A bakery sold 120 chocolate cupcakes in a day,
which was 24% of the total number of cupcakes
sold that day. How many total cupcakes did the
bakery sell that day?

Answer:

the correct one is c

Step-by-step explanation:

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Two closed container with ball having the diameter of 60 mm, the container having the smaller surface area is Container B.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.

We have the diameter of the ball as 60 mm

In container A we can see it is a cylinder:

Therefore, the four balls will give us the height of cylinder as

(4x60 = 240mm)

Area of cylinder is given as = 2πrh

A = 2 π (30) (240)

A = 45,239 mm²

In container B we can see it is a cube:

Length = 120 mm

Area of cube  = 6a²

A = 6(120)²

A = 86,400 mm²

After comparing both the container square we can say that the Container B has more surface area than the container A.

86,400>45,239.

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Answer:

13

Step-by-step explanation:

13x75000=975000

Check for reasonableness...

975000/75000=13

So the answer is 13 gallons.

P.S. There will still be 25,000 drops left, which is 1/3 of a gallon.

The simplified value represented in the complex number form |(8+9i)(8+9i)| is equal to 145.

The product of the complex numbers are,

|(8+9i)(8+9i)|

We can expand the expression (8 + 9i)(8 + 9i) using the FOIL method,

(8 + 9i)(8 + 9i)

= 8(8) + 8(9i) + 9i(8) + 9i(9i)

= 64 + 72i + 72i + 81(i²)

Value of i² = -1.

= 64 + 144i - 81

= -17 + 144i

Then, to find the absolute value of this complex number, we take the square root of the sum of the squares of its real and imaginary parts .

Modulus of complex number is,

|(-17 + 144i)|

= √((-17)² + (144)²)

= √(289 + 20736)

= √(21025)

= 145

Therefore, the value of the complex number |(8 + 9i)(8 + 9i)| is equal to 145.

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To prove that AC ⊕ EC, we need to show that quadrilateral DEFG being a rectangle and BC ⊕ DC implies that AC ⊕ EC.

To begin, we know that quadrilateral DEFG is a rectangle. In a rectangle, opposite sides are equal in length and parallel to each other.

Given that BC ⊕ DC, we can infer that BC and DC are not equal in length.

Since DEFG is a rectangle, this means that AB and DE are also not equal in length, as they are opposite sides. Similarly, AD and BC are not equal in length.

Now, let's consider triangle ABC. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Applying this to triangle ABC, we have:

AB + BC > AC
AD + DC > AC

Since AB and DC are not equal in length, and BC and AD are not equal in length, we can conclude that AC is the longest side in triangle ABC.

Now, let's look at triangle CDE. Again, using the same rule for triangles:

AC + CE > EC
AD + DE > EC

Since AC is the longest side in triangle ABC, and AD is not equal in length to DE, we can conclude that AC is longer than EC.

Therefore, we have proved that if quadrilateral DEFG is a rectangle and BC ⊕ DC, then AC ⊕ EC.

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Answer:

The expression you provided is a binomial expression raised to the third power, where the binomial is (a^2 + 2ab + b^2). Using the binomial expansion formula for (a+b)^3, we can simplify the expression as follows:

(a^2 + 2ab + b^2)^3 = [(a+b)^2 + ab]^3 [using the identity (a^2 + 2ab + b^2) = (a+b)^2 + ab]

= [(a+b)^2 + ab][(a+b)^2 + ab][(a+b)^2 + ab]

Expanding each term, we get:

= [(a+b)^4 + 2ab(a+b)^2 + a^2b^2][(a+b)^2 + ab]

= [(a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4) + 2ab(a^2 + 2ab + b^2) + a^2b^2][(a+b)^2 + ab]

= [(a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4) + 2a^3b + 4a^2b^2 + 2ab^3 + a^2b^2][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 12a^2b^2 + 6ab^3 + b^4 + 3a^2b^2) + (2a^3b + 4a^2b^2 + 2ab^3 + a^2b^2)ab][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + (2a^4b + 6a^3b^2 + 6a^2b^3 + 2ab^4)][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2ab(a^3 + 3a^2b + 3ab^2 + b^3)][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2ab(a+b)^3][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2ab(a+b)(a+b)^2][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2ab(a+b)(a^2 + 2ab + b^2)][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2a^3b + 4a^2b^2 + 2ab^3 + 2a^2b^2 + 4ab^3 + 2b^4][(a+b)^2 + ab]

14 people gave the modal response

In a survey, modal response is the most frequently occurring response to a question. It can be used to identify the most important issues or concerns of a population.

You will notice the key says one circle represents 4 people. So half circle represents 2 people. Thus, we can say:

Swedish = 4 + 4 + 2 = 10

German = 4 + 4 = 8

French = 4 + 4 + 4 + 2 = 14

Since French has the highest number of people (i.e. 14 people). Therefore, 14 people gave the modal response.

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To check if the given function y = √(c - x³/x) is a general solution of the differential equation (3x + 2y²)dx + 2xydy = 0, we can start by solving the equation (1) for c to obtain an equation in the form F(x, y) = c.

The given differential equation is (3x + 2y²)dx + 2xydy = 0. We want to check if the function y = √(c - x³/x) satisfies this equation.

To do so, we can substitute y = √(c - x³/x) into the differential equation and see if it simplifies to 0. Substituting y into the equation, we have:

(3x + 2(c - x³/x)²)dx + 2x(c - x³/x)dy = 0.

We can simplify this equation further by multiplying out the terms and simplifying:

(3x + 2(c - x³/x)²)dx + 2x(c - x³/x)dy = 0,

(3x + 2(c - x⁶/x²))dx + 2x(c - x³/x)dy = 0,

(3x + 2c - 2x³/x²)dx + 2xc - 2x³dy = 0.

Simplifying this equation, we get:

(3x + 2c - 2x³/x²)dx + (2xc - 2x³)dy = 0.

As we can see, the simplified equation is not equal to 0. Therefore, the given function y = √(c - x³/x) is not a general solution of the differential equation (3x + 2y²)dx + 2xydy = 0.

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Answer:

18.1

Step-by-step explanation:

All radii of a circle are congruent (same length), which means if we draw in a radius from the center to the end of the 16.3, it would be the same length of x.

Now we can use sa very simple theorem.... the pythagorean therom!

\(7.9^{2} + 16.3^{2} = x^{2} \\62.41 + 265.69 = x^{2} \\328.1 = x^{2} \\18.1 = x\)(rounded)

I hope this helps you.

Colleen's average rate over the last 9 hours of her trip is 81 miles / 9 hours = 9 miles per hour.

1. To find the average rate, we need to divide the total distance traveled in the last 9 hours by the time taken.
2. In the first 2 hours, Colleen traveled 20 miles, so in the next 9 hours, she traveled 101 - 20 = 81 miles.
3. Therefore, her average rate over the last 9 hours is 81 miles / 9 hours = 9 miles per hour.

Therefore, Colleen's average rate over the last 9 hours of her trip is 81 miles / 9 hours = 9 miles per hour.

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Answer:

Step-by-step explanation:

do 21 ÷ 4 = 5.25

Now we have 5.25 miles for each inch. So all we have to do is multiply 5.25 by 13 to find the answer:

5.25 × 13 = 68.25

Let me know if this helped!

The total distance she swim in all is 1/3

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

Island = 2/9 km

Boat = 1/9 km

Using the above as a guide, we have the following:

Total = Island + Boat

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

Total = 2/9 + 1/9

Evaluate the sum

Total = 1/3

hence, the total distance she swim in all is 1/3

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The missing probability in the table can be found by subtracting the sum of the probabilities of the known values from 1. First, let's calculate the sum of the known probabilities:0.24 + 0.30 + 0.14 + 0.11 + 0.09 = 0.88

Next, subtract this sum from 1 to find the missing probability:
1 - 0.88 = 0.12

Therefore, the missing probability, P(H = 0), is 0.12.


To find the missing probability in the table, we can subtract the sum of the probabilities of the known values from 1. The known probabilities in the table are 0.24, 0.30, 0.14, 0.11, and 0.09. Adding these probabilities together gives us 0.88. To find the missing probability, we subtract this sum from 1. The calculation is 1 - 0.88 = 0.12. Therefore, the missing probability, P(H = 0), is 0.12.


The American Community Survey conducted by the US Census Bureau collects information about households in the US, and one variable of interest is the number of people residing in each household. In this case, we have a partially completed probability distribution table for the number of people, denoted as HHH, residing in randomly selected US households based on data from 2014. The table includes the probabilities for the values 1, 2, 3, 4, and 5+. However, the probability for H = 0 is missing.

To find the missing probability, we need to calculate the sum of the probabilities of the known values and subtract it from 1. Adding the probabilities of the known values together gives us 0.24 + 0.30 + 0.14 + 0.11 + 0.09 = 0.88.

Next, we subtract this sum from 1 to find the missing probability: 1 - 0.88 = 0.12.

Therefore, the missing probability, P(H = 0), is 0.12.

The missing probability in the table for the number of people residing in a randomly selected US household is 0.12. This means that there is a 12% chance of randomly selecting a US household with zero people residing in it.

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The system of equations is 3x - 2y = 1 and y = 5x - 4

The equations are given as:

Ax + By = C

y = mx + b

The solution is given as (1,1).

This means that:

Ax + By = C

A(1) + B(1) = C

A + B = C

y = mx + b

1 = m(1) + b

1 = m + b

By assuming values for the variables in the equation, we have:

A + B = C ⇒ 3 - 2 = 1

1 = m + b ⇒ 1 = 5 - 4

Hence, the system of equations is

3x - 2y = 1

y = 5x - 4

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The  values of x will f(x) > 0 for x < 0, and f(x) < 0 for -6 < x < 0 and x > -6.

To determine the values of x for which f(x) > 0, we need to find the intervals where the function is positive. Let's analyze the function f(x) = x*-x³-6x².

First, let's factor out an x from the expression to simplify it: f(x) = x(-x² - 6x).

Now, we can observe that if x = 0, the entire expression becomes 0, so f(x) = 0.

Next, we analyze the signs of the factors:

1. For x < 0, both x and (-x² - 6x) are negative, resulting in a positive product. Hence, f(x) > 0 in this range.

2. For -6 < x < 0, x is negative, but (-x² - 6x) is positive, resulting in a negative product. Therefore, f(x) < 0 in this range.

3. For x > -6, both x and (-x² - 6x) are positive, resulting in a negative product. Thus, f(x) < 0 in this range.  

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The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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Answer: 67

Step-by-step explanation:

We see a pattern where we multiply the number we added by previously by two.

For example, from 5 to 7, it is 2.

From 7 to 11, we add by 4.

From 11 to 19, we add by 8.

From 19 to 35, we add by 16.

This means the next number would be 32, adding 35 by 32 gives us 67,

Answer:

easy peasss

Step-by-step explanation:

i like pees

Answer:

-25

Step-by-step explanation:

Withdrawal means to take out. So you're taking out $25 out of your account, therefore it would be a negative.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The integer to represent a withdrawal of $25 would be -$25.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount withdrawal = $25

The integer to represent a withdrawal of $25 would be -$25.

Because withdrawal means we are taking the amount out of our account.

Thus,

The integer to represent a withdrawal of $25 would be -$25.

Option A is the correct answer.

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The formula for constructing a confidence interval estimate for the mean when the population standard deviation is unknown is given as: CI = x ± tα/2 * s/√n Where; CI = Confidence Interval x = Sample Mean tα/2 = t-distribution value at α/2 level of significance, n-1 degrees of freedom. s = Sample Standard Deviation n = Sample Size

Given; Sample Size (n) = 229 Sample Mean (x) = 30.1 hg Sample Standard Deviation (s) = 7.9 hg Confidence Level = 90%, which means that the level of significance (α) = 1 - 0.90 = 0.10 or α/2 = 0.05 and degree of freedom = n-1 = 228 Substituting the values into the formula, we get; CI = 30.1 ± t0.05, 228 * 7.9/√229We find t 0.05, 228 from the t-distribution table or calculator at α/2 = 0.05 level of significance and degree of freedom = 228, as follows:t0.05, 228 = ±1.646 (to three decimal places) Therefore; CI = 30.1 ± 1.646 * 7.9/√229CI = 30.1 ± 1.207CI = (30.1 - 1.207, 30.1 + 1.207)CI = (28.893, 31.307) The confidence interval estimate of the mean is (28.893, 31.307).Yes, these results are reliable because the sample size (n = 229) is greater than or equal to 30 and the data is normally distributed. Also, the confidence interval estimate of the mean is relatively narrow, which shows that the sample is relatively precise.

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The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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Answer:

Step-by-step explanation:

Step 5=x+x-2=-148

2x-2=-148

2×=-148+2

2x=-146

2×÷2=-146÷2

X=-73

Step 6 .No 1=73

No.2=75

Answer:

\(128 \pi/5 units^3\)

Step-by-step explanation:

The volume of the solid revolution is expressed as;

\(V = \int\limits^2_0 {\pi y^2} \, dx\)

Given y = 2x²

y² = (2x²)²

y² = 4x⁴

Substitute into the formula

\(V = \int\limits^2_0 {4\pi x^4} \, dx\\V =4\pi \int\limits^2_0 { x^4} \, dx\\V = 4 \pi [\frac{x^5}{5} ]\\\)

Substituting the limits

\(V = 4 \pi ([\frac{2^5}{5}] - [\frac{0^5}{5}])\\V = 4 \pi ([\frac{32}{5}] - 0)\\V = 128 \pi/5 units^3\)

Hence the volume of the solid is \(128 \pi/5 units^3\)

Answer:

a= 36°

Step-by-step explanation:

The shape given has a 90 degree angle. To fins the angle measurement of a, subtract 54 degrees from 90.

90 - 54 = 36

Answer:

total angel is 90

a+54=90

a=90-54

a=36

The calculated value of the total population of the country is 8530000

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

3582600 is 42%. of the total population of the country

This means that

42%. of the total population of the country = 3582600

Express as product

So, we have

42% * the total population of the country = 3582600

Divide both sides by 42%

the total population of the country = 3582600 /42%

Evaluate

the total population of the country = 8530000

Hence, the total population of the country is 8530000

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The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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Answer:

About 300 people.

Step-by-step explanation:

Since the number of people who went on Saturday (374) is about 30% of the total number of people who attended the library (1266), it is expected that about 300 people went to the Social Issues section of the 1000 that attended on Sunday.

The confidence interval for the proportion of employees that worked overtime in the last week is (0.72, 0.94).

To construct the confidence interval, we use the formula for the confidence interval for proportions. Given that the proportion of employees who worked overtime is 0.83, and the margin of error is 0.11, we can calculate the standard error using the formula:

SE = margin of error / 2

In this case, SE = 0.11 / 2 = 0.055.

To find the lower and upper limits of the confidence interval, we subtract and add the standard error from the sample proportion, respectively:

Lower limit = proportion - SE

Upper limit = proportion + SE

Calculating the limits, we have:

Lower limit = 0.83 - 0.055 = 0.775

Upper limit = 0.83 + 0.055 = 0.885

Therefore, the confidence interval for the proportion of employees that worked overtime in the last week is approximately (0.72, 0.94). This means that we can be 95% confident that the true proportion of employees who worked overtime falls within this interval.

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Answer:

Step-by-step explanation:

We are expected to solve for the total number of balloons they can get with $100

given that the expression for the total cost of balloons is given as

2b+12<100

We can proceed to solve for the total number of balloons they can buy, by solving for b we have

2b+12=100

2b=100-12

2b=88

divide both sides by 2 we have

2b/2=88/2

b= 44

Therefore they would get a total of 44 balloons  

Answer:

1:2

Step-by-step explanation:

Given ΔPQT ~ ΔPRS

The ratios of the sides of these triangles is the same

We are given QT = 15 and PS = 30

QT/PS= 15/30 = 1/2 or in proportion notation:

Therefore the scale factor 1/2 which can be written as 1:2