Help please! :)

Directions: Answer each question below, showing all pertinent work.
Solve all using Estimate.

A. –42.3 ÷ 3.4

B. 16.1 – (–14.7)

C. –15.52 + 54.25

D. ‐67.8 ‐ 5.72

1.Brock had $3084 in his checking account. He wrote checks for $350 for rent, $275 for auto repair, and
$169 for a loan payment. Find the amount remaining in his account.

2.Linda’s paycheck was for $2312. She spent $157 on rent, $322 on food, $478 on child care, $234 on
transportation, and $290 on other things. She put the rest of her paycheck in savings. How much did
she put in savings?

False. Exponent can be as big as it wants

Finding the numeric value of the regression equation, the best prediction of Riley's height is given by:

65.84 inches.

To find the numeric value of a function, we replace each instance of the variable in the function or in the expression by the desired value.

The regression equation in this problem gives the armspan of a person, represented by y, as a function of the height x as follows:

y = 1.123x - 6.443.

Riley has an armspan of 67.5 inches, hence y = 67.5, and we can find the best prediction for his height replacing the lone instance of y in the equation by 67.5 and solving for x, as follows:

67.5 = 1.123x - 6.443.

1.123x = 67.5 + 6.443

x = (67.5 + 6.443)/1.123

x = 65.84 inches, which is the best prediction.

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Answer:

It’s B

Step-by-step explanation:I did it on edge 2022 got it right!

Answer:

12-month option is cheaper per month

Step-by-step explanation:

A gym offers a 12-month membership for $125 or an 8-month membership for $90. Which option has the lesser price per month?

12-month option:

125/12 = $10.42

8-month option:

90/8 = $11.25

12-month option is cheaper per month.

The simplified expression for this problem is given as follows:

(3²)^(1/3) = 3^(2/3) = [tex]\sqrt[3]{9}[/tex]

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

The exponents for this problem are given as follows:

2 and 1/3.

Hence the product is of:

2 x 1/3 = 2/3.

Converting the fractional exponent to a rational expression, we have that:

3^(2/3) = [tex]\sqrt[3]{3^2} = \sqrt[3]{9}[/tex]

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Answer:

a.3.95x^2+1

9999999999999999999999999

Answer:

D

Step-by-step explanation:

first find the zeros on the graph and their multiplicity.

zeros: -1, 2

mult: 3, 2

the equation that fits is f(x)=(x+1)^3(x-2)^2

Answer:

265

Step-by-step explanation:

the nth term of an arithmetic progression is given by

[a+(n-1)d]

where "a" is the first term, "d" is the common difference and "n" is the term you're looking for

from the question, a= 17

d=4

n=63

substituting, [17+(63-1)4]=[17+248]=265

Hello,

The temperature changes at rate of -1.5 degree celsius every hours and the reading of temperatures starts at 0 degree celsius which can be modeled into the linear equation of f(t) = -1.5t where f(t) is the temperature function and t is time.

The problem then asks, “what was the temperature 7 hours ago?” This question asks for the temperature 7 hours ago which means t = -7 in this case since we are solving for temperature 7 hours ago, not next 7 hours.

Time being negative in this scenario means in past or hours ago, generally time cannot be negative as it’s scalar quantity.

Substitute t = -7 in the temperature function, this’ll result in:

Therefore, 7 hours ago, the temperature was at 10.5 degree celsius. Please let me know if you have any questions!

Answer:

See below

Step-by-step explanation:

A)  Recursive Definition

The value of each term in a sequence that starts at 13 is reduced by 1.5 for each step in the sequence.

B)  Definition for nth Term

   D(n) = D(1)+(n-1)(-1.5)

    D(1) = 13

     D(n) = 13+(n-1)(-1.5)

Examples:

   D(5) = 13 + (5-1)*(-1.5)

   D(5) = 13 + (4)*(-1.5)

   D(5) = 13 - 6, or 7

------------------

    D(7) = 13 + (7-1)*(-1.5)

    D(7) = 13 + (6)*(-1.5)

    D(7) = 4

Polygons A'B'C'D' are not described by the rem preimage. The initial form before a change is known as the preimage. The transformation in the example below involves both a rotation and a dilation.

When three or more line segments are connected to one another, a polygon is created, which is a closed, two-dimensional, plane shape. Most frequently, when learning about geometry, we run into polygons.

A closed two-dimensional figure with three or more straight lines is what a polygon is defined as in geometry. Poly means "many" and gon means "angle" in Greek, making up the word "Polygon." We are surrounded by a wide variety of polygons.

An illustration of this is the hexagonal shape of a honeycomb. Every polygon has a unique structure, and they are all divided into different groups according to how many sides they have and other factors. This means that all polygons are closed plane shapes.

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Answer:

Point-slope form: y - 6 = -1/3(x + 6)

Slope-intercept form: y = -1/3x + 4

SOLUTION

The total cost of the books is $8

Calculating 20% off gives

Therefore the amount paid is $6.40

The coordinates of the mid- point are (5, 16)

Given,

The midpoint of the line,  given any points A (x₁, y₁) and B(x₂, y₂) .

In the question, we are given that the midpoint  is (3, 11) and (7, 21).

and, to find the co- ordinates of the line.

Now, We know that the Formula of mid point

M = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).

Here, the points are (3, 11) and (7, 21)

Therefore,

(x, y)  =  ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).

=> (x, y) = [( [tex]\frac{3+7}{2}[/tex]) , ([tex]\frac{11 + 21}{2}[/tex]) ]

=> (x , y) = (10/2 , 32/ 2)

=> (x ,y) = (5 , 16)

Hence, The coordinates of the mid- point are (5, 16)

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The reason for the required step using the property of equality are as follow:

7. Addition property of equality.

8. Symmetric property of equality.

9. Reflexive property of equality.

10.Symmetric property of equality.

As given,

The reason for the required step using the property of equality are as follow:

7. 4x - 10 = 7 - 2x

4x+2x - 10 = 7

6x -10 = 7

Here

Addition Property of Equality is applied.

If x, y,  and z are real numbers, and x=y

then

x+ z=y+ z

8. 6 = x

x = 6

Here Symmetric Property of Equality is applied.

If x and y are real numbers, then

x = y

y = x

9. 4 = 4

Here Reflexive Property of Equality is applied.

If x is a real number, then

x = x

10. -3 = x

x = -3

Here Symmetric Property of Equality is applied.

If a is a and b are real numbers then,

a = b

b = a

Therefore, The reason for the required step using the property of equality are as follow:

7. Addition property of equality.

8. Symmetric property of equality.

9. Reflexive property of equality.

10.Symmetric property of equality.

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Four siblings whose ages are consecutive integers. If the sum of their ages is 86 then The eldest sibling is 20, followed by siblings 21, 22, and 23.

Consecutive means in order.  Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.

Let x = the one sibling

Let x + 1 = the second sibling

Let x + 2 = the third sibling

Let x+4 = the fourth sibling.

If you add the four siblings together they equal 86

(x) + (x +1) + (x + 2) + (x+3) = 86  I put the parentheses in so that you can see each sibling, but it is not needed.

x + x+ 1 +x + 2 + x+ 3 = 86  Combine like terms

4x + 6 = 86 Subtract 6 from both sides

4x = 80

x = 20

The eldest sibling is 20, followed by siblings 21, 22, and 23.

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Answer: infinitely many solutions

Step-by-step explanation:

21 + 21 < 63

Calculate

42 < 63

infinitely many solutions

Answer: 8 1/2

I can't give an explanation though

Answer:

go to gogle

Step-by-step explanation:

The consecutive age is 6 and 7 and Malik is 6 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let their Consecutive age be x, x+1

So, x(x+ 1)= 42

x²+ x - 42 = 0

x² + 7x- 6x - 42=0

x( x+ 7)- 6 ( x+ 7)= 0

(x+ 7)( x-6)= 0

x = 6, -7

Hence, the consecutive age is 6 and 7.

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Exponential Model

Some phenomena can be modeled as an exponential function of the form:

Where Po is the initial value, r is the rate of change, and t is the time.

If the value of P decreases in time (decaying function), then r is negative. If the value of P increases in time (growth), then r is positive.

We know an investment of Po=$4500 has been losing value (decay) at a rate of r = -2.5% = -0.025 each year.

The value of the investment when t = 5 years is:

Calculating:

The investment will be worth $3964.93 in 5 years

Answer: y=2/3x-2.03

Step-by-step explanation: This may not be exactly correct, and I don't know if you're using standard form, but I used demos the graphing calculator to make a graph, and that matches down to the 0.03 of the line.

I hope this helps, brainliest would be appreciated <3

Answer:

4 = -27x^2+12x

5 = 2x^3+x^2

6 = -5x^2+4x-1

7 = x-y+2z

Step-by-step explanation:

Simple collecting like terms and distributive properties.

The Cost of 68 shirts is 841. The total cost formula is used to calculate a total by combining the variable and fixed costs of providing goods.

How to find Cost :

Substitute x=68 in the above equation

so ,  f(x) = 12 (68)+25

       f(x) = 841

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Option(A) i.e, 60 sq. feet is an answer.

The area of a rectangle is the number of unit squares that its perimeter includes. A rectangle's area is the area it takes up within the confines of its four sides. The area of a rectangle is determined by its dimensions. A rectangle's area is essentially equal to the product of its length and breadth. A shape's area is defined as the "space enclosed within the perimeter or the boundary" of the given shape.

The area of a rectangle can be calculated using the formula Area of rectangle = length × width.

Given, length = 15 feet, width = 4 feet

put these values in given formula,

Area of rectangle =  15 * 4

                              = 60 square feet

Hence, the answer is option(A)  i.e, 60 sq. feet.

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Answer:

4 1/2

Step-by-step explanation:

Add the fractions:

11/6+8/3

11/6+16/6

27/6

27/6=4.5

Answer:

all integers are rational numbers

Step-by-step explanation:

Answer:

x=0.3

Step-by-step explanation:

-0.4x-4.15=x-1.6-2.97

-0.4x-x=-(1.6-2.97)+4.15

-1.4x=0.42

x=0.3

Answer:

x=0.3

Step-by-step explanation:

On solving the inequality we get that values 7 and 8 are solutions to the inequality, hence, option 3.

Here, we are given an inequality as follows-

9 < 3x + 4

Inequalities are solved in a similar manner as we solve equations.

Subtracting 4 from both sides of the inequality we get-

9 - 4 < 3x + 4 - 4

5 < 3x

dividing both sides by 3, we get-

5/3 < 3x/3

5/3 < x

x > 5/3

5/3 in decimal can be written as 1.66

Thus,

x > 1.66

From the given options only 7 and 8 are greater than 1.66.

Thus, on solving the inequality we get that values 7 and 8 are solutions to the inequality, hence, option 3.

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For given[tex]$\mathrm{n}$[/tex] and [tex]$\mathrm{X}_{(1)}$[/tex], we can obtain the confidence interval [tex]$(\mathrm{a}, \mathrm{b})$[/tex].

Let[tex]$\mathrm{X}_1, \mathrm{X}_2, \ldots, \mathrm{X}_{\mathrm{n}}$[/tex] be a sequence of size [tex]$\mathrm{n}$[/tex] from the exponential distribution with rate[tex]$\lambda$.[/tex] Then the probability density function of the random is a given [tex]$\mathrm{f}\left(\mathrm{x}_{\mathrm{i}}, \lambda\right)=\lambda \exp (-\lambda \mathrm{x}) ; \quad 0 \leq \mathrm{x} < \infty$[/tex]

Let us consider a ordered random sample of size [tex]$\mathrm{n}$[/tex] as [tex]$\mathrm{X}_{(1)}, \mathrm{X}_{(2)}, \ldots, \mathrm{X}_{(\mathrm{n})}$[/tex]. Then [tex]$\mathrm{X}_{(1)}$[/tex] is the smallest of the sample. The density function of the smallest sample [tex]$\mathrm{X}_{(1)}$[/tex] is give by

[tex]$$\mathrm{f}\left(\mathrm{X}_{(1)}, \lambda\right)=\mathrm{n}\left[1-\mathrm{F}_{\mathrm{x}}(\mathrm{x}, \lambda)\right]^{\mathrm{n}-1} \times \mathrm{f}(\mathrm{x}, \lambda)$$[/tex]

As the cumulative density  is given by

[tex]=\int_0^{\mathrm{x}} \mathrm{f}(\mathrm{x}, \lambda) \mathrm{dx} \\&=\int_0^{\mathrm{x}} \lambda \times \exp (-\lambda \mathrm{x}) \mathrm{dx} \\&=1-\exp (-\lambda \mathrm{x})\end{aligned}$$[/tex]

The density of the minimum of the sample is given by

[tex]=\mathrm{n} \times[1-(1-\exp (-\lambda \mathrm{x}))]^{\mathrm{n}-1} \times \lambda \times \exp (-\lambda \mathrm{x})$[/tex]

[tex]$$\begin{aligned}&=\mathrm{n} \times[\exp (-\lambda \mathrm{x})]^{\mathrm{n}-1} \times \lambda \times \exp (-\lambda \mathrm{x}) . \\&=\mathrm{n} \lambda \times \exp (-\mathrm{n} \lambda \mathrm{x})\end{aligned}$$[/tex]

Thus, here [tex]$\mathrm{X}_{(1)}$[/tex] follows gamma distribution with parameter [tex]$\alpha=1 \quad$[/tex] and [tex]$\beta=\frac{1}{n \lambda}$[/tex].

We make use of the condition that if Y follows Gamma distribution with parameter with parameter [tex]$\alpha$[/tex]and [tex]$\beta$[/tex]. Then, we have

[tex]$\frac{2 \mathrm{Y}}{\beta} \sim \chi^2(2 \alpha, \mathrm{n}-1)$[/tex]

Thus we have that

[tex]\mathrm{T}=\frac{2 \mathrm{X}_{(1)}}{\frac{1}{\mathrm{n} \lambda}} \sim \chi^2(2, \mathrm{n}-1)$$[/tex]

[tex]$$\begin{aligned}\mathrm{b} &=\frac{\chi^2\left(1-\frac{\alpha}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2\left(1-\frac{0.03}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2(0.985, \mathrm{n}-1)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\\mathrm{a} &=\frac{\chi^2\left(\frac{0.03}{2}, \mathrm{n}-1\right)}{2 \mathrm{X}_{(1)} \times \mathrm{n}} \\&=\frac{\chi^2(0.015, \mathrm{n}-1)}{2 \mathrm{X}_{(1)} \times \mathrm{n}}\end{aligned}$$[/tex]

Therefore for given[tex]$\mathrm{n}$[/tex] and [tex]$\mathrm{X}_{(1)}$[/tex], we can obtain the confidence interval [tex]$(\mathrm{a}, \mathrm{b})$[/tex].

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Answer: you have to add 60 mL of the 70% solution.

Step-by-step explanation:

If you have 180 mL of a 30% alcohol mixture, then (180mL)(0.30) = 54mL of that solution is alcohol.

Similarly, if you have x mL of a 70% alcohol mixture, then (x mL)(0.70) = 0.70x mL of that solution is alcohol.

When you combine these two liquids, you will have (180 + x) mL of liquid and you want it to be 40% alcohol.

So, you simply need to solve the equation:

180(0.30) + x(0.70) = (180 + x)(0.40)

54 + 0.70x = 72 + 0.40x     (distribute the 0.40)

0.30x = 18        (subtract 54 from both sides and subtract 0.40x from both sides)

x = 60

So, you have to add 60 mL of the 70% solution.

Hope this helps!  :)

Answer: y=15, AQ=31, QX=14

Step-by-step explanation:

2y+1+y+1=45

3y=45

•1/3 to both sides

y=15

then substitute 15 for y in the other equations to get the result