A coffee shop has booths and counter seating. Each booth can
seat 4 people. Another 20 people can sit at the counter. Which
expression shows how many customers can be seated in the coffee
shop?
A) 200 – 4 B) 200 14 C) Ab-20 D) 4b + 20
​

if you have the total number of students at School A, you can find out how many students scored between 26 and 28 by multiplying that number by 0.25.

To interpret this statement, let's break it down:

1. **25% of the students:** This refers to a percentage of the total number of students at School A. It means that out of all the students at School A, 25% fall into the category described next.

2. **got a score greater than 25 but less than or equal to 28:** This describes a range of scores. Specifically, it indicates that the students in question scored above 25 but equal to or less than 28.

Putting it together, the statement means that among all the students at School A, 25% of them scored between 26 and 28 (inclusive).

If we represent the total number of students at School A as \( N \), then the number of students who scored between 26 and 28 would be [tex]\( 0.25 \times N \)[/tex]since 25% is equivalent to[tex]\( \frac{1}{4} \).[/tex]

Therefore, if you have the total number of students at School A, you can find out how many students scored between 26 and 28 by multiplying that number by 0.25.

complete question:-

25% of the students at School A got a score greater than 25 but less than or equal to 28.

Answer:

The volume of the irregular figure is [tex]470\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the irregular figure is equal to

[tex]V=BL[/tex]

where

B is the area of the front of the L-shaped figure

L is the length of the figure

Find the area B

The area of of the front of the L-shaped figure is equal to the area of two rectangles

[tex]B=(9)(3)+(9-5)(8-3)[/tex]

[tex]B=(9)(3)+(4)(5)[/tex]

[tex]B=27+20=47\ cm^{2}[/tex]

we have that

[tex]L=10\ cm[/tex]

Find the volume

[tex]V=BL[/tex]

[tex]V=(47)(10)=470\ cm^{3}[/tex]

Answer:

-6x ≥ 24

x = ≤ 4

Step-by-step explanation:

Number = x

The product of the number and -6.

-6x

The product is at least 24.

-6x ≥ 24

Solve the problem

-6x ≥ 24

Divide by -6 and we change the sign

x = ≤ 4

Answer:

Step-by-step explanation:

4x - 8, 4x just means four of x, and eight less means to subtract 8.

Final answer:

The algebraic expression for 'eight less than four times a number' is '4x - 8', where x represents the number.

Explanation:

To write an algebraic expression for "eight less than four times a number," we first consider what the expression tells us:

Four times a number hints at a multiplication of some number, let's call it x, by 4, which we write as 4x.

Eight less than something means we need to subtract 8 from that something.

Therefore, combining these two steps, the algebraic expression that represents "eight less than four times a number" is 4x - 8.

Answer:

Ans: -5

Step-by-step explanation:

__ + 3 = -2

You bring the 3 to the other side

-2 - 3 = -2 + -3 = -5

-5 is the answer for your problem

The answer is:

D. [tex]8\sqrt[3]{5}[/tex]

To solve the problem, we need to remember the following roots properties:

[tex]a^{\frac{m}{n} }=\sqrt[n]{a^{m} }[/tex]

[tex]a\sqrt[n]{b} =\sqrt[n]{a^{n}*b} \\\\\sqrt[n]{ab}=\sqrt[n]{a}*\sqrt[n]{b}[/tex]

So, we are given the expression:

[tex](8.320)^{\frac{1}{3} }[/tex]

Then,  writing its equivalent expression, we have:

[tex]\sqrt[3]{8.320}[/tex]

Now, simplyfing, we have:

[tex]\sqrt[3]{8.320}=\sqrt[3]{2560}=\sqrt[3]{512*5}\\\\\sqrt[3]{8.320}=\sqrt[3]{512*5}=\sqrt[3]{8^{3} .5}\\\\\sqrt[3]{8.320}=\sqrt[3]{8^{3} .5}=\sqrt[3]{8}*\sqrt[3]{5} \\\\\sqrt[3]{8.320}=\sqrt[3]{8}*\sqrt[3]{5}=8*\sqrt[3]{5}[/tex]

Hence, we have that the correct option is:

D. [tex]8\sqrt[3]{5}[/tex]

Have a nice day!

Answer:

the answer is where the 2 points intersect... A. (2,3)

Step-by-step explanation:

Answer:

The correct option is A.

Step-by-step explanation:

The given system of equations is

[tex]y=-\frac{1}{2}x+4[/tex]

[tex]y=2x-1[/tex]

All the points on a line is are the solutions of the equation of line.

From the graph it is clear that the lines intersect each other at point (2,3). It means both the lines passes through the point (2,3) and point (2,3) is the solution of given system of equations.

Since (2,3) is the solution of given system of equations, therefore the correct option is A.

Answer:

Ф = 14° ⇒ to the nearest degree

Step-by-step explanation:

* Lets revise the trigonometry functions

- Assume that we have a right triangle ABC

∵ m∠B = 90°

∴ AC is the hypotenuse ⇒ opposite to the right angle

∴ AB and BC are the legs of the right angles

- Let angle ACB called Ф

∵ sinФ = opposite/hypotenuse

∴ sinФ = AB/AC

∵ cosФ = adjacent/hypotenuse

∴ cosФ = BC/AC

∵ tanФ = opposite/adjacent

∴ tanФ = AB/BC

* Now lets solve the problem

- We will consider the bike ramp is the ΔABC

∵ AB = 1.5 feet

∵ ∠ACB is Ф

∵ The length of the ramp is the hypotenuse

∴ AC = 6 feet

- W have the length of the opposite to Ф and the hypotenuse

∴ We will chose the sin function

∵ sinФ = AB/AC

∴ sinФ = 1.5/6 ⇒ use the inverse of sin to find Ф

∴ Ф = sin^-1 (1.5/6) = 14.47 ≅ 14° ⇒ to the nearest degree

Answer:

14°

Step-by-step explanation:

Looking at the triangle with green border,

with respect to the angle [tex]\theta[/tex], the side 1.5 ft is "opposite" and the side 6 ft is "hypotenuse" of the triangle.

Which trigonometric ratio relates opposite with hypotenuse? It is sine. Thus we can write:

[tex]Sin\theta=\frac{opposite}{hypotenuse}=\frac{1.5}{6}=0.25\\Sin\theta=0.25\\\theta=Sin^{-1}(0.25)=14.48[/tex]

Hence, the angle is 14.48°

rounded to nearest degree, it is 14°

Answer:

A  36[tex]\pi[/tex] [tex]cm^{3}[/tex]

Step-by-step explanation:

The formula for the volume of a sphere is [tex]\frac{4}{3}\pi r^{3}[/tex]. Because we are given the radius, 3 (centimeters), of the sphere, all we would need to do is plug 3 in for [tex]r[/tex], and solve.

[tex]\frac{4}{3}\pi (3)^{3}[/tex]

Using the order of operations (Parentheses, Exponents), we can solve for [tex](3)^{3}[/tex], which is 27 (think 3*3*3).

Then, we simply Multiply [tex](\frac{4}{3})(\pi)(27)[/tex], to get [tex]36\pi[/tex].

With our unit, centimeters cubed ([tex]cm^{3}[/tex]), our sphere's volume is 36[tex]\pi[/tex] [tex]cm^{3}[/tex].

The answer is provided in the image attached.

Answer:

Possible, but very unlikely

Step-by-step explanation:

In a school of 150 students, the probability that at least two people have the same birthday is possible but very unlikely.

In a year, we have 365 total possible birthdays. If one student was born on 1st of January say, then the second student has 364 possible birth-dates assuming that they have different birthdays. This implies there is a higher probability that the second student has a different birthday.

Moreover, considering the school has only 150 students which is less than the total possible birth-days in a year, 365, the chances of two or more students sharing a birthday is possible but would be very unlikely.

Final answer:

The event that at least two people have the same birthday in a school of 150 students is possible and likely, according to the principles of probability theory and the 'birthday paradox'.

Explanation:

In considering whether it is possible and likely that at least two people have the same birthday in a school of 150 students, we can refer to the birthday paradox. This mathematical probability phenomenon shows that, with just 23 people, there is a roughly 50% chance of two individuals sharing a birthday.

The probability increases significantly with each additional person to the point that in a group of 150 students, it is highly likely that at least two people will share the same birthday. This scenario is an interesting application of probability theory where our intuition might not align with the mathematical reality due to the non-intuitive properties of combinatorics and probability.

We do not arrive at this conclusion by adding probabilities of non-mutually exclusive events incorrectly, which would exceed 100% certainty. Instead, we calculate the probability of all students having unique birthdays, and subtract this from 1 to find the complement probability that at least two students share a birthday. This approach correctly keeps the calculated probability between 0 and 1, as per probability theory's third law.

In the case of 150 students, the calculated likelihood is so close to 1 (almost certain) that we can confidently classify the event as possible and likely.

Answer: E

Step-by-step explanation:

Answer E hope this helped

Answer:

[tex]P = 0.4[/tex]

Step-by-step explanation:

If each number X has the same probability of occur then the probability for each number is:

[tex]P = \frac{1}{10}[/tex]

Note that X is a discrete random variable, and the probability of obtaining an X number is independent for each trial.

So the probability that X is less than 3 is:

[tex]P (X <3) = P (1) + P (2)[/tex]

But [tex]P (1) = P (2) = \frac{1}{10}[/tex]

So:

[tex]P (X <3) = P (1) + P (2) = \frac{2}{10} = \frac{1}{5}[/tex]

Also

[tex]P (X> 8) = P (9) + P (10) = \frac{1}{10} = \frac{1}{5}[/tex]

Finally

[tex]P (X <3\ or\ X> 8) = \frac{1}{5} +\frac{1}{5} = \frac{2}{5} = 0.4[/tex]

Answer:

52 sodas

Step-by-step explanation

h=hotdogs

s= sodas

1.5h+.5s=78.5

You know that Emily sold 35 hotdogs so you replace h with 35.

Therefore, 1.5(35)+.5s=78.5

52.5+.5s=78.5

.5s=26

s=52

Answer:

[tex]x1=\frac{-2+\sqrt{26/3}}{2}[/tex]

[tex]x2=\frac{-2-\sqrt{26/3} }{2}[/tex]

Step-by-step explanation:

To find the zeros of the quadratic function f(x)=6x^2 + 12x – 7 we need to factorize the polynomial.

To do so, we need to use the quadratic formula, which states that the solution to any equation of the form ax^2 + bx + c = 0 is:

[tex]x=\frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]

So, the first thing we're going to do is divide the whole function by 6:

6x^2 + 12x – 7 = 0 -> x^2 + 2x - 7/6

This step is optional, but it makes things quite easier.

Then we using the quadratic formula, where:

a=1, b= 2, c = -7/6.

Then:

[tex]x=\frac{-2±\sqrt{2^{2}-4(1)(-7/6)}}{2}[/tex]

[tex]x=\frac{-2±\sqrt{4 +14/3}}{2}[/tex]

[tex]x=\frac{-2±\sqrt{26/3}}{2}[/tex]

So the zeros are:

[tex]x1=\frac{-2+\sqrt{26/3}}{2}[/tex]

[tex]x2=\frac{-2-\sqrt{26/3}}{2}[/tex]

Answer:

I'm not sure but I believe it's 50-12p=26

Step-by-step explanation:

Answer:

The third box: (50-12p=26)

Step-by-step explanation:

50-12p=26

-12p=26-50

-12p=-24

p=2

The price of each ride was $2.

Since the other answers gave you a negative, it would not have given you thr right answer.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x=3y&\text{subtract}\ 3y\ \text{from both sides}\\3x-2y=14\end{array}\right\\\\\left\{\begin{array}{ccc}x-3y=0&\text{multiply both sides by (-3)}\\3x-2y=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-3x+9y=0\\3x-2y=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad7y=14\qquad\text{divide both sides by 7}\\.\qquad\qquad y=2\\\\\text{put the value of y to the first equation:}\\x=3(2)=6[/tex]

Answer:

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}=17[/tex]

Step-by-step explanation:

Let the theme park sold number of tickets = x

Theme park charges $500 for group booking more than 25 tickets.

In addition to this theme park charges $20 per ticket for up to 100 tickets.

So charges of 100 tickets = 500 + (100×20) = $2500

For more than 100 tickets theme park charges $17, so charges for x tickets will be = 500 + (100×20) + 17(x - 100)

= 2500 + 17(x - 100)

Cost of one ticket of the theme park = [tex]\frac{2500+17(x-100)}{x}[/tex]

Now we have to write the limit equation when number of tickets purchased becomes very high.

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}=17[/tex]

[By solving limit as below

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}= \lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}[/tex]

since [tex]\lim_{x \to \infty}(\frac{1}{x})=0[/tex]

Therefore, [tex]\lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}=0+17-0[/tex]

= 17 ]

Answer:

The correct answer is C) 7,200.

Step-by-step explanation:

In order to find the answer for this, start by using the formula for momentum.

Mo = M*V

Mo = 120 * 60

Mo = 7,200

The momentum is 7200 kg-m/s.

Given: An object

Mass = 120 kg

Velocity = 60 m/s

We have to find the momentum of an object.

We know, momentum is given by:

⇒ Momentum = Mass × Velocity

⇒ Momentum = 120 × 60

⇒ Momentum = 7200 kg-m/s

Therefore, the momentum of an object is 7200 kg-m/s.

Hence, option (C) is correct.

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Answer: 4 hours

Step-by-step explanation: 20-8=20

20/5= 4hours

Answer:

V=1472.6

Step-by-step explanation:

Volume of a cone=π*r^2*h/3

The volume of an oblique shape is the same as a non oblique shape. Also, 15/2 is our radius

V=π*r^2*h/3

V=π*7.5^2*(25/3)

V=pi*56.25*8.33333...

V=1472.62155637

V=1472.6

If the height and radius of the oblique cone are 25 units and 7.5 units. Then the volume of the oblique cone will be 1472.62 cubic units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

If the height of the oblique cone is 25 units and the diameter of the cone is 15 units.

Then the volume of the oblique cone will be

Volume = 1/3 (πr²h)

Then the radius of the cone will be

r = 15/2

r = 7.5 units

Then the volume will be

Volume = 1/3 (π × 7.5² × 25)

Volume = 1/3 (4417.86)

Volume = 1472.62 cubic units

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Answer:

25.

The question is on  kinematic equations and free fall

An expression for h, displacement is given by;

h=v.t +1/2 at²................... where v is initial velocity, t is time and a is acceleration due to gravity

Given v=10ft/s d=-50 and a= -32.2 ft/s²..............................substitute the values in

h=v.t +1/2 at².

-50=10t + 1/2( -32.2)t²

-50=10t-16.1t²

16.1t²-10t-50=0..........................the function for height h in feet

b)  Solve 16.1t²-10t-50=0 using the quadratic formula

t= (-b ± √b² - 4ac )/2a

a=16.1  b= -10   and c= -50

t=( 10 ± √ (-10)² - 4 × 16.1 × -50 ) / 2×16.1

t= (10± √3320 )/ 32.2

t= (10± 57.62 ) / 32.2

t=67.62/32.2 = 2.1 sec or  - 47.62/32.2 = -1.5 sec

26.

a)The question is on  kinematic equations and free fall

An expression for h, displacement is given by;

h=v.t +1/2 at²................... where v is initial velocity, t is time and a is acceleration due to gravity

Given v=3ft/s  h= -1.3 ft and a= -32.2 ft/s²

substitute vales in;

h=v.t +1/2 at²

1.3=3t+1/2(32.2)t²

1.3=3t+16.1t²

16.1t²+3t-1.3=0...........................the function for h

b) Solve for t in 16.1t²+3t-1.3=0 using the quadratic formula

a=16.1        b=3      c= -1.3

t= (-3 ± √ -3² - 4×16.1× -1.3) / 2×16.1

t= ( -3 ± √ 9 + 83.72 ) / 32.2

t= (-3 ± 9.6 )/32.2

t= (-3+9.6)/32.2  = 6.6/32.2 = 0.2049 or

t= (-3-9.6)/32.2 = -12.6/ 32.2 = -0.391

c)  if the ball hit the rim at one half foot above the ground, find the distance it covered before hitting the rim

1.3-0.5=0.8 ft......................displacement

applying h=v.t +1/2 at²

0.8=3t+16.1t²

16.1t²+3t-0.8=0.......................solve using the quadratic formula

a=16.1  b=3    c= -0.8

t=(  -3 ± √3²- 4×16.1×-0.8  )/2×16.1

t=( -3±√9+51.52 )/ 2× 16.1

t = (-3 ± √60.52 )/32.2

t=( -3±7.78 )/ 32.2

t= (-3+7.78 )/32.2 =0.148 sec   or  t= (-3-7.78)/32.2 = -0.335 sec

Answer:

a.

Step-by-step explanation:

The key thing to look for here is the vertex. The vertex is the middle of the graph. In the graph, the vertex is located as (2,3)

To write your equation, use the formula y = a|x-h|+k. (h,k) is your vertex [h is the x-coordinate k is the y-coordinate]. So, substitute your vertex into the equation.

[Notice the equation says -h, not h. That's why you have to put -2 into the equation, not positive 2.]

So, your equation will be y=|x-2|+3.

I hope this helps!

Answer:

account c

Step-by-step explanation:

took on quiz 100%

Answer: C. Account C

Step-by-step explanation:

Answer:

survey

Step-by-step explanation:

because she wants to know the opinions of the girls

Hi!

I think it would be a survey because then the people would give their opinions, which is what she wants.

Hope this helps!

Answer:

cosA/cosB =  1

Step-by-step explanation:

We know that cos = Adjacent Side/hypothenuse.

Then Cos(A)= AC/AB = 3/4.24 = 0.707

Cos(B) = BC/AB = 3/4.24 = 0.707

Then cosA/cosB = 0.707/0.707 = 1

Answer:

The correct answer is

CosA/CosB =1

Step-by-step explanation:

Points to remember

Trigonometric ratios

Cos θ = Adjacent side/Hypotenuse

From the figure we can see a right angled triangle.

To find the value of CosA/CosB

CosA = Adjacent side/Hypotenuse

 =AC/AB = 3/4.24

Cos B =  Adjacent side/Hypotenuse  

 = BC/AB = 3/4.24

CosA/CosB = (3/4.24)/(3/4.24) = 1

Therefore the value of CosA/CosB = 1

Since the sum of the opposite angles of a cyclic quadrilateral are supplementary, the value of d is equal to 80°.

In Mathematics, the measure of the sum of two (2) adjacent angles would be equal to 180º when a quadrilateral is inscribed in a circle. Generally speaking, any cyclic quadrilateral would have all of its vertices on the circumference of a circle.

This ultimately implies that, the sum of the opposite angles of a quadrilateral that is inscribed in a circle (cyclic quadrilateral) are supplementary;

m∠c + 96 = 180°

m∠d + 100 = 180°

Now, we can solve for the value of d by by subtracting 100 from both sides of the equation as follows;

m∠d + 100 - 100 = 180° - 100

m∠d = 80°

Answer:

The answer is D.

Step-by-step explanation:

This is because the first part of the expression is the conjugate and youre given -5. The second part of the expression is the imaginary part and youre given 4i.

Answer:

C

Step-by-step explanation:

Given a complex number in the form

a + bi then the conjugate is a - bi

Note the real part remains unchanged while the sign of the imaginary part is negated.

Given

- 5 + 4i then the conjugate is - 5 - 4i → C

Answer:

A

Step-by-step explanation:

To calculate the scale factor k, find the ratio of corresponding sides

[tex]\frac{XZ}{AC}[/tex] = [tex]\frac{18}{3}[/tex] = 6

[tex]\frac{YZ}{BC}[/tex] = [tex]\frac{24}{4}[/tex] = 6

Hence the scale factor k = 6 → A

Answer:  The correct option is (A) 6.

Step-by-step explanation:  We are given to find the scale factor of dilation from triangle ABC to triangle XYZ.

From the figure, we note that

The lengths of the sides of triangles ABC and XYZ are as follows :

AB = 5 units, BC = 4 units, AC = 3 units, XY = 30 units, YZ = 24 units and XZ = 18 units.

We know that

[tex]\textup{Scale factor}=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.[/tex]

Therefore, for the given triangles, we get

[tex]\textup{Scale factor}=\dfrac{XY}{AB}=\dfrac{30}{5}=6.[/tex]

Thus, the required scale factor of dilation is 6.

Option (A) is CORRECT.

Answer:

d. x= +-11.18

Step-by-step explanation:

The value of x in the quadratic equation  3x² = 375 is  ± 5√5.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, An equation 3x² = 375.

x² = 375/3.

x² = 125.

x = ± 5√5.

So, the value of x in the equation  3x² = 375 is 5√5.

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