by 8+5-2
Combine like terms to create an equivalent expression. 1.3 b 7.8 − 3.2 b
The equivalent expression is -1.9b + 7.8.
What is an equivalent phrase?There is a concept known as an analogous expression, which is an expression that has the same value as another expression but has a different appearance.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
Combine similar phrases now:
The definition of like words is the terms that have the same variable raised to the same power. Only the numerical coefficients can change in algebra.
When we combine the term b's coefficient, we get
1.3b + 7.8–3.2b
= (1.3−3.2)⋅b + 7.8
By condensing the equation, we obtain
= (- 1.9) +b + 7.8
= −1.9b + 7.8
There is a condensed equivalent formula of -1.9b + 7.8.
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Find a polynomial f(x) of degree 4 that has the following zeros.
5, 0, -9, -2
Leave your answer in factored form.
Answer: (x-5)(x)(x+9)(x+2)
Step-by-step explanation:
A salad dressing is made by mixing yogurt and mayonnaise in the ratio 3:5
Karolina makes 800 ml of the salad dressing.
How much yogurt does she use?
Give your answer in milliliters (ml)
The amount of yogurt that Karolina used when making 800 ml of salad is 300 ml.
What is ratio?Ratio is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another quantity. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.
A salad dressing is made by mixing yoghurt and mayonnaise in the ratio
3:5.
For 800 ml of salad dressing:
Amount of yoghurt = (3 / (3 + 5)) * 800 ml
Amount of yoghurt = 300 ml
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The answer is 300 ml!!!
What would be the order of these quadratic functions when they are
arranged from the narrowest graph to the widest graph?
f(x) = -5x²
g(x) = 0.5x²
h(x) = 3x²
(1) f(x), g(x), h(x)
(2) g(x), h(x), f(x)
(3) h(x), f(x), g(x)
(4) f(x), h(x), g(x)
please help ASAP
Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.
What does the word function mean?A relationship that explains how two variables relate to one another is represented by the word "functions," which is frequently used in mathematics. There are three: a variable, which can be any type of input, and predictor variables, which are the results of the function or equation.
Here,
A quadratic function's "width" can be calculated using the coefficient before the variable.
The graph will be narrower than the parent graph if the coefficient is more than one (f(x)=x2), and
wider if the coefficient is less than one. Thus, from widest to narrowest:
f(x)=0.5x²
f(x)=3x²
f(x)=-5x²
Therefore , the solution to the given problem of function comes out to be f(x)=0.5x² is the narrowest graph.
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what’s the coefficient of 8y
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Sarah made baket on ome of her hot in a baketball game. If he continue to make baket at the ame rate, how many baket will Sarah make in her next 6 hot
Sarah will make 6 baskets in her next 6 shots.
If Sarah made a basket on one of her first shots in a basketball game, and she continues to make baskets at the same rate, we can use that information to predict the number of baskets she will make in her next 6 shots.
Since we know that Sarah made a basket on one of her first shots, we can assume that the probability of her making a basket on any given shot is 1/1 or 100%.
If the probability of Sarah making a basket on any given shot is 100%, then we can expect her to make a basket on all 6 of her next shots. Therefore, Sarah will make 6 baskets in her next 6 shots.
Therefore, Sarah will make 6 baskets in her next 6 shots.
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Triangle D has been dilated to create triangle D′. Use the image to answer the question.
Answer:
3
Step-by-step explanation:
Dilating a shape will proportionately affect its side lengths.
To find the scale factor between the given triangles, take one side on the larger triangle and divide it by the corresponding side on the smaller triangle. I will divide the triangles' top sides (24 and 8).
[tex]\textrm{scale factor} = \dfrac{24}{8} = 3[/tex]
So, the scale factor used was 3.
Help, I need to answer this question
Answer:
Step-by-step explanation:
factors of 8
Answer:
F- of a 8* i think
Step-by-step explanation:
How do you find the factor of a remainder theorem?
The Remainder Theorem states that if a polynomial P(x) is divided by (x - c), the remainder is P(c). To find the factor of a polynomial using the Remainder Theorem, you can use the following steps:
Start by assuming that the polynomial can be factored into (x - c) and some other polynomial Q(x).Divide P(x) by (x - c) using polynomial long division, and find the remainder R(x).Use the Remainder Theorem to set P(c) = R(c) = 0.Solve for c to find the value that makes P(c) = 0.Use the value of c found in step 4 to factor (x - c) out of P(x).Repeat the process with the remaining polynomial Q(x) until the polynomial is completely factored in.Example:
P(x) = x^3 + 3x^2 + 2x -6
Factor = (x-2)
P(2) = 8 + 12 + 4 - 6 = 0
So, the factor of P(x) is (x-2)
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Select one correctly for brainliest!
A. 60
B. 75
C. 65
D. 50
The m ∠SPR of the rhombus with sides PQRS is 65, option C.
How to find the angle of a rhombus?Only the opposite angles of a rhombus are equal. A rhombus's diagonal angle is 90 degrees.
There are two ways to find the angle SPR of the rhombus, PQRS;
If ∠PQR = 50° then, ∠PQR = ∠PSR (opposite sides)
∠OSR = 1/2 x 50° = 25° where SQ bisects ∠PSR
∠ORS + ∠ROS + ∠OSR = 180°
∠ORS + 25° + 90° = 180°
∠ORS = 180° - 115°
∠ORS = 65°
Also, it can be calculated thus:
Because rhombus adjacent sides are supplementary, it can be written as; ∠QRS + ∠PQR = 180°
∠QRS = 180° - ∠PQR
∠QRS = 180° - 50°
∠QRS = 130°
Even though a rhombus' diagonal is an angular bisector, the ∠PRS is half of the ∠QRS.
Therefore ∠SPR = ∠QRS/2
∠SPR = 130°/2
∠SPR = 65°
The value of ∠SPR is half the angle because the opposite angles are equal therefore each side has 65°.
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How do you factor a polynomial with 3 factors?
Step 1: Group the first two terms together, followed by the last two terms. Step 2: Extract a GCF from each binomial separately. Step 3: Remove the common binomial. It's worth noting that if we multiply our answer by itself, we get the original polynomial.
What is polynomial?A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Step 1: Combine the first two terms, then the last two terms. Step 2: Separately extract a GCF from each binomial. Step 3: Get rid of the common binomial. It's worth noticing that dividing our solution by itself yields the original polynomial. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
Here,
Step 1: Combine the first two terms, then the last two terms. Step 2: Separately extract a GCF from each binomial. Step 3: Get rid of the common binomial. It's worth noticing that dividing our solution by itself yields the original polynomial.
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I need help asap, if you really know the answer. there are 4 correct answers
The quotient of five times x and fifteen
Answer:
the answer to your question is 3.
Please help me with this.
The required dimensions of the dilated kitchen is 8.5 inch by 13.09.
What is scale factor?The scale factor is defined as the ratio of modified change in length to original length.
Here,
Current dimension of the graph = 8.5 inch by 11 inch
Final dimension of the graph = 24 inch by 36 inch
Now,
Dilated dimension of the kitchen
Length = 24 / 8.5 × 3 = 8.5 inch
Width = 36/11 × 4 = 13.09
Thus, the required dimensions of the dilated kitchen is 8.5 inch by 13.09.
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How do I solve 4y^2=81 by factoring
So on solving the provided question we cans say that factors of 4y^2=81 are - y = +9/4 and - 9/4
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
factors of 4y^2=81
are -
y = +9/4 and - 9/4
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