x(z ÷ 3)^2 where x = 4 and z = 9 calculate

Step-by-step explanation:

If your age is ' a ' then your max heart rate = 220 - a

The total number of t-shirts principal ordered in $1520 for the school store is given 214.

Let us consider the number of t-shirts the principal ordered be equal to 'x'.

The cost of each t-shirt is equal to $7.

⇒ The total cost of 'x' t-shirts =  7x dollars.

Shipping cost is a flat rate for any order, regardless of the number of t-shirts =  $22

Total cost of the order (including shipping) =  $1520.

Required equation is equal to,

7x + 22 = 1520

Subtract 22 from both sides of the equation we get,

⇒ 7x = 1498

Divide both sides of the equation by 7 we get,

⇒ x = 214

Therefore, the number of t-shirts ordered by  principal for the school store is equal to  214.

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Answer:

a two-dimension surface formed by two number lines.

Answer: x 3= 27/125

Step-by-step explanation:

The length of the long diagonal of the cube is 3sqrt(3) inches.

Let's denote the length of one side of the cube as "a". Then the cube has a volume of a^3, a surface area of 6a^2 (since a cube has 6 faces with side length a), and a total edge length of 12a (since each face has 4 edges of length a).

Using the given equation, we can write

a^3 + 3(12a) = 2(6a^2)

Simplifying this equation, we get

a^3 + 36a = 12a^2

a^3 - 12a^2 + 36a = 0

a(a^2 - 12a + 36) = 0

a(a - 6)^2 = 0

The only positive solution for "a" is a = 6 (since a cannot be zero or negative). Therefore, the cube has a side length of 6 inches.

To find the length of the long diagonal of the cube, we can use the Pythagorean theorem. The long diagonal passes through the center of the cube and connects two opposite corners. The distance from the center to a corner is half the length of the long diagonal. Let's call this distance "d".

Using the Pythagorean theorem, we can write

d^2 = (6/2)^2 + (6/2)^2 + (6/2)^2

d^2 = 3(6^2)/4

d = (sqrt(3)×6)/2

d = 3sqrt(3) inches

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The total students who are going on the field trip are 320 students out of 400 students which has been obtained by using the concept of fractions.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

If 4 out of 5 students are going on the field trip, then the fraction of students going on the field trip is 4/5.

To find out how many students are going on the field trip, we can multiply this fraction by the total number of students:

Number of students going on the field trip = (4/5) x 400

Number of students going on the field trip = 320

Therefore, 320 students are going on the field trip.

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We may conclude after answering the presented question that rectangle Therefore, the expression for the width of the porch is x + 2 feet.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

area of a rectangle

Area = length x width

To do this, we can factor the expression for the area, which gives us:

x² + 9x + 14 = (x + 2)(x + 7)

Area = length x width

(x + 2)(x + 7) = (x + 7) x width

x + 2 = width

Therefore, the expression for the width of the porch is x + 2 feet.

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To measure central tendencies in the data collected from the Consumer Price Index (CPI), the dental director should use measures of central tendency, such as the mean, median, and mode.

The mean is the average of a set of numbers and is calculated by adding all the numbers together and then dividing by the total number of numbers. The median is the middle number when the numbers are placed in order from least to greatest. The mode is the number that appears most often in a set of numbers.

Using these measures of central tendency will allow the dental director to gain a better understanding of the CPI data, as they will be able to identify the center point of the data and also see how frequently particular values appear. This can help in making informed decisions about policies and other changes.

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Answer:

1. irrational

2. irrational

3. rational

4. rational

5. irrational

6. rational

Step-by-step explanation:

A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction.

1.) pi is a never ending number which means that, according to the definition above, it must be IRRATIONAL

2.) the line above the 46 means that it is repeating, making it IRRATIONAL

3.) the square root of 100 is 10, making it RATIONAL

4.) -16 is an integer (a whole number that can be positive, negative, or zero), making it RATIONAL

5.) the square root of 21 results in a long decimal that cannot be converted into a fraction, by the definition above, it is IRRATIONAL

6.) 10 is a whole number, making it RATIONAL

The function f a. f(0) represents the bonds after 0 years. That is the immediate value of bond in dollars at 0 year. b. f(4.5) represents the value of the bond 4.5 years later.

A function in mathematics is a rule that designates a certain output value for each input value. Each input from the domain has precisely one output in the range, forming a relationship between two sets known as the domain and the range. The letter f(x), where x is the input variable and f(x) is the output variable, is a common way to represent a function. The output variable is specified by the function's rule, but the input variable can accept any value from the function's domain.

For the given graph of the function:

a. f(0) represents the bonds after 0 years. That is the immediate value of bond in dollars at 0 year.

b. f(4.5) represents the value of the bond 4.5 years later.

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Answer:

C

Step-by-step explanation:

The red graph is obtained by shifting the graph of f(x) = 4 - x² upwards by some amount. We can see that the highest point on the red graph occurs at x = 0, where the value is 4.

To shift the graph of f(x) upwards by 3 units, we can add 3 to the entire function:

f(x) + 3 = 4 - x² + 3

= 7 - x²

So the equation of the red graph is:

g(x) = 7 - x²

Therefore, the correct answer is option C: g(x) = 7 - x².

The equation of the quadratic function that passes through these points is:

[tex]y = -3x^2 - 12x - 8.[/tex]

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, which means it contains one variable with an exponent of 2. The general form of a quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

Using polynomial interpolation with these 5 points, we can find a quadratic polynomial that passes through all the points. Let the equation of the polynomial be [tex]y = ax^2 + bx + c[/tex].

Using the point (0, -8), we get:

[tex]-8 = a(0)^2 + b(0) + c[/tex]

c = -8

Using the point (-1, 1), we get:

[tex]1 = a(-1)^2 + b(-1) - 8[/tex]

a - b = 9

Using the point (-3, 1), we get:

[tex]1 = a(-3)^2 + b(-3) - 8[/tex]

9a - 3b = 27

Using the point (-4, -8), we get:

[tex]-8 = a(-4)^2 + b(-4) - 8[/tex]

16a - 4b = 0

Using the point (-2, 4), we get:

[tex]4 = a(-2)^2 + b(-2) - 8[/tex]

4a - 2b = 12

Solving this system of equations, we get:

a = -3

b = -12

c = -8

Therefore, the equation of the quadratic function that passes through these points is:

[tex]y = -3x^2 - 12x - 8.[/tex]

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Answer:  3

Step-by-ste3p explanation:

when some syrup from a bottle was poured into the container, it got half full. The volume of the syrup poured from the bottle into the container in millimeters is 576,000 cubic millimeters.

Since for solving the problem we need to find the volume of the container in millimeters. We are given the length, breadth, and height which are 12 cm,8 cm, and  36 cm.Now the volume of the container is:

V = l x w x h = 12 cm x 8 cm x 36 cm = 3,456 cubic cm. Now  we convert the above result  into millimeters by  multiplying by 1,000, so we get V= 3456 x 1000= 34560000 cubic mm

Now to find the volume of the syrup that was poured into the container,  we know that the container was one-third full before the syrup was added and half full after the syrup was added.onsidering x to be the volume of the syrup poured from the bottle into a container and n to be the volume of the syrup in the container after it was added:

1/3(V) + x = 1/2(V), where v is the  volume of the container in millimeters, so we substitute the calculated value of the volume we get :

=>1/3(V) + x = 1/2(V)

=>x = 1/2(V) - 1/3(V)

=> x = 1/6(V) = 1/6(3,456,000)  = 576,000 cubic mm

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Answer:

Step-by-step explanation:

To find out how much more fabric is required for the chair than the footstool, we need to subtract the amount of fabric required for the footstool from the amount of fabric required for the chair.

The amount of fabric required for the chair is 5/7 of a yard.

The amount of fabric required for the footstool is 2/3 of a yard.

So to find the difference, we need to subtract:

5/7 - 2/3

To do this, we need to find a common denominator, which is 21 in this case. We get:

(15/21) - (14/21) = 1/21

Therefore, Aron needs 1/21 more yard of fabric to cover the chair than the footstool.

By using circumference of circle, we find that In one slice of pizza you will get about 8 olive pieces from Mario's Pizzeria.

The circumference of circle of a 20-inch diameter pizza can be calculated as follows:

Circumference = π × diameter

Circumference = 3.14 × 20

Circumference = 62.8 inches

If there is at least one olive piece per inch of crust, then there will be 62.8 olive pieces on the outer crust of the entire pizza.

If the pizza is cut into eight slices, each slice will have 1/8th of the total circumference of the pizza. Therefore, each slice will have:

62.8 inches ÷ 8 slices = 7.85 inches of outer crust

Since there is at least one olive piece per inch of crust, each slice will have approximately 8 olive pieces on the outer crust.

Therefore, you can expect to get about 8 olive pieces in one slice of pizza from Mario's Pizzeria.

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When the equilibrium point is above the potential GDP line, the economy is experiencing inflationary pressure.

In the AD/AS model, whether the economy is in a recession is illustrated by how close the equilibrium is to the potential GDP line. The potential GDP line represents the maximum level of output that an economy can produce with its existing resources and technology.What is the AD/AS model?The AD/AS model is a graphical representation of the macroeconomic relationship between aggregate demand (AD) and aggregate supply (AS). This model is used to explain the behavior of the economy by demonstrating how changes in the level of aggregate demand and aggregate supply can impact the economy's level of output and prices.

The model's AD curve represents the total demand for all goods and services in an economy at different price levels. The AS curve represents the total supply of all goods and services in the economy at different price levels.

The intersection of the AD and AS curves represents the equilibrium point where the economy's output level and price level are determined. The economy is in a recession when the equilibrium point is below the potential GDP line.

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Johnny has 1258 more pineapples than Bobby.

Bobby has 37 pineapples, Johnny has 35 times more pineapples than Bobby. To find how many more pineapples does Johnny have than Bobby, we can use the below formula,

More pineapples = Johnny's pineapples - Bobby's pineapples

Let x be the number of pineapples that Bobby has. Therefore, the number of pineapples owned by Johnny is 35x.

It is given that Bobby originally has 37 pineapples, thus x = 37. The number of pineapples Johnny has = 35*37 = 1295

Thus, difference in number of pineapples between Johnny and Bobby:

=1295-37 = 1258

Therefore, Johnny has 1258 more pineapples than Bobby.

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The corrected version has a base of 0.7, representing exponential decay, and has the function[tex]y = a(1-r)x[/tex] as [tex]y = 2.55(0.7)x[/tex] with a [tex]0.3[/tex] decay factor.

Explain function?

A function is a link or statement that contains one or more values. Both inputs and outputs are numerous. With each input, there is only one output. The links between the inputs and the results are described by the function.

The error the student made is in Step 2 where they incorrectly wrote the function in the form [tex]y = a(1-r)*.[/tex]The correct form for exponential decay is [tex]y = a(1-r)^x[/tex], where x is the number of time periods. So, the correct equation for the given function is [tex]y = 2.55(0.7)^x.[/tex]

To find the decay factor, the student should have subtracted the base from 1, instead of multiplying it by -1. Therefore, the correct decay factor is [tex]1 - 0.7 = 0.3.[/tex]

So, the corrected version of the solution is:

Step 1: As the function's base is[tex]0.7[/tex], it simulates exponential decay.

Step 2: The function in the form [tex]y = a(1-r)^x is y = 2.55(0.7)^x.[/tex]

Step 3: The decay factor is [tex]0.3.[/tex]

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Answer: d

Step-by-step explanation:

the slope is positive 200 because she is gaining 200 points for every minute which is x. 200x or 200 multiplied by x is her slope and her y intercept is 3200

The surface area of the cylinder is approximately 127.17 cm².

Surface area of cylinder is the total space covered by the flat surfaces of the bases of the cylinder and its curved surface. The formula for the surface area of a cylinder is: 2πr² + 2πrh.

To solve this problem, we first need to find the radius of the cylinder. The diameter of the cylinder is 3 cm, so the radius is half of that:

r = 3/2

= 1.5 cm

We need to substitute the values we know into the formula for surface area:

= 2π(1.5)² + 2π(1.5)(12)

= 2π(2.25) + 2π(18)

= 4.5π + 36π

= 40.5π

We will now approximate the value of π to get the numerical answer, so, our Surface Area will be:

= 40.5π

= 40.5 * π

= 40.5 * 3.14

≈ 127.17 cm²

Answered question "A cylinder is 12 cm tall and has a diameter of 3 cm. What is the surface area?"

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According to the information provided, k and m are crossing lines with an angle of 86°. We know this because k and m are straight lines.

The angles add up to 180 degrees.

Then we receive,

[tex]a + 86 =180[/tex]

Or, a = 180 -86

Or, a = 94°.

As a result, an is 94°.

The angle an is 94 degrees.

Supplementary angle are formed when two angles add to 180 degrees. When additional angles are added together, they form a straight angle, or 180 degrees. In these other words, if indeed the sum of angles 1 and 2 equals 180 degrees, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" to one another in this context.

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Answer:

157 pounds I'm pretty sure the equation would be 1.65c=p

Step-by-step explanation:

p is 1 because no given varible since p=1 pound 1.65 would equal p they 157 pounds bc 260.10/1.65 gives you 157 rounded

The total area of the composite figure is 114.25 square feet.

The area of a circle of diameter D is:

A = 3.14*(D/2)²

And the area of a triangle of base B and height H is:

A = B*H/2

We can decompose the figure into two simpler ones, a triangle of base of 10ft and height of 15 ft, whose area is:

A = 10ft*15ft/2 = 75ft²

And half of a circle of diameter of 10ft, whose area is:

A = 0.5*3.14*(10ft/2)² = 39.25 ft²

Then the total area of the figure is:

area =  75ft² + 39.25 ft² = 114.25 ft²

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Answer:

Step-by-step explanation:

EZ

its 21

The sample proportion would be 0.5.we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.

To determine what sample proportion would yield a p-value of 0.05, we must first understand the formula for calculating a p-value. The formula for a p-value is p-value = 1 - [tex](1 - proportion)^n[/tex], where n is the sample size. By manipulating this equation, we can solve for the proportion when the p-value is equal to 0.05. We can isolate the proportion by taking the inverse of both sides of the equation, which yields: proportion = 1 - [tex](1 - 0.05)^(1/n)[/tex]. Since the sample size is 90, we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.

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The vertical distance between (2, 11/3) and (2, -4/3) is -5 units.

The distance formula is a mathematical equation used to find the distance between two points in a plane. It is derived from the Pythagorean theorem and is expressed as:

d = √((x₂- x₁)²+ (y₂ - y₁)²)

The distance formula can also be extended to three-dimensional space by adding an additional term to the equation.

The two points (2, 11/3) and (2, -4/3) have the same x-coordinate, which means they lie on a vertical line. To find the vertical distance between these two points, we simply subtract their y-coordinates:

Vertical distance = (y-coordinate of second point) - (y-coordinate of first point)

= (-4/3) - (11/3)

= -15/3

= -5

Therefore, the vertical distance between (2, 11/3) and (2, -4/3) is -5 units. Since this is a negative value, it means that the second point is located 5 units below the first point.

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This shows that they read less frequently than 95.7% of their classmates in the same grade level.

In statistics, a percentile is a metric that is used to express where one observation stands in relation to a larger group of data. It displays the proportion of data points that fall under a given value. For instance, if a student achieves a score in the 90th percentile on a standardised test, it signifies that they outperformed 90% of their peers who also took the test. As an alternative, if a child is taller than 25% of children their age and shorter than 75%, their height is in the 25th percentile for their age.

given

We must first compute the z-score using the following formula to determine the percentile of the child's reading proficiency.

z = (x - μ) / σ

where x represents the child's reading rate, represents the grade-level mean reading rate, and represents the standard deviation.

Inputting the values provided yields:

z = (46.2 - 85) / 22

z = -1.727

We can calculate or use a conventional normal distribution table to obtain the value of 0.0428 for the region to the left of z = -1.727. The child's reading rate is at the 4.28th percentile according to this statistic.

As a result, the child's reading proficiency is 4.3 percentile (rounded to one decimal place).

This shows that they read less frequently than 95.7% of their classmates in the same grade level.

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Answer:

Step-by-step explanation:

Your equation is 0.75L +  0.5L + x = 2L
x = Orange juice

0.75L + 0.5L = 1.25L
2L - 1.25L = 0.75L

[tex]\frac{0.75L}{2L}[/tex] is your fraction
[tex]\frac{75}{200}[/tex]  simplified is [tex]\frac{3}{8}[/tex]
I hope this helped,

Step-by-step explanation:

For Part A, use the function f(x) to find the average of tests taken.

X is number of test taken

f(x) is the average score given said num of tests taken,x,

We want after test number 3 so using the function,

[tex]f(x) = 0.2x + 79[/tex]

Plug in. 3 for x, and we will get our answer.

[tex]f(3) = 0.2(3) + 79 = 79.6[/tex]

Part B: Use the table for the answer.

When 2 test are taken, the average test score is

84

So part B is 84.

Part C:

[tex]f(2) = 0.2(2) + 79 = 79.4[/tex]

[tex]g(2) = 84[/tex]

Since

[tex]g(2) > f(2)[/tex]

The science class had a higher average after 2 tests

Answer:

you shoulda payed attention in class

Step-by-step explanation:

also u know it's bad when the test is so hard you can't even cheat on it