50 points!!!
7. Write and solve an inequality for the value of x.

We have exponential decay of roughly 40% per time unit.

We have to  y=(0.88)^4t in the form y=a(1+r)^t or y=a(1−r)^t to determine whether it represents exponential growth or exponential decay. Round a and r to the nearest hundredth if necessary.

y=(0.88)^4t

y=1( (0.88)^4 )^t

y=1( 0.59969536 )^t

Set 0.59969536 equal to 1-r and solve for r

1-r = 0.59969536

-r = 0.59969536-1

-r = -0.40030464

r = 0.40030464

r = 0.40

This means we have,

y=a( 1 - r )^t

y=1( 1 - 0.40 )^t

which means a = 1 and r = 0.40 approximately

We have exponential decay of roughly 40% per time unit.

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The probability that Mrs. Barnes checks homework if the students take a pop quiz is 0.77, the correct option is D.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Given;

Mrs. Barnes’s class determined the probability that she will check homework on a randomly chosen day is 0.42;

They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9;

Then the probability that Mrs. Barnes does not check homework if the students take a pop quiz;

P= 0.42*0.60 + 0.58*0.90

P = 0.252 + 0.522

P = 0.774

P ≈ 0.77

Therefore, the probability will be 0.77

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Answer:

Step-by-step explanation: 122x2=144

Answer: x = 12, - 12

Step-by-step explanation:

To find the area of an equilateral triangle with side 12 cm, we can use the formula:

Area = (√3/4) * (side length)^2

Substituting the value of the side length, we get:

Area = (√3/4) * 12^2

Area = (√3/4) * 144

Area = (√3/4) * 1212

Area = (√3/4) * 1212 = (√3/4)144 = (√3)12(12/4) = (√3)123 = 1212*√3 cm^2

So, the area of the equilateral triangle is 1212√3 cm^2.

Answer:

  (c)  √65

Step-by-step explanation:

You want to know the magnitude of the vector (7, -4).

The magnitude of a vector is the root of the sum of the squares of its components.

  |(7, -4)| = √(7² +(-4)²) = √(49 +16) = √65

The magnitude of the vector is √65.

Answer:

√65

Step-by-step explanation:

The number of solutions to an equation x₁ + x₂ + x₃ = 11 are 55

Consider given equation x₁ + x₂ + x₃ = 11,

wherex₁, x₂, and x₃ are non-negative integers.

We can oberve that x₁ is the number of ones before the first zero, x₂ the number of ones between the first and the second zero, x₃ is the number of ones after the second zero.

So, we can say that there is a one to one correspondence between the solutions and reorderings of 11 ones and 2 zeros.

So, the number of solutions to given equation would be,

n = ¹¹C₂

Using combination formula [tex]^nC_r=\frac{n!}{r!\times(n-r)!}[/tex],

¹¹C₂ = 11! / (2! × (11 - 2)!)                  

¹¹C₂ = 55

So, n = 55

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The complete question is:

How many solutions does equation x₁ + x₂ + x₃ = 11 have where x₁, x₂, and x₃  are non negative integers?.

Answer:

24 because every 1 cup of flour equals 24 number of cookies so it keeps on adding up eg. 6 cups of flour would equal 144 cookies.

Answer:

  x=0

Step-by-step explanation:

You want the value of x that cannot be in the domains of either f(x) = 2/x or g(x) = (x+1)/x.

The domain of a function is the set of input values for which the function is defined.

These functions f(x) and g(x) are "undefined" when x=0, because that would cause division by zero.

  x cannot be zero

Answer:

4 and 2?

Step-by-step explanation:

4+2=6 im pretty sure thats what you mean

The equation of the line if the y-intercept i (0,6) and the lope i 15 is:

B. y = 15x 6

The equation of the line is given in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis and is given as (0,6). Therefore, the value of b is 6. The slope is given as 15. Therefore, the equation of the line is y = 15x + 6. This equation means that for every unit increase in x, y increases by 15 units and the line passes through the point (0,6)

This method is applicable for other equations as well, as long as they are in slope-intercept form (y = mx + b). The slope-intercept form is a way to represent a linear equation where the slope and the y-intercept are known. If the equation is not in that form, it can be rearranged to make it so. Once the equation is in slope-intercept form, you can identify the slope and the y-intercept which can be useful in understanding the characteristics of the line such as its direction and position in the coordinate plane.

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H₂ is two moles.

The molecular mass of an element is described as the sum of the masses of all the atoms present in the molecule.

Molecular mass is acquired by adding the atomic masses of all atoms with the number of atoms in the molecule.

H₂ has two atoms, so a mole of H₂ would have 1 mole of H₂ molecules, and when broken down into atoms, 2 moles of atoms.

Think about it like pairs of shoes. If you have 6 pairs of shoes, you have 12 pairs of shoes.

CO₂ has 3 atoms, 2N₂0 has 3 atoms, and there are already 2 moles, so that would be 6 moles of atoms; 2NaCl has 2 atoms but again, that 2 indicates that you'd have 4 moles of atoms, and H₂SO₄ has 7 atoms.

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Therefore, the price of the complete meal is $9.00 before tax.

Percentage:

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

As per the data given in the above question are as bellow,

The details provided are as follow,

Provided that 20% of the expense of breakfast is $1.8.

To calculate the total cost of the breakfast before the tip, we may apply proportions.

Set x as the price of a full breakfast:

Therefore 0.2 = 1.8

So, 1.0 = x

0.2x = 1.8 x 1.0

x = 1.8/0.2

x = 9

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Note: The correct question is as bellow,

Mira has breakfast at a restaurant. She leaves a 20%, percent tip of $1.80. What is the price of Mira's breakfast, before tip?

Answer:

47.5

Step-by-step explanation:

95 divided by 2 is equal to 47 with a remainder of 1.

To divide 95 by 2, you need to perform long division.

Here's the step-by-step process:

Write the dividend (95) inside the division bracket, and the divisor (2) outside the bracket.

Place the quotient above the division bracket.

__

2 | 95

Start with the leftmost digit of the dividend (9) and divide it by the divisor (2). Since 9 is smaller than 2, we move to the next digit.

__

2 | 95

4

Bring down the next digit of the dividend (5) to the right of the remainder

(1) obtained from the previous step.

__

2 | 95

4 1

Divide 15 by 2. The quotient is 7, and the remainder is 1.

__

2 | 95

47 1

Since there are no more digits in the dividend, we have completed the division.

The quotient is 47, and the remainder is 1.

Therefore, 95 divided by 2 is equal to 47 with a remainder of 1.

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Answer:

  f(x) = 3x

Step-by-step explanation:

You want the relation 3x -y = -6x +2y written as a function of x.

This is solved the same way any 3-step linear equation is solved:

Now you have the function written in terms of x:

  y = 3x

In functional notation, this is ...

  f(x) = 3x

Multiplying both sides by 7 undoes the division of x by 7 in the original problem. Therefore, option A is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x/7 -4=-6

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Multiplying both sides of equation by 7, we get

x-28=-42

Add both sides of equation by 28, we get

x=-42+28

x=-42

Therefore, option A is the correct answer.

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The recommended range for longitude and latitude coordinates is -180 to 180 and -90 to 90, respectively.

The use latitude and longitude to coordinates

To denote degrees, use the degree sign.

To denote decimals, use periods.

Your spreadsheet should have Latitude listed before Longitude.

When plotting a point, (x, y)-coordinates are used. The horizontal movement from the origin along the x-axis is represented by the value of x, while the vertical movement along the y-axis is represented by the value of y. A helpful hint is to always put latitude (either north or south) before longitude when providing a coordinate (east or west). Degrees, minutes, and seconds are used to divide latitude and longitude.

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To make a 360mL mixture that contains 9% vinegar, use 288 mL of the first brand and 72 mL of the second brand.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand contains 13% vinegar. The chef wants to make 360 milliliters of a dressing that is 9% vinegar.

to set up an equation that will match the word problem. Let's call the amount of the first brand, F, and the amount of the second brand, S.

We want the total mixture to be 360mL so: F + S = 360

Also, you want the total mixture to contain 8% vinegar so:

.08F + .13S = .09(360)

Now, we can solve the system of equations using substitution.

F + S = 360

.08F + .13S = .09(360)

F = 360 - S      [solve 1st equation for F]

.08(360 - S) + .13S = .09(360)    [substitute into 2nd equation]

28.8 -0.08s+0.13s = 32.4

0.05s = 3.6

S = 72

F + 72 = 360     [substitute answer for S back into original equation]

F = 288

Therefore, To make a 360mL mixture that contains 9% vinegar, use 288 mL of the first brand and 72 mL of the second brand.

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Answer:

Step-by-step explanation:

2^-4=0.0625

we can divide by any number to to make an equivalent expression. (Note it is more easier when it is not a repeating decimal.)

we can do 0.0625/2= 0.03125 with this answer we can make an equivalent expression

1(0.03125+0.03125)=0.0625

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{2^{-4}}[/tex]

[tex]\mathsf{= \dfrac{1}{4 \times 4 \times 4 \times 4}}[/tex]

[tex]\mathsf{= \dfrac{1}{2^4}}[/tex]

[tex]\mathsf{= \dfrac{1}{2 \times 2 \times 2 \times 2}}[/tex]

[tex]\mathsf{= \dfrac{1}{4 \times 4}}[/tex]

[tex]\mathsf{= \dfrac{1}{16}}[/tex]

[tex]\huge\text{Therefore, your answer could possibly be: }[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{1}{16}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The numbers of a, b and c that make the equation true are given as follows:

a = 6, b = 2, c = 8.

The equation for this problem is defined as follows:

a + b = c.

The value of a is given as follows:

a = 6.

Hence:

6 + b = c.

b and c are single-digit even numbers, hence they can be obtained by trial and error as follows:

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Explanation:

The given equation y = 3x-5 is of the form y = mx+b

Parallel lines have the same slope, which means the answer also has a slope of 3.

Plug in the given point (x,y) = (-4,5) along with the slope m = 3 so we can determine the y intercept.

y = mx+b

5 = 3*(-4)+b

5 = -12+b

5+12 = b

17 = b

b = 17

We go from y = mx+b to y = 3x+17 as the final answer.

The product of 2/3 and ¾ is 6/12 that is 0.5.

To find the product of the given equation

[tex]\frac{2}{3} * \frac{3}{4} \\\\\frac{2*3}{4*3} \\\\\frac{6}{12\\}\\\\\\frac{1}{2} \\\\0.5[/tex]

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Simply the fraction to its lowest word before multiplying it. Simplify it in the case of mixed fractions. Multiply the denominator by the denominator and the numerator by the numerator once the fraction has been made simpler. The fractional product is then obtained in p/q form.

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The probability  that a student chosen at random speaks Spanish but not French is 0.66

What is probability ?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.

Given ,

At a college, 20% of students speak Spanish, 6% speak French, and 4% speak both languages.

Conditional probability

let P(I) = 0.06, P ( S & I) = 0.04 and P (S) = 0.20

Finally to find P ( S  given I )

we use the theorem

P ( S given I ) = P (S & I) / P (I)

=  0.04 / 0.06

= 4/6

= 2/3 = 0.66

Hence, The probability  that a student chosen at random speaks Spanish but not French is 0.66

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After solving the quotient (2x^3 - 3x - 10) ÷ (x - 2) is 2x^2 + 4x + 5.

In the given question, we have to find the quotient (2x^3 - 3x - 10) ÷ (x - 2).

The given expression is (2x^3 - 3x - 10) ÷ (x - 2).

We must use the synthetic division approach to determine the quotient.

By artificial division,

1) Identify the term's coefficients.

2) Decrease the initial coefficient, which is 2.

3) Putting 4 under the second coefficient 0 (2×2 = 4) now. Together, we get 4.

4) We take 4 and double it by 2, which gives us 8. Put 8 under coefficient 3 in the third place. Together, we get 5.

5) Next, divide 5 by 2. We get 10. Under the fourth coefficient, put 10. Together, we get 0.

x-2 ) 2x^3          - 3x - 10 ( 2x^2 + 4x + 5

        2x^3 - 4x^2

       -       -

      ___________

                   4x^2 - 3x

                   4x^2 - 8x

                  -       -

              ______________

                               5x - 10

                               5x - 10

                              -      -

                         ____________

                                  0

Hence, after solving the quotient (2x^3 - 3x - 10) ÷ (x - 2) is 2x^2 + 4x + 5.

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The complete question is:

What is the quotient (2x^3 - 3x - 10) ÷ (x - 2)?

The person who drink more water is Troy and he drinks 0.3 L more than Whitney

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem, we have to do the conversion of units with the given information:

Information about the problem:

By converting the unit from mL to L, we have:

1500 mL * (1 L / 1000 mL ) = 1.5 L

Comparing the volume of water that Whitney and Troy drink we have:

1.8 L > 1.5 L

Troy > Whitney

Troy drinks more water than Whitney

Calculating how much water Troy drinks more, we get:

Volume difference = Troy - Whitney

Volume difference = 1.8 L - 1.5 L

Volume difference = 0.3 L

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The height of the popcorn box is 8.75 inches.

What is the rectangular prism?

A rectangular prism is a three-dimensional geometric shape with six rectangular faces. It is also known as a rectangular cuboid, or simply a cuboid. It has three dimensions: length, width, and height. It can be represented by the formula: V = lwh where l is the length, w is the width, and h is the height.

We can use the formula for the volume of a rectangular prism to solve this problem. The formula is:

V = l * w * h

where V is the volume, l is the length, w is the width, and h is the height. We know that the volume of the box is 35 cubic inches and that the length and width are 2 inches each. So we can substitute those values into the formula and solve for h:

35 = 2 * 2 * h

To find h, we'll divide both sides of the equation by 4.

h = 35/4 = 8.75

Hence, the height of the popcorn box is 8.75 inches.

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Answer: a) 190cm³

              b) 76cm³

(refer to the image to see all the steps and workings I did related to these diagrams)

In mathematics, the system of equations is typically solved using the substitution method. In this approach.

The first step is to solve the equation for one variable and then insert the variable's value into the other equation.

x+y=20 ___ (1) and x=10 ___ (2) are given. x = 20-y is what we get from equation 1. To determine the value of y, substitute this value in equation 2. Now, substitute the value of y in equation 1, and we obtain x=15, which corresponds to x+5=20.

In algebraic expressions, substitution refers to the process of replacing the variables (letters) with their numerical values. The expression's total value can then be calculated.

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From the given shapes, The value of c and d are 4 and 6.

An region in two dimensions known as a shape is determined by a collection of lines, curves, or angles.

The locations of its points define its perimeter.

Geometric (such as a square, triangle, circle, etc.) or organic (such as free-form) shapes are both possible. Images, symbols, and designs are all made out of shapes in art and design.

According to its attributes, such as area, perimeter, and angle, forms are characterised and categorised in mathematics.

Space, such as that found in a plane or in three dimensions, can also be described by shape.

To construct things like bridges and buildings, architects and engineers use forms.

Objects and their interactions with one another are described by forms in physics.

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The value for the input when the output is −3 is 6.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given y = f(x)

and f(x) = -2/3x + 1

to find the value of x when f(x) = -3

substitute the value of f(x)

f(x) = -2/3x + 1

-3 = -2/3x + 1

-2/3x = -3 - 1

2/3x = 4

x = 4*3/2

x = 6

Hence the input is 6.

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