A bakery can make 30 donuts every 15 minutes. What is the unit rate at which the bakery makes donuts?

Answer:

The length of BC = 28 units

Step-by-step explanation:

* In triangle ABC

∵ Angles B and C are congruent

∴ m∠B = m∠C

* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length

∴ AB = AC

∵ AB = 4x - 7

∵ AC = 2x + 7

∴ 4x - 7 = 2x + 7 ⇒ collect like terms

∴ 4x - 2x = 7 + 7

∴ 2x = 14 ⇒ divide both sides by 2

∴ x = 14 ÷ 2 = 7

* Now we can find the length of BC

∵ The length of BC = 4x ⇒ substitute the value of x

∴ The length of BC = 4 × 7 = 28 units

To find the length of side BC of the triangle, you can use the fact that angle B and angle C are congruent. Set up an inequality using the lengths of side AB and side AC, and solve for x. Substitute x with an appropriate value to find the length of side BC.

To find the length of side BC of the triangle, we can use the fact that angle B and angle C are congruent. Let's represent the length of side AB as 4x - 7 and the length of side AC as 2x + 7. Since the sum of the lengths of the two smaller sides of a triangle must be larger than the length of the largest side, we can set up an inequality: 4x - 7 + 2x + 7 > 4x. Simplifying this inequality, we get 6x > 0, which tells us that x must be greater than 0.

Since side BC is labeled as 4x, we can substitute x with any positive value greater than 0. For example, if we let x = 1, then side BC would have a length of 4(1) = 4 units.

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x = -21

explanation: a trick i used was just do -3 times 7 and get my answer -21. if you are unsure if the answer is right just check your work with a calculator. -21 divided by 7 is -3 so -21 is the value of x. please mark brainliest !!

Answer:

5 more minutes (total of 20 minutes per applicant)

Step-by-step explanation:

Divide an hour by 1/3 (60/3 = 20 minutes)

Divide an hour by 1/4 (60/4= 15 minutes)

By spending 1/3 of an hour (20 minutes) instead of 1/4 of an hour (15 minutes), she spent 5 more minutes meeting all applicants.

The first answer is correct

Answer:

3 + 9 + 27 + ...

Step-by-step explanation:

3 + 9 + 15 + ... is not a geometric series because it has no common ratio.

[tex]\frac{15}{9}\ne \frac{9}{3}[/tex]

3 + 9 + 27 + ... is a geometric series because there is a common ratio;

[tex]r=\frac{27}{9}=\frac{9}{3}=3[/tex]

3, 9, 27, ... is a geometric sequence and not a series. The sum of all the  terms in a geometric sequence forms a geometric series.

3, 9, 15, ... is a not a geometric series.

Answer:

The answer is parabola; (y')² - 8x' = 0 ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* x² - 8y = 0

∵ A = 1 , B = 0 , C =

∴ B² - 4AC = (0)² - 4(1)(0) = 0

∵ B² - 4AC = 0

∴ it will be a parabola.

∵ Ф = 90°

* The point (x , Y) will be (x' , y')

∵ x = x'cosФ - y'sinФ and y = x'sinФ + y'cosФ

∵ cos(90) = 0 and sin(90) = 1

∴ x = -y' and y = x'

* lets substitute x and y in the first equation

∴ (-y')² - 8(x') = 0

∴ (y')² - 8x' = 0

* We notice that the x' took the place of y and y' took the place of x

∴ The parabola rotated around the origin by 90°

∴ The equation of the parabola is (y')² - 8x' = 0

* The answer is parabola, with angle of rotation 90°

* The equation is (y')² - 8x' = 0

* Look to the graph

- The blue is x² - 8y = 0

- The green is (y')² - 8x' = 0

Answer:

the correct answer is D)

parabola

Answer:

54 times you can fill a cone with the grain that is stored in the container

Step-by-step explanation:

step 1

Find the volume of the paper cone

The volume of the cone is

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]r=4\ cm[/tex]

[tex]h=9\ cm[/tex]

[tex]\pi=3.14[/tex]

substitute the values

[tex]V=\frac{1}{3}(3.14)(4)^{2} (9)=150.72\ cm^{3}[/tex]

step 2

Divide the total volume of the container by the volume of one paper cone

[tex]\frac{8,138.88}{150.72}=54[/tex]

Answer:

Its 54

Step-by-step explanation:

The simplest direct ratio of boys to girls in the room is 3:4, which means for every 3 boys, there are 4 girls. This is determined by finding the greatest common divisor of the two quantities. Other possible ratios such as 6:8, 9:12, 12:16, and 15:20 are multiples of this base ratio.

The question is asking for us to form all the possible ratios of boys to girls in the given situation. We are given that there are 42 boys and 56 girls. The simplest ratio of boys to girls can be determined by finding the greatest common divisor (GCD) of both numbers and then dividing both numbers by it. The GCD of 42 and 56 is 14, so if we divide both numbers by the GCD, we get the ratio of 3:4. This implies that for every 3 boys, there are 4 girls. However, other possible ratios could use multiple of these numbers. Therefore, the possible ratios of boys to girls in this scenario also include 6:8, 9:12, 12:16, 15:20, and so on.

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Answer:

g(x) = 2sin(x) + 3

Step-by-step explanation:

f(x) = sin(x)

transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.

so

g(x) = 2sin(x) + 3

Answer:

In the morning, the packing rates per hour was 45. In the afternoon, the packing rates per hour was 40. The difference is 5.

ANSWER

a. A variable is an unknown number or value represented by a letter

EXPLANATION

In mathematics, we use letters to represent an unknown quantity or number.

For instance, we can use the letter , t, to represent time taken to cover a given distance.

We can use the letter , s, to represent displacement or distance covered by an object.

The letters that we use to represent the unknown values or numbers are called variables.

The correct answer is A.

A variable is a characteristic that can change in value across different instances. It can be represented by any letter and can be numerical or categorical. In mathematical contexts, it often represents an unknown value in an equation.

A variable, which can be represented by any letter, and not just 'x', is a characteristic that can vary in value across different instances. It could refer to different types of measurables such as a numerical variable like 'x' representing the number of points earned by a student or a categorical variable like 'y' representing someone's party affiliation. Variables in mathematical contexts are often used in equations to represent unknown values.

For example, if 'x' represents the number of children in a family, each different integer value of 'x'(0, 1, 2, 3, etc) specifies a unique family structure. Therefore, option A : 'A variable is an unknown number or value represented by a letter' is the correct choice.

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Answer:

The probability that the sample mean would be greater than 77.21 WPM = 0.9945

Step-by-step explanation:

Mean number of Words per Minute  = u  = 81

Standard Deviation = s = 17

sample size = n = 130

Target value = x = 77.21

we can find the probability by converting x to z-score.

The formula for z-score = [tex]\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]

using given values, z-score =  [tex]\frac{77.21-81}{\frac{17}{\sqrt{130} } }[/tex]

=> -2.54

using the z table, we can find the find the probability of -2.54, that is 0.9945.

Therefore, the probability that the sample mean would be greater than 77.21 WPM = 0.9945  

The probability that the sample mean would be greater than 77.21 WPM is approximately [tex]\(0.9945\)[/tex] (rounded to four decimal places).

To find the probability that the sample mean is greater than 77.21 WPM, we need to use the Central Limit Theorem.

Here's the step-by-step process:

1. Identify the given information:

Population mean [tex](\(\mu\))[/tex]: 81 WPM

Population standard deviation [tex](\(\sigma\))[/tex]: 17 WPM

Sample size [tex](\(n\))[/tex]: 130

Sample mean [tex](\(\bar{x}\))[/tex]: 77.21 WPM

2. Calculate the standard error of the mean (SEM):

[tex]\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{17}{\sqrt{130}} \approx \frac{17}{11.4018} \approx 1.4910 \][/tex]

3. Find the Z-score for the sample mean:

[tex]\[ Z = \frac{\bar{x} - \mu}{\text{SEM}} = \frac{77.21 - 81}{1.4910} \approx \frac{-3.79}{1.4910} \approx -2.543 \][/tex]

4. Use the Z-score to find the probability:

We look up the Z-score of -2.543 in the standard normal distribution table.

[tex]\[ P(Z < -2.543) \approx 0.0055 \][/tex]

This is the probability that the sample mean is less than 77.21 WPM. Since we need the probability that the sample mean is greater than 77.21 WPM, we subtract this value from 1.

[tex]\[ P(\bar{x} > 77.21) = 1 - P(Z < -2.543) = 1 - 0.0055 = 0.9945 \][/tex]

Answer:

I'm pretty sure the answer is 21.26

I hope thats right if not sorry mark me brainliest

The circumference of the wheel is 21.26 inch

The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.

Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.

Given:

Area of wheel= 36

πr² = 36

r²= 36/ 3.14

r = 3.385

Now,

Circumference of the wheel is

=2πr

=2*3.14*.3.385

=21.264 inches

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Answer:

48

Step-by-step explanation:

divide 30 by 5/8

Answer: 48 cars washed yesterday.

Step-by-step explanation:

Given : An automatic car wash uses [tex]\dfrac{5}{8}[/tex] gallon of soap on each car that is washed.

Yesterday,the ,car wash used a total of 30 gallons of soap.

Then, the number of car washed yesterday is given by :-

[tex]30\div\dfrac{5}{8}\\\\=30\times\dfrac{8}{5}=48[/tex]

Hence, 48 cars washed yesterday.

Answer: The probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens  < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.

i.e.  0.2<0.42<0.7<0.87

Step-by-step explanation:

Since we have given that

1) the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles

Probability would be [tex]\dfrac{\text{Red Marble}}{Total\ marble}}=\dfrac{5}{12}=0.42[/tex]

2) the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples

Probability would be [tex]\dfrac{Peach}{Total}=\dfrac{7}{10}=0.7[/tex]

3) the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens

Probability would be [tex]\dfrac{Green}{Total}=\dfrac{4}{20}=\dfrac{1}{5}=0.2[/tex]

4) the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls

Probability would be [tex]\dfrac{Golf\ ball}{Total}=\dfrac{13}{15}=0.87[/tex]

We need to arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability occurrence:

So, 0.2<0.42<0.7<0.87

Hence, it becomes

the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens  < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.

Answer:

57.82 gallons will be needed to fill the tank

Step-by-step explanation:

Final answer:

Leo's fish tank can hold approximately 57.8 gallons of water to the nearest tenth, calculated by finding the volume of the tank in cubic inches and then converting that to gallons using the conversion factor.

Explanation:

To calculate how many gallons of water can fill the fish tank to the nearest tenth, we need to find the volume of the tank in cubic inches and then convert that to gallons using the given conversion factor.

Step 1: Calculate the volume of the tank in cubic inches

The volume of the tank (V) is given by the formula V = length × width × height.

V = 24 in. (length) × 37 in. (width) × 15 in. (height) = 13,320 cubic inches.

Step 2: Convert cubic inches to gallons

Using the conversion factor 1 gallon = 230.4 cubic inches:

Number of gallons = Volume in cubic inches ÷ Conversion factor

Number of gallons = 13,320 in³ ÷ 230.4 in³/gal ≈ 57.8 gallons

Therefore, Leo's fish tank can hold approximately 57.8 gallons of water when filled to the top.

Events A and B are independent events because the product of their probabilities (P(A)P(B)) equals the probability of the intersection of both events (P(A∩B)).

To determine if events A and B are independent events, we need to check if the product of their probabilities equals the probability of their intersection. According to the formula for independent events:

P(A AND B) = P(A)P(B)

Given:

P(A) = 1/4

P(B) = 2/5

P(A∩B) = 1/10

Let's calculate the product of P(A) and P(B):

P(A)P(B) = (1/4) × (2/5) = 1/10

Since P(A∩B) also equals 1/10, which is the same as the product of P(A) and P(B), it is therefore true that:

P(A AND B) = P(A)P(B)

This implies that events A and B are indeed independent because their combined probability equals the product of their probabilities.

Answer:

B

Step-by-step explanation:

An equivalent expression is an expression which is equal to 10k + 17 - 7j - 18 - 11k. You can expand or simplify an expression to make an equivalent expression. Combine like terms to form a new equivalent expression. Like terms are terms which have the same base or variable.

10k + 17 - 7j - 18 - 11k

10k -11k + 17 - 18 - 7j                Move to group like terms together.

-k - 1 - 7j

This is the same solution as B written in a different order.

Answer:

BBBBBBBBBBBBBBBBBBBBBBB

Step-by-step explanation:)

➷ cos41 = x/55

x = cos41 x 55

x = 41.50902

The correct option would be 41.51

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

41.51

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos41° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{55}[/tex]

Multiply both sides by 55

55 × cos41° = x

⇒ x = 41.51 ( to the nearest hundredth )

Answer:

35 times

Step-by-step explanation:

The points Anita has remaining for a prize is  2580 - 480 = 2100 points

Since each time she earns 60 points, to get 2100 points, she needs to go:

[tex]\frac{2100}{60}=35[/tex] times

She needs to go 35 times

Answer:

35 times

Step-by-step explanation:

1. The given curves intersect one another three times:

[tex]x^3=9x\implies x(x^2-9)=0\implies x=0,\pm3[/tex]

The area of the bounded region is

[tex]\displaystyle\int_{-3}^3|x^3-9x|\,\mathrm dx[/tex]

[tex]x^3-9x[/tex] is odd, but the absolute value makes it even. More formally,

[tex]|(-x)^3-9(-x)|=|-x^3+9x|=|x^3-9x|[/tex]

which means the integral is equivalent to

[tex]\displaystyle2\int_0^3|x^3-9x|\,\mathrm dx[/tex]

For [tex]0\le x\le 3[/tex], the definition of absolute value tells us that

[tex]|x^3-9x|=9x-x^3[/tex]

so the integral evaluates to

[tex]\displaystyle2\int_0^3(9x-x^3)\,\mathrm dx=\left(9x^2-\frac{x^4}2\right)\bigg|_{x=0}^{x=3}=\frac{81}2=40.5[/tex]

2. Using the disk method, the volume is given by the integral

[tex]\displaystyle\pi\int_0^\pi\sin^2(\sin x)\,\mathrm dx[/tex]

Use a calculator to get the result 1.219.

Answer:

A

Step-by-step explanation:

The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.

This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.

An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.

Answer:

A.

Step-by-step explanation:

I just got 100% on the quiz.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange x + 5y = 10 into this form

Subtract x from both sides

5y = - x + 10 ( divide all terms by 5 )

y = - [tex]\frac{1}{5}[/tex] x +2 ← in slope- intercept form

with slope m = - [tex]\frac{1}{5}[/tex]

• Parallel lines have equal slopes, hence

y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (1, 3) into the partial equation

3 = - [tex]\frac{1}{5}[/tex] + c ⇒ c = [tex]\frac{16}{5}[/tex]

y = - [tex]\frac{1}{5}[/tex] x + [tex]\frac{16}{5}[/tex] ← equation of parallel line

Answer:

A) y = − 1 /5 x +  16/ 5

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{x^2-8x+16}[/tex]

Step-by-step explanation:

The expression, written in full, looks like this:

[tex]\dfrac{x+3}{x^2-x-12}\cdot\dfrac{x-4}{x^2-8x+16}[/tex]

To simplify this expression, it would help us out a lot if we could factor the expressions in the denominators. Let's handle [tex]x^2-x-12[/tex] first:

[tex]x^2-x-12=\\=x^2-4x+3x-12\\=x(x-4)+3(x-4)\\=(x-4)(x+3)[/tex]

Next, we can factor [tex]x^2-8x+16[/tex]:

[tex]x^2-8x+16=\\=x^2-4x-4x+16\\=x(x-4)-4(x-4)\\=(x-4)(x-4)\\=(x-4)^2[/tex]

Substituting these back into our original expression, we get

[tex]\dfrac{x+3}{(x-4)(x+3)}\cdot\dfrac{x-4}{(x-4)^2}[/tex]

On the left, we can cancel an (x+3) in the numerator and denominator, and on the right, we can cancel an (x-4), simplifying the expression to

[tex]\dfrac{1}{x-4}\cdot\dfrac{1}{x-4}[/tex]

Multiplying the two together gives us the fraction

[tex]\dfrac{1\cdot1}{(x-4)\cdot(x-4)}=\dfrac{1}{(x-4)^2}[/tex]

Since [tex](x-4)^2=x^2-8x+16[/tex], we can rewrite this fraction in simplified form as

[tex]\dfrac{1}{x^2-8x+16}[/tex]

Answer:

Car 1 : 40 gallons

Car 2 : 15 gallons

Step-by-step explanation:

F = Car 1 Fuel Efficiency

S = Car 2 Fuel Efficiency

F + S = 55

40F + 35S = 2125

Using the first equation...

S = 55 - F

Then substitute into the second equation.

40F + 35(55 - F) = 2125

Simplify

40F + 1925 - 35F = 2125

5F + 1925 = 2125

5F = 200

F = 40

Then plug it back into S = 55 - F

S = 15

Plug it back into F + S = 55 to check.

Hope this helps.

Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.

Let car 1 fuel efficiency = x

Let car 2 fuel efficiency = y.

Based on the information given,

x+ y = 55 ...... i

40x + 35y = 2125 ...... ii

Therefore, y = 55 - x ..... iii

Put equation iii into ii

40x + 35(55 - x) = 2125

40x + 1925 - 35x = 2125

Collect like terms

40x - 35x = 2125 - 1925

5x = 200

x = 200/5

x = 40

Since x + y = 55.

y = 55 - 40 = 15

Therefore, Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.

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Answer with step-by-step explanation:

We are given three different expressions and we are to write an equivalent exponential equation for them.

We know that the standard form of a logarithmic expression is given by:

[tex]y = log_a ( x )[/tex] which is equivalent to the exponential form  [tex]x = a ^ y[/tex].

1. [tex] log _ {10} (0.1) = -1 [/tex] ---> [tex]10^{-1}=0.1[/tex]

2. [tex] log _ {3} 9 = 2 [/tex] ---> [tex]3^2=9[/tex]

3. [tex] log _ 5 ( \frac { 1 } { \sqrt { 5 } } ) = -\frac { 1 } { 2 } [/tex] ---> [tex]5^{-\frac{1}{2} }=\frac{1}{\sqrt{5} }[/tex]

Answer:

150 ft

Step-by-step explanation:

triangle area formula= (b*h)/2

25 time 12 is 300. divide 300 by 2 and get 150.

Answer:

A = 150 ft^2

Step-by-step explanation:

The area of a triangle is found by using

A = 1/2 b*h where b is the base and h is the height

A = 1/2 (12)*25

A = 6*25

A = 150 ft^2

Answer:

x=2

Step-by-step explanation:

10=16(x-2)^2+10

Subtract 10 from each side

10-10=16(x-2)^2+10-10

0 =16(x-2)^2

Divide by 16

0/16 = 16/16 (x-2)^2

0 = (x-2)^2

Take the square root of each side

sqrt(0) = sqrt(  (x-2)^2)

0 = x-2

Add 2 to each side

0+2 = x-2+2

2 =x

[tex]Cancel \ 10 \ on \ both \ sides.\\\\0 = 16(x - 2)^2\\\\\\Divide \ both \ sides \ by \ 16.\\0 = (x - 2)\\\\\\Now take the square root of both sides.\\\\0 = x - 2\\\\\\Add 2 to both sides.\\\\2 = x\\\\Switch sides.\\\\\fbox{x = 2}[/tex]

Answer: true :))

Step-by-step explanation:

Public relations is part of business and administrative support as it helps manage a business's image and relationship with the public. Meanwhile, bureaucracy plays a role in not only enforcing policies but also in policy formation.

Public relations is indeed a part of business and administrative support. Businesses use public relations to manage and protect their image and relationship with the public. It's a key component to business administration as it helps businesses improve their brand awareness, manage crises, and strengthen relationships with stakeholders.

The question about bureaucracy is a separate query and in this context, the statement is false. Bureaucracy is not only involved in enforcing policies to ensure people comply, but it is also involved in the process of policy formation. Through different departments and offices, information is gathered, policy proposals are developed and recommendations are made to decision-makers.

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