A pizza shop sells large pizzas for $10 plus $0.75 per topping. It also sells medium pizzas for $8 plus $1.25 per topping. A family orders one large pizza and one medium pizza. If they ordered the same number of toppings for each pizza and the two pizzas cost the same, how many toppings did they order?

Answer:

logarithmic & absolute

No option given is a correct option completely.

Various functions have been given in the question.

We have to find which of them do not have an x-intercept.

What is the process to find the x-intercept ?

To find x-intercept , set y = 0 and solve for x.

Let us discuss each parent function one by one:

1. Quadratic:

y = \(x^{2}\)

When we put x = 0, we get y = 0

Therefore, it has intercept at (0, 0).

2. Absolute Value:

y = |x|

When we put x = 0, we get y = 0

Therefore, it has intercept at (0, 0).

3. Rational:

y = \(\frac{1}{x}\)

When we put x = 0 , we get y = 0

Therefore, it doesn't have intercept at (0, 0).

4. Exponential:

y = \(b^{x}\)

b is any base

When we put x = 0 , we doesn't get y =0

Therefore, it doesn't have intercept at (0, 0).

5 . Logarithmic:

y = log (x)

When we put x = 0 , we get y = Not defined

Therefore, it doesn't have intercept at (0, 0).

6. Square root :

y = √ x

When we put x = 0 , we get y = 0

Therefore, it has intercept at (0, 0).

Thus , none of the options are perfectly correct.

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Step-by-step explanation:

sides of 2 triangles are proportional

x/12=28/21

x=16

=======================================================

Explanation:

The diagonal pieces are 28 and 21. They pair up to get the fraction 28/21

The horizontal pieces are x and 12, in the same order from left to right. The order is important (so things pair up properly). We get the fraction x/12

-------

Set the two fractions equal to each other and solve for x

28/21 = x/12

28*12 = 21*x .... cross multiply

336 = 21x

21x = 336

x = 336/21 .... divide both sides by 21

x = 16

In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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The length of the shorter leg of the triangle ABC is approximately 24.49 units. Let's denote the right triangle ABC, where C is the right angle.

Let D be the midpoint of AB, and E be the foot of the altitude from C to AB. Then we have:

CD = 1/2 AB (definition of median)

CE = 12 (given altitude to the hypotenuse)

Let x be the length of the shorter leg of the triangle ABC. Then we have:

AE = x (definition of altitude)

EB = AB - x (definition of complementary leg)

By the Pythagorean theorem, we have:

AC^2 = AB^2 + BC^2

(2CD)^2 = AB^2 + x^2

AB^2 = 4CD^2 - x^2

By the similarity of triangles AEC and ABC, we have:

CE/AC = AE/AB

12 / (AB + BC) = x / AB

AB = x / (12/x + 1)

Substituting AB into the previous equation, we get:

4CD^2 - x^2 = x^2 / (12/x + 1)^2

Simplifying and solving for x, we get:

x^4 - 576x^2 - 14400 = 0

This is a quadratic equation in x^2, so we can solve for it using the quadratic formula:

x^2 = [576 ± sqrt(576^2 + 4*14400)] / 2

x^2 = [576 ± 624] / 2

Since x is a length, we take the positive square root:

x^2 = 600

x ≈ 24.49

Therefore, the length of the shorter leg of the triangle ABC is approximately 24.49 units.

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Answer:

a

Step-by-step explanation:

plato

Security deposit is paid in advance to protect landlords against nonpayment.

percentage, a relative value indicating hundredth parts of any quantity.

A security deposit is a sum of money paid by a tenant to a landlord or property manager before moving in, with the purpose of protecting the landlord in case the tenant does not fulfill their obligations under the lease agreement, such as not paying rent, damaging the property or leaving it unclean at the end of the lease.

The amount of the security deposit is usually equal to one or two months' rent, and it is refundable at the end of the lease term, provided that the tenant has complied with all the terms of the lease.

If the tenant has breached the lease agreement, the landlord may use the security deposit to cover the unpaid rent or any damages caused by the tenant.

Hence, Security deposit is paid in advance to protect landlords against nonpayment.

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The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

-1

Step-by-step explanation:

Slope formula: (y₂ - y₁) / (x₂ - x₁)

= (2 - 1) / (1 - 2)

= -1

The answer is $112.70  The Question is a simple Sales tax rate calculating problem.

Multiplying the purchase price by the sales tax rate will provide the sales tax. Don't forget to round the sales tax rate from percent to decimal. The price of the purchase is increased after the sales tax has been calculated. The entire cost is what the client pays as a result.

Sales tax rate = Sales tax percent / 100.

Sales tax = List price x Sales tax rate.

Given,

Rate of sandwich is = $4. 00

Rate of drink is = 94$

The rate of a meal that Her grandson ordered is =$6. 35.

What was the total price of all three items when 8% sales tax was added?

Total price of all three items without tax = 4 + 94 + 6.35

= $104.35

Total price of all three items with tax = (100% + tax) * Price

= (100% + 8%) * 104.35 = 108% * 104.35

= 1.08 * 104.35 = 112.698

≅ $112.70

The estimation to check if the result is reasonable by putting the answer in the original equation.

E.g. x + 4 = 10; x = 10 - 4

We get that x = 6

Plug in x = 6 in x + 4 = 10.

6 + 4 = 10.

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We can see that 7 is the total that is most likely to result, since it has the highest number of possible ways to roll it (6).


1) To find the probability of rolling a 10, we need to determine how many ways we can roll a 10 and then divide that by the total number of possible outcomes.

To roll a 10, we can get a 4 on one dice and a 6 on the other, or a 5 on one dice and a 5 on the other. So there are 2 ways to roll a 10.

The total number of possible outcomes is 6 x 6 = 36, since each dice has 6 possible outcomes.

Therefore, the probability of rolling a 10 is 2/36, which can be simplified to 1/18.

To find the probability of rolling higher than 10, we need to determine how many ways we can roll a total of 11, 12, or 13, and then divide that by the total number of possible outcomes.

To roll an 11, we can get a 5 on one dice and a 6 on the other, or a 6 on one dice and a 5 on the other. To roll a 12, we can get a 6 on both dice. To roll a 13, we can get a 6 on one dice and a 6 on the other.

So there are 4 ways to roll higher than 10.

Therefore, the probability of rolling higher than 10 is 4/36, which can be simplified to 1/9.

2) To find the probability of rolling an odd number, we need to determine how many ways we can roll an odd number and then divide that by the total number of possible outcomes.

To roll an odd number, we can get a 1, 3, or 5 on one dice and any number on the other dice, or we can get a 2, 4, or 6 on one dice and a 1, 3, or 5 on the other dice.

So there are 18 ways to roll an odd number.

Therefore, the probability of rolling an odd number is 18/36, which can be simplified to 1/2.

3) To find the total that is most likely to result, we need to determine which total has the most possible ways to roll it.

We can create a table to show how many ways we can roll each total:

Total | Number of Ways

2 | 1

3 | 2

4 | 3

5 | 4

6 | 5

7 | 6

8 | 5

9 | 4

10 | 3

11 | 2

12 | 1

From the table, we can see that 7 is the total that is most likely to result, since it has the highest number of possible ways to roll it (6).

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Answer:

$0.78

Step-by-step explanation:

You divide the $7.80 by 10 to get the cost of one tulip.

The common difference is 5

The formula for the nth term of an arithmetic sequence is ;

Tn = a + ( n - 1)d

Given that the parameters are;

Substitute the values

T₆ = 10 + ( 6-1) d

Subtract the values

35 = 10 + 5d

collect like terms

25 = 5d

Divide the values, we have;

d = 5

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a. The equilibrium solution (y = 0) is stable.

b. The limit of \(\( y(t) \)\) as \(\( t \)\) approaches infinity is 0.

A function's derivative with respect to an independent variable is what is referred to as differentiation. In calculus, differentiation can be used to calculate the function per unit change in the independent variable. Let y = f(x) represent the function of x.

The nonlinear differential equation is given as:

\(\( \frac{{dy}}{{dt}} = -y^2 \)\)

a) Classifying Equilibrium Solutions:

To find the equilibrium solutions, we set the derivative equal to zero:

\(\( -y^2 = 0 \)\)

The only solution is (y = 0). Therefore, the equilibrium solution is (y = 0).

To classify the stability of the equilibrium solution, we examine the sign of the derivative \(\( \frac{{dy}}{{dt}} \)\) around the equilibrium point.

For \(\( y < 0 \), \( \frac{{dy}}{{dt}} > 0 \)\), indicating that the function is increasing and moving away from the equilibrium solution.

For \(\( y > 0 \), \( \frac{{dy}}{{dt}} < 0 \)\), indicating that the function is decreasing and moving towards the equilibrium solution.

Hence, the equilibrium solution (y = 0) is stable.

b) Determining the Limit:

Given that \(\( y(0) = 2 \)\), we need to determine the limit of \(\( y(t) \) as \( t \)\) approaches infinity, if it exists.

The differential equation \(\( \frac{{dy}}{{dt}} = -y^2 \)\) can be separated and solved:

\(\( \frac{{dy}}{{y^2}} = -dt \)\)

Integrating both sides:

\(\( \int \frac{{dy}}{{y^2}} = -\int dt \)\)

\(\( -\frac{1}{y} = -t + C \)\)

Simplifying, we have:

\(\( \frac{1}{y} = t + C \)\)

Rearranging the equation:

\(\( y = \frac{1}{t + C} \)\)

Since we are given \(\( y(0) = 2 \)\), we can substitute this into the equation to find the value of (C):

\(\( 2 = \frac{1}{0 + C} \)\)

Solving for \(\( C \)\), we get \(\( C = \frac{1}{2} \)\).

Therefore, the solution to the differential equation is:

\(\( y = \frac{1}{t + \frac{1}{2}} \)\)

Taking the limit as (t) approaches infinity:

\(\( \lim_{{t \to \infty}} \frac{1}{t + \frac{1}{2}} = 0 \)\)

Hence, the limit of \(\( y(t) \)\) as \(\( t \)\) approaches infinity is 0.

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Answer:

x = 14√3

y = 7√3

Step-by-step explanation:

By applying sine rule in the given triangle,

sin(60°) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

\(\frac{\sqrt{3} }{2}=\frac{21}{x}\)

x = \(\frac{42}{\sqrt{3}}\)

x = 14√3

By applying cosine rule in the given triangle,

cos(30°) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

\(\frac{1}{2}=\frac{y}{x}\)

\(\frac{1}{2}=\frac{y}{14\sqrt{3}}\)

y = 7√3

Answer:

x = 12

Step-by-step explanation:

Since the triangle is isosceles then the legs are congruent.

Sum the 3 sides and equate to 52, that is

2x - 4 + 2x - 4 + x = 52

5x - 8 = 52 ( add 8 to both sides )

5x = 60 ( divide both sides by 5 )

x = 12

The value of theta in the given right angles triangle is 28°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

We know sin is equal to the opposite over the hypotenuse with respect to the reference angle.

The given triangle has an opposite of of length 8 units and an adjacent of 15 units.

We know, hypotenuse² = opposite² + adjecent²

hypotenuse² = 64 + 225.

hypotenuse² = 289.

hypotenuse = √289.

hypotenuse = 17.

Therefore, sinФ = 8/17 units.

Ф = sin⁻1(8/17).

Ф = 28°.

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Answer:

x= 21

Step-by-step explanation:

(x+6)^1/3-5=-2

Solve for x

Add 5 to each side

(x+6)^1/3-5+5=-2+5

(x+6)^1/3=3

Cube each side.

((x+6)^1/3)^3=3^3

x+6 = 27

Subtract 6 from each side

x+6-6 = 27-6

x= 21

Answer:

x = 21

Step-by-step explanation:

\(\sf(x+6)^\frac{1}{3} -5=-2\)

First, add 5 to both sides.

\(\sf(x+6)^\frac{1}{3} =-2+5\\\\\sf(x+6)^\frac{1}{3} =3\\\\\sqrt[3]{(x+6)} =3\)

Cube both sides.

\(\sqrt[3]{(x+6)} =3\\\\x+6=3^3\\\\x+6=27\)

Subtract 6 from both sides.

\(x+6=27\\\\x=27-6\\\\x=21\)

The solution sets of the two equations represent planes in 3D space, with the second plane shifted downward parallel to the first plane.

The given equations are:

x₁ + 2x₂ - 7x₃ = 0

x₁ + 2x₂ - 7x₃ = -4

To describe and compare their solution sets, we need to find the values of x₁, x₂, and x₃ that satisfy each equation.

For the equation x₁ + 2x₂ - 7x₃ = 0:

The solution set of this equation represents all the points (x₁, x₂, x₃) in 3-dimensional space that satisfy the equation. It forms a plane in 3D, as there are three variables and one equation.

For the equation x₁ + 2x₂ - 7x₃ = -4:

Similarly, the solution set of this equation represents the points (x₁, x₂, x₃) that satisfy the equation. It also forms a plane in 3D.

Comparing the two solution sets:

Both equations represent planes in 3D space. However, the second equation is obtained by shifting the plane of the first equation downward by 4 units along the z-axis (-4 on the right-hand side of the equation). This means the two planes are parallel, as they never intersect. The second plane is located below the first plane by a distance of 4 units along the z-axis.

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Answer:

happy vets day

Step-by-step explanation:

Answer:

0.8

Step-by-step explanation:

because you just had to add

Answer: 0.4

Step-by-step explanation: picture below

*see attachment for the diagrambifbthe mapping

Answer:

{x | x = –5, –3, 1, 2, 6}

Step-by-step explanation:

The domain of a function includes all input values entered in the oval for input, while the range includes all the values in the output oval.

From the mapping given in the attachment, we have the following possible values of the function in the input oval as: -5, -3, 1, 2, 6.

These x-values make up the domain of the function, and represented as: {x | x = –5, –3, 1, 2, 6}

The given production function Y = zK^2N^2 does not satisfy all of the properties of production functions. It violates the property of constant returns to scale.

A production function is a mathematical representation of the relationship between inputs (factors of production) and outputs (goods or services). It is expected to satisfy certain properties for it to be considered a valid production function.

One of the key properties of production functions is constant returns to scale, which means that if all inputs are scaled up or down proportionally, the output should also be scaled up or down by the same factor. In the given production function Y = zK^2N^2, we can observe that the exponents of both capital (K) and labor (N) are 2. This implies that doubling both inputs should result in a quadrupling of output (2^2 * 2^2 = 4). However, this violates the principle of constant returns to scale, as the output is increasing at an increasing rate, not a constant rate.

Therefore, the given production function fails to satisfy the property of constant returns to scale. Other properties such as positive marginal products and non-negativity of inputs may still hold, but without constant returns to scale, the production function does not conform to all the expected properties.

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hello

the answer to the question is:

length of JK = length of JL = r or radius

\( A \: = \frac{θ}{360} \times \pi {r}^{2} \\ 36\pi \: = \frac{160}{360} \times \pi {r}^{2} \\ {r}^{2} = 81 \: - > r = jk \: = 9\)

The probability that a randomly selected teacher makes less than $46,800 per year is 0.0808

According to the question,

If X is random variable follows normal distribution

The average teacher's salary in Connecticut = $57,337

The standard deviation = $7500

We have to find the probability that a random selected teachers makes less than $46,800 = P( X < 46,800 )

subtracting by $57337  and dividing by $7500

=>  P( X- 57337 / 7500 < 46,800-57337 / 7500)

=> P( z < -10537 / 7500)

=> P(z < -1.404)

Using z- probability distribution table ,

=> 0.0808

If we take 85 sample of teachers,

Then the probability that the sample mean is less than $56,200 = P(x < 56200)

subtracting by $57337  and dividing by $7500

=> P(x-57337 / 7500 < 56200 - 57337 / 7500)

=> P( z < -0.1516)

Using z- probability distribution table ,

=> 0.4404

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Answer:

k = \(\frac{25}{12}\)

Step-by-step explanation:

Using the rules of logarithms

log x - log y = log(\(\frac{x}{y}\) )

log a = log b ⇒ a = b

Given

logk - log(k - 2) = log25, then

log (\(\frac{k}{k-2}\) ) = log25, thus

\(\frac{k}{k-2}\) = 25 ( multiply both sides by (k - 2)

25(k - 2) = k

25k - 50 = k ( subtract k from both sides )

24k - 50 = 0 ( add 50 to both sides )

24k = 50 ( divide both sides by 24 )

k = \(\frac{50}{24}\) = \(\frac{25}{12}\)

Answer:

c i believe is the answer

Step-by-step explanation:

Answer: a) To find the height of the pyramid, we can use the Pythagorean theorem. Let H be the height of the pyramid, and let M be the midpoint of QR. Then, PM is half of PQ, which is 15 cm. We can use the Pythagorean theorem to find H:

H^2 = PQ^2 - PM^2

H^2 = 30^2 - 15^2

H^2 = 675

H = sqrt(675) = 5 sqrt(3) cm

b) To find the angle that PS makes with the base QRST, we can use trigonometry. Let A be the foot of the perpendicular from P to the base QRST, and let B be the midpoint of PS. Then, we have:

tan(angle PSB) = AB / PB

Since triangle PAB is a right triangle, we can use the Pythagorean theorem to find AB:

AB^2 = AP^2 - PB^2

AB^2 = H^2 + (PQ/2)^2 - PB^2

AB^2 = (5 sqrt(3))^2 + (15/2)^2 - PB^2

AB^2 = 225/4 + 75 - PB^2

AB^2 = 375/4 - PB^2

Since triangle PBS is also a right triangle, we can use the Pythagorean theorem to find PB:

PB^2 = PS^2 - BS^2

PB^2 = (2 H)^2 - (PQ/2)^2

PB^2 = 4 (5 sqrt(3))^2 - (15/2)^2

PB^2 = 500 - 56.25

PB^2 = 443.75

Substituting these values into the equation for tan(angle PSB), we get:

tan(angle PSB) = sqrt(375/4 - 443.75) / sqrt(443.75)

tan(angle PSB) = -0.4385

Since angle PSB is in the second quadrant, we have:

angle PSB = 180 degrees + arctan(-0.4385) = 152.4 degrees (rounded to one decimal place)

c) To find the total surface area of the pyramid, including the base, we can divide the pyramid into four triangular faces and a square base. The area of each triangular face can be found using the formula:

area = (1/2) base * height

where the base is the length of one edge of the square base, and the height is the height of the pyramid. The area of the base is simply the area of the square QRST, which is (20 cm)^2 = 400 cm^2. Therefore, we have:

area of each triangular face = (1/2) (20 cm) (5 sqrt(3) cm) = 50 sqrt(3) cm^2

total surface area = 4 (50 sqrt(3) cm^2) + 400 cm^2 = 200 sqrt(3) cm^2 + 400 cm^2

total surface area = (200 + 200 sqrt(3)) cm^2 ≈ 532.4 cm^2 (rounded to one decimal place)

Step-by-step explanation:

There are a few methods to doing this, but lets make every number a fraction. (You could make them all percentages or decimals if you want, but it is more difficult in my opinion.)
Miguel: 1/8
Gina: 13/100
Jatziry: 10/100 = 1/10
Kwa: 1/9
Now we need to find the least common denominator, which is 1800.
Now you have these fractions:
Miguel: 225/1800
Gina: 234/1800
Jatziry: 180/1800
Kwa: 200/1800
Now you can easily list these in order

180/1800 < 200/1800 < 234/1800 < 225/1800
Jatziry < Kwa < Gina < Miguel

Sorry if I made any mistakes, I realized Jatziry was a part of the problem halfway through.

Answer:

25%

Step-by-step explanation:

ratio is 3B : 1G  (this means, out of 4 sections, 3 are boys and 1 are girls)

this means that 3/4 of class is boys and 1/4 are girls

1/4 equals 25%

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Answer:

1) I would remove the '-2' first by adding '2' to both sides. Technically, it does not matter the order you remove the '5' or '-2' though it would be more of a hassle if you were to remove the number associated w/ a variable as you would do extra steps when there is a possibility to do it in less steps. So, ideally, it does matter but depending on your perspective.

2) You would begin by turning '1' into a fraction that has the same denominator as the fraction it is to be added to. This would get you 7/7. Then, you add 7/7 to 4/7 in order to get your final answer of 11/7. You could also just put the two numerical values together as '1 4/7' but I am inferring they want it in an improper fraction format. The steps to get an improper fraction are ideal since it is the simplest way to get to the final answer.

If you have any more questions please comment them and I will be happy to answer them if I can ^^