On the first day of summer, an ice cream shop offers a 15%
15
%
discount on all orders. Which pair of expressions represents the price of an order that was originally x
x
dollars?

Responses

0. 85x
0. 85
x
and 1−0. 15x
1
−
0. 15
x
0. 85 x and 1 − − 0. 15 x

0. 85x
0. 85
x
and x−0. 15x
x
−
0. 15
x
0. 85 x and x − − 0. 15 x

0. 15x
0. 15
x
and 1−0. 15x
1
−
0. 15
x
0. 15 x and 1 − − 0. 15 x

0. 15x
0. 15
x
and

The length of the enlargement of the cube, given the scale factor and the length, would be 12 cm.

When a shape is enlarged by a scale factor of k, all its dimensions are multiplied by k. In this case, the scale factor is 1 1/2, which can be written as 3/2 in fraction form. Therefore, the length of the enlargement is:

Length of enlargement = Scale factor x Original length

Length of enlargement = (3/2) x 8 cm

Length of enlargement = 12 cm

So, the length of the enlargement is 12 cm.

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let's recall that a year has 12 months, thus 15 months is really 15/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$9800\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{15}{12}\dotfill &\frac{5}{4} \end{cases} \\\\\\ I = (9800)(0.05)(\frac{5}{4}) \implies I = 612.5[/tex]

The equation f(x) = 0 has four complex zeros: ±2i and 1 ± √2i, each with a multiplicity of 1.

To solve the equation f(x) = 0, we need to factor the polynomial f(x) into linear factors and then find the zeros of the equation.

Step 1: Factor the polynomial f(x) into linear factors.
f(x) = x ^ 4 + 2x ^ 3 + x ^ 2 + 8x - 12
= (x^2 + 4)(x^2 - 2x + 3)

Step 2: Find the zeros of the equation by setting each factor equal to zero and solving for x.
x^2 + 4 = 0
x^2 = -4
x = ±√(-4)
x = ±2i

x^2 - 2x + 3 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
x = (-(-2) ± √((-2)^2 - 4(1)(3)))/(2(1))
x = (2 ± √(-8))/2
x = (2 ± 2√2i)/2
x = 1 ± √2i

State the multiplicity of each zero.
The zeros of the equation are ±2i and 1 ± √2i. Each zero has a multiplicity of 1.

Use the table from your calculator to find any real zeros, then use synthetic division to find the remaining zeros.
There are no real zeros in this equation, as all of the zeros are complex numbers. Therefore, there is no need to use the table from the calculator or synthetic division to find the remaining zeros.

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(a) The proportion of observations in a standard normal distribution that satisfies z > -1.66 is 0.0475, or approximately 4.75%.

(b) The proportion of observations in a standard normal distribution that satisfies -1.66 < z < 1.66 is 0.9050, or approximately 90.50%.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

To find the proportion of observations in a standard normal distribution that satisfies each of the statements, we need to use a standard normal distribution table or calculator.

(a) z > -1.66

We need to find the area to the right of z = -1.66 on a standard normal distribution table or calculator. This is equivalent to finding the area to the left of z = 1.66 since the standard normal distribution is symmetrical.

Using a standard normal distribution table or calculator, we find that the area to the left of z = 1.66 is 0.9525. Therefore, the area to the right of z = -1.66 is:

1 - 0.9525 = 0.0475

So, the proportion of observations in a standard normal distribution that satisfies z > -1.66 is 0.0475, or approximately 4.75%.

(b) -1.66 < z < 1.66

We need to find the area between z = -1.66 and z = 1.66 on a standard normal distribution table or calculator.

Using a standard normal distribution table or calculator, we find that the area to the left of z = 1.66 is 0.9525 and the area to the left of z = -1.66 is 0.0475 (as calculated in part (a)). Therefore, the area between z = -1.66 and z = 1.66 is:

0.9525 - 0.0475 = 0.9050

Therefore, the proportion of observations in a standard normal distribution that satisfies -1.66 < z < 1.66 is 0.9050, or approximately 90.50%.

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Using the unitary method we found that the actual distance between Snohomish to Seattle is 32 miles.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. We typically utilise this technique for maths computations. This method allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

Given,

The measured distance from Snohomish to Seattle on a road map = 3.2 inches

The scale of the map is given as:

  1 inch = 10 miles

The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. The use of scale is necessary for generating an accurate map and makes it simple to establish the real size of any area on the map.

The actual distance can be found using the unitary method.

So it is given 1 inch on the map = 10 miles on the road

Then 3.2 inches on the map = 10 * 3.2 = 32 miles on the road

Therefore using the unitary method we found that the actual distance between Snohomish to Seattle is 32 miles.

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Shiro purchased 11 pounds of beef and 4 pounds of chicken.

Shiro purchased a total of 18 pounds of meat, spending $96.

We can designate the beef as x pounds, and the chicken as y pounds. To find the solution, we set up two equations:

6x + 4.5y = 96 x + y = 18

To solve this system of equations, we can subtract 6x from both sides of the first equation, giving us 4.5y = 96 - 6x.

We can substitute this expression into the second equation, giving us x + (96 - 6x) = 18.

We can then simplify this equation, giving us 7x = 78, and thus x = 11.

Now we can substitute x = 11 into the original equation, 6x + 4.5y = 96, to find y = 4.

Therefore, Shiro purchased 11 pounds of beef and 4 pounds of chicken.

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Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:)

Bonjour !

Il faut isoler x.

3x + 4 = 2x + 9

3x - 2x = 9 - 4

x = 5

To find the missing quantity, we will plug in the given values into the formula for simple interest and solve for the unknown variable. The formula for simple interest is I = Pxrxt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Given:
P = $4000
r = 8% = 0.08
t = 3 years

Plugging in the given values into the formula, we get:

I = $4000 x 0.08 x 3

Simplifying the equation, we get:

I = $960

Therefore, the missing quantity is the interest, I, which is equal to $960.

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The x-values that R(x) cannot be are -1, -2, 2, 3, 10, and 1.

R(x) cannot be at x=-1, -2, 2, 3 because these are the values of the function at these points. Additionally, R(x) cannot be at x=10 and x=1 because these are the holes of the function. Therefore, the x-values that R(x) cannot be are -1, -2, 2, 3, 10, and 1.

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Points A and Q are connected by a line. To get the length of AR, measure the distance between A and Q and multiply that value by k. To find point R, mark off the length of AR along a ray that extends from point A in the direction of Q.

In mathematics, a ray is a segment of a line with a known starting point but no known endpoint. It can go on forever in that one direction. A beam cannot be measured since it lacks a terminal. fun facts A ray is similar to the sun's rays.

In geometry, a ray is a line that, starting from a single terminal, extends indefinitely in one direction (or point of origin). A ray is represented by a beam of sunlight travelling across space; while the sun is the ray's goal, it continues to travel forever.

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Complete question -

The rule for the function g(x) when completed is g(x) = -10, -15 ≤ x < -10; g(x) = -8, -10 ≤ x < -8; g(x) = -6, -8 ≤ x < -1; g(x) = 2, -1 ≤ x < 1; g(x) = 4, 1 ≤ x < 10; g(x) = 8, 10 ≤ x < 15

Given

The graph of the function g(x) such that the function g(x) is a piecewise function and each sub-function is represented by horizontal lines

To complete the function definition, we write out the y value and the domain of the functions based on the current domain

Following the above statements, we have the following function definition for g(x)

g(x) = -10, -15 ≤ x < -10

g(x) = -8, -10 ≤ x < -8

g(x) = -6, -8 ≤ x < -1

g(x) = 2, -1 ≤ x < 1

g(x) = 4, 1 ≤ x < 10

g(x) = 8, 10 ≤ x < 15

The above is the definition of the function g(x)

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The probability of rolling a triangle is 50%

From the question, we have the following parameters that can be used in our computation:

Sides = 12

triangles = 6

Circles = 3

Squares = 3

The die has a total of 6 + 3 + 3 = 12 sides.

Since there are 6 triangles on the die, the probability of rolling a triangle is:

P(triangle) = number of favorable outcomes / total number of outcomes

Substitute the known values in the above equation, so, we have the following representation

P(triangle) = 6 / 12

Evaluate

P(triangle) = 50%

Hence, the probability of rolling a triangle on the die is 1/2 or 0.5.

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a. For A2 = 0, it is proved that  (I - A)-1 = I + A.

b.  For A3 = 0, (I - A)-1 = I + A + A2.

a. If A2 = 0, then  (I - A)-1 = I + A

Proof:

(I - A)-1 = (I + A)-1

(I + A)-1 = (I + A)(I - A)-1

(I + A)(I - A)-1 = I + A

Therefore, (I - A)-1 = I + A

b. If A3 = 0 then  (I - A)-1 = I + A + A2

Proof:

(I - A)-1 = (I + A + A2)-1

(I + A + A2)-1 = (I + A + A2)(I - A)-1

(I + A + A2)(I - A)-1 = I + A + A2

Therefore, (I - A)-1 = I + A + A2

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Answer:

True both each.

Step-by-step explanation:

Your teacher would probably like you to remember the Trig Identities or allow you to have a cheat sheet for the Quiz or Test.

[tex]\frac{sin(\alpha )}{sin^{2}(\alpha) +cos2\alpha } \\\\\frac{sin(\alpha )}{sin^{2}(\alpha) +[cosx^{2} (\alpha)-sinx^{2} (\alpha )]} \\\\\frac{sin(\alpha )}{sin^{2}(\alpha) +cosx^{2} (\alpha)-sinx^{2} (\alpha )}\\\\\frac{sin(\alpha )}{[sin^{2}(\alpha) +cosx^{2} (\alpha)]-sinx^{2} (\alpha )}[/tex]

[tex]\frac{sin(\alpha )}{1-sinx^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos(\alpha )*cos(\alpha )}\\\\\frac{sin(\alpha )}{cos(\alpha )}*\frac{1}{cos(\alpha )} \\\\tan(\alpha )*sec(\alpha )\\\\\frac{1}{cot(\alpha )}*sec(\alpha )\\\\\frac{sec(\alpha )}{cot(\alpha )}[/tex]

The result of this synthetic division is the quotient (1 2/3 5/3)

To divide two polynomials using synthetic division, we need to write the dividend as a binomial of the form (x-r) and the divisor in its linear form. In this case, the binomial is (x+2) and the linear form is 3x2+7x+2.

Quotient:
3/3=1

2/3=2/3

Coefficients of dividend: 3 7 2

Quotient: 1 2/3

Product of quotient and binomial: (x+2)

(3x2+7x+2) - (x+2): 3x+5 2

Quotient:
3/3=1

2/3=2/3

5/3=5/3

The result of this synthetic division is the quotient (1 2/3 5/3).

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Answer: To find the number of stamps on each page, we can divide the total number of stamps by the number of pages:

263 stamps ÷ 9 pages = 29.22 stamps per page (rounded to two decimal places)

Since we want to place the same number of stamps on each page with as few left over as possible, we can round down to the nearest whole number:

29 stamps per page

To find out how many stamps were left to put in an envelope, we can multiply the number of pages by the number of stamps per page, and then subtract from the total number of stamps:

263 stamps - (29 stamps per page x 9 pages) = 8 stamps left over to put in an envelope

Therefore, the completed sentences are:

29 stamps were placed on each page.

8 stamps were put in an envelope.

Step-by-step explanation:

The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²

Surface area is the total area that the surface of an object occupies. It is a measure of how much area is covered by the exterior of an object. The formula for the surface area of a cylinder is:

Where r = radius of the base and h = height of the cylinder.

Here we have

Diameter of the cylinder = 2.8 cm

Radius of the cylinder = 2.8/2 = 1.4 cm

Height of the cylinder = 3.7 cm  

Using the formula,

The surface area of a cylinder SA= 2πr² + 2πrh

The surface area of the cylinder

= 2π(1.4)² + 2π(1.4)(3.7)

= 2π(1.4)² + 2.8π(3.7)

Here, the total surface area of the cylinder will equal the amount of wrapping paper needed to completely cover the cylinder

Therefore,

The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²

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hi i think its A. SA = 2π(1.4)2 + 2.8π(3.7) hope this helped have a nice day! :)

x = 23°

4) To find the value of Angle B, we can use the alternate interior angles theorem, which states that if two parallel lines are cut by a transversal, the alternate interior angles are equal. In this case, we can say that ∟AB=∟CD, since ABCD is a parallelogram. Therefore, we can set 6x-15 = 4x-11 and solve for x to get x = 4. Plugging this back in, we can find that ∟AB = 6(4)-15 = 15°.

5) To find the value of Angle R, we can use the same method as above. We can set ∟QR=∟PS, since PQRS is a parallelogram. Therefore, we can set 8x-12 = 3x+5 and solve for x to get x = 7. Plugging this back in, we can find that ∟QR = 8(7)-12 = 56°.

7) To find the measure of x, we can use the fact that the quadrilateral is a rhombus. A rhombus is a quadrilateral with all four sides equal in length, so we can say that ∟AB = ∟CD. Therefore, we can set 23=x and solve for x to get x = 23°.

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The fraction when a 100-square grid has 70 shaded squares will be 7/10.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, a 100-square grid has 70 shaded squares.

The fraction will be:

= Number it shaded square / Total square

= 70 / 100

= 7 / 10

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A 100-square grid has 70 shaded squares. Explain how you could express this model as a fraction.

Answer:

The fraction when a 100-square grid has 70 shaded squares will be 7/10.

Lowering interest rate by a government's central bank can have a significant impact on the economy, as it affects the cost of borrowing money for businesses and individuals, as well as the return on savings and investments.

Lowering interest rate reduces the cost of borrowing money, making it easier for businesses and individuals to access credit. It can also encourage consumers to spend more money, as they may have more disposable income due to lower borrowing costs or higher investment returns.

It can also lead to increased inflation, as businesses and individuals have more money to spend and demand for goods and services increases and reduced returns on savings and investments, which can discourage people from saving and lead to more spending

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The following are the correct convertion for the units of mass:

8000 mg converted to gram is 8 g

80 g converted to kilogram is 0.08 kg

0.8 kg converted to g is 800 g.

Gram (g) is the base unit of mass in the metric system. The milligrams (mg) and kilograms (kg) are derived units.

1 gram = 1000 milligrams (mg)

1000 grams = 1 kilogram (kg)

8000 mg = (8000/1000) g

8000 mg = 8 g

80 g = (80/1000) kg

80 g = 0.08 kg

0.8 kg = (0.8 × 1000) g

0.8 kg = 800 g.

In conclusion, 8000 mg converted to gram is 8 g, 80 g converted to kilogram is 0.08 kg, and 0.8 kg converted to g is 800 g.

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The value of the expression −16 + 12 is −4.  

Subtraction is a basic arithmetic operation that involves finding the difference between two numbers. It is denoted by the minus sign (-) and is performed by subtracting the second number from the first number.

We can subtract fractions, decimals, and negative numbers by following the same principles of subtraction.

Here we have

The numerical expression −16 + 12    

As we know

12 is 4 greater than 16 and 16 has a negative sign

Therefore,

The value of the expression −16 + 12 is −4.  

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Answer:

7.55

Step-by-step explanation:

3.50 + x = 11.05, x = 11.05 - 3.50, x = 7.55

Answer:

Step-by-step explanation:

Let [tex]x[/tex] be the cost of a juice bottle. Then

[tex]3.50+5x=11.05[/tex]

Solve this:

[tex]5x=7.55[/tex]   (subtracted 3.50 from both sides)

[tex]x=7.55/5=1.51[/tex]  (divided both sides by 5)

So juice bottles cost $1.51

The right rectangular prism's longest line segment measures around 14.79 cm in length.

We are aware that the rectangular prism's body diagonal makes up the longest line segment inside a right rectangular prism. The longest distance is that between points A and D. AD is the longest line segment as a result. To determine a line segment's length, use a scale. Straight line segments can be measured with it.

The Pythagorean theorem can be used to determine how long the space diagonal is:

a = length = 12.6 cm

b = width = 3.2 cm

c = height = 7 cm

You may determine the space diagonal (d) by using:

d = sqrt(a² + b² + c²)

Substituting the values, we get:

d = sqrt(12.6² + 3.2² + 7²) cm

d = sqrt(159.76 + 10.24 + 49) cm

d = sqrt(219) cm

d ≈ 14.79 cm

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Question:

What is the measurement of the longest line segment in a right rectangular prism that is 12.6 centimeters long, 3.2 centimeters wide, and 7 centimeters tall, and that connects two vertices that are not on the same face of the prism?

The length of the rectangular prism is 13 centimetres.

The volume of a rectangular prism is 208 cm³. The area of one end is 16 cm². The length of the rectangular prism can be found as follows:

Therefore,

volume of a rectangular prism = lwh

where

Hence, let's find the length

volume of a rectangular prism = lwh

208 = 16 × l

16l = 208

divide both sides by 16

l = 208 / 16

l = 13 cm

Therefore,

length of the prism = 13 cm

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Answer: 0.875 h or for a fraction 8 3/4

Step-by-step explanation:

June spent 15 minutes practicing her piano, 30 minutes cleaning her room and 7.5 minutes putting away her dirty laundry so a total of 52.5 minutes

Answer:

8 3/4

Step-by-step explanation: IK IM SORRY im sooo confusing!! And it makes me frustrated too...

The identity cos²θ/2 is (1 + cosθ)/2

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can use the half-angle identity for the cosine function to solve this problem:

cos²θ/2 = (1 + cosθ)/2

Therefore, to find cos²θ/2 , we need to know the value of cosθ.

If the value of cosθ is known, we can substitute it into the half-angle identity to find cos²θ/2

Hence, the identity cos²θ/2 is (1 + cosθ)/2

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The size of angle ACB is approximately 50.66°.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

We are given that;

Angle ABC= Angle ACD + 31°

Now,

Since angle ABC is twice angle BAC, we can write:

angle BAC = x

angle ABC = 2x

angle ACB = 180° - (angle BAC + angle ABC)

Substituting these values into the equation for angle ACD, we get:

angle ACD = angle ABC + 31° = 2x + 31°

Since angles ACB and ACD form a straight line, we can write:

angle ACB + angle ACD = 180°

Substituting the values we know, we get:

(angle BAC + angle ABC) + (angle ABC + 31°) = 180°

3x + 31° = 180°

3x = 149°

x = 49.67°

Therefore, the angle of triangles answer will be 50.66°.

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The equation of the line with slope -(2)/(3) passing through the point (3, 4) is y = -(2)/(3)x + 6. To find the equation of a line that passes through a given point with a given slope, we can use the point-slope formula. The point-slope formula is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point that the line passes through. In this case, the slope is -(2)/(3) and the point is (3, 4).

Plugging these values into the point-slope formula, we get:

y - 4 = -(2)/(3)(x - 3)

We can then rearrange the equation to get it into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:

y - 4 = -(2)/(3)x + 2
y = -(2)/(3)x + 6

So, the equation of the line with slope -(2)/(3) passing through the point (3, 4) is y = -(2)/(3)x + 6.

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