patricia baked some cupcakes for sale. she put half of the cupcakes equally into 6 big boxes and the other half equally into small boxes. There were 45 cupcakes in 3 big boxes and 8 small boxes altogether.
a) How many cupcakes dud Patricia bake?
b) She sold all the small boxes and collected $189. How much did she sell each small box for?​

9514 1404 393

Answer:

  1. a linear model

  3. y = 24.97x +417.59

  4. 75 workers

Step-by-step explanation:

1. A graph of the data seems to show it nearly follows a straight line. We have used a linear function to model the data.

3. The linear regression model is ...

  y = 24.97x +417.59

4. The graphing calculator shows the point (x, y) ≈ (75.4, 2300) is on the line of best fit. Marco should recommend 75 workers for production of 2300 units per hour.

If you want to solve the linear equation ...

  2300 = 24.97x +417.59

you get ...

  x = (2300 -417.59)/24.97 ≈ 75.4

About 75 workers are needed.

Copying the data set into another program allows you to leverage the capabilities of that program for Statistical analysis.

The provided data set can be copied into another program, such as a spreadsheet or a statistical software program, to perform various data analysis tasks. Let's explore some common operations that can be performed using the data set.

1. Descriptive Statistics: By copying the data set into a spreadsheet or statistical software, you can calculate various descriptive statistics, such as the mean, median, mode, standard deviation, and range of the data. These statistics provide insights into the central tendency, variability, and distribution of the data.

A

1   4

2   8

3   9

4   5

5   2

6   7

7   7

8   5

9   8

2. Data Visualization: Once the data set is copied, you can create visualizations to better understand the data. This can include bar charts, histograms, line plots, or box plots, depending on the nature of the data and the insights you want to gain.

3. Data Manipulation: Copying the data set into a spreadsheet allows you to manipulate and transform the data as needed. You can perform operations like sorting, filtering, grouping, and calculating new variables based on existing ones. This enables you to extract meaningful information from the data set.

4. Statistical Analysis: If you are using statistical software, you can conduct advanced statistical analyses on the data set. This may involve regression analysis, hypothesis testing, analysis of variance (ANOVA), or clustering techniques, depending on the specific research question or objective.

5. Data Integration: If you have additional data sets or variables related to the given data set, copying it into a program allows you to merge or join different data sets, thereby enriching the analysis and providing a more comprehensive understanding of the data.

Overall, copying the data set into another program empowers you to perform a wide range of data analysis tasks, enabling you to explore, understand, and draw meaningful insights from the data.

In summary, copying the data set into another program allows you to leverage the capabilities of that program for statistical analysis, calculations, and visualizations, enabling you to gain deeper insights and draw meaningful conclusions from the data.

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Answer:

The answer is 22. Sorry if I am wrong

Answer:

18

Step-by-step explanation:

Let's use x and y

x + y = 42

1/3x = 1/6y + 5

Multiply by 3 on both sides

x = 1/2y + 15

SUBSTITUTE X

1/2y + 15 + y = 42

Combine the two ys

1 1/2y + 15 = 42

minus 15 on both sides

1 1/2y = 27

y = 18

Now, find x by substituting y

x + y = 42

x + 18 = 42

x = 24

X is the greater number, y is the smaller number.

The smaller number is 18

a) The value of number is, 9.

b) The value of number is, 6.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

a) When you double my number and subtract 9, you get my original number.

b) When you double my number and add 5, you get 17.

For a;

Let a number = x

So, We can formulate;

When you double my number and subtract 9, you get my original number.

⇒ 2x - 9 = x

Solve for x;

⇒ 2x - 9 = x

⇒ 2x - x = 9

⇒ x = 9

For b;

When you double my number and add 5, you get 17.

⇒ 2x + 5 = 17

Solve for x;

⇒ 2x + 5 = 17

⇒ 2x = 17 - 5

⇒ 2x = 12

⇒ x = 6

Thus, We get;

a) The value of number is, 9.

b) The value of number is, 6.

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Step-by-step explanation:

The situation described can be modeled using a linear equation, where the balance of the savings account increases by a fixed amount every month. Specifically, the equation that represents this situation is:

balance = $5000 + $825 * months

where "months" represents the number of months that have passed since the account was opened. The slope of this line is constant at $825, indicating that the balance is increasing by the same amount every month.

Therefore, the model for this situation is linear.

The exact value of the given trigonometric function cot(π/3) is √3/3.

The cotangent (cot) of an angle is defined as the ratio of the adjacent side to the opposite side of a right triangle.

Here, given that an angle of π/3, which is not a right angle.

So, we need to use the trigonometric identities to find the value of cot(π/3).

cot(θ) = 1/tan(θ)

where θ is an angle in radians.

We know that the tangent of π/3 is √3, as this is the opposite side (which is the same as the sine) divided by the adjacent side (which is the same as the cosine) of a 30-60-90 right triangle.

So, cot(π/3) can be expressed as:

cot(π/3) = 1/tan(π/3)

= 1/√3

Multiplying the numerator and denominator by √3/√3, we get:

cot(π/3) = √3/3

Therefore, the exact value of cot(π/3) is √3/3.

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Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.

For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:

150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms

Therefore, 150 pounds is approximately equal to 68.0388 kilograms.

In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.

It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.

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Answer:1/4 of robot

Step-by-step explanation:

Answer:

-9.7

Step-by-step explanation:

Given

x + y when x =2.1 and y = -11.8​



Solution

x+y

substitute x=2.1 and y=-11.8

2.1+(-11.8)

2.1 - 11.8 = -9.7



The final answer is -9.7

Answer:

By flipping the second fraction (finding its reciprocal) we change the equation mathematically. In order to maintain the equation mathematically, we must turn the division question into a multiplication question.

Step-by-step explanation:

so basically what you have to do is

Answer:

I think 164

Step-by-step explanation:

1312/8

Mo must release this ball approximately halfway between straight-ahead and straight-up because the angle subtended must be 45 degrees with the horizontal axis.

Distance can be defined as the amount of ground covered (traveled) by a physical object, regardless of its direction, starting point or ending point.

In order to achieve the furthest travel distance, Mo must release this ball approximately halfway between straight-ahead and straight-up because the angle subtended must be 45 degrees with the horizontal axis, as shown in the image attached below.

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Using the Pythagoras theorem, we can find the value of x to be = 10ft.

Option B is correct.

The right-angled triangle's three sides are related in line with the Pythagoras theorem, also referred to as the Pythagorean theorem. The hypotenuse of a triangle's other two sides add up to a square, according to the Pythagorean theorem, which states that.

Here in the question,

We have 2 right-angled triangles.

So, base of the large triangle, x

= √ (13² - 12²) + √ (13² - 12²)

= √ 5² + √ 5²

= 5 + 5

= 10ft.

Therefore, the length of the side, x = 10ft.

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Answer:

The correct answer should be A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

Answer:

M(3,2) and N(3,1)

Step-by-step explanation:

The correct points which are vertices of the pre-image are,

M(3, 2) and N(3, 1)

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangle was rotated 270° about the origin.

Since, it doesn't mention which direction, we will review both clockwise and anti-clockwise rotation.

See attached where top rectangle represents the pre-image before anti-clockwise and bottom one - before clockwise rotation.

Now let's check the points given:

K(–3, –1)

No

M(–3, 2)

No

M(3, 2)

Yes, top one

N(–3, 1)

No

N(3, 1)

Yes, top one

So based on correct points of pre-image we can state it was rotation anti-clockwise.

Thus., The correct points which are vertices of the pre-image are,

M(3, 2) and N(3, 1)

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Answer:

1. C

2. A

3. A

Step-by-step explanation:

1. It is the Symmetric Property of Congruence because the definition is literally what it says.

2. Incomplete sentences don't matter as long as you have the right stuff.

3. Step 2 is wrong because it should be Definition of Midpoint.

If Curtis is attempting to defend a step in his proof paragraph. He should apply the symmetric property of congruence so that he can demonstrate that AB=BC and that BC=AB. It's best to choose C.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

A)If Curtis is trying to justify a step in his paragraph proof. Symmetric Property of Congruence that he should use as a result he can show AB=BC therefore BC=AB. Option C is correct.

B)All of the following would make a formal proof incomplete except Incomplete sentences. Option A is correct.

C)Step 2 in the proof has a flaw Because it is not a symmetric property while they show congruency because it must be a midpoint definition. Option A is correct.

Thus, if Curtis is trying to justify a step in his paragraph proof. Symmetric Property of Congruence that he should use as a result he can show AB=BC therefore BC=AB. Option C is correct.

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Answer: 18x-  9

Step-by-step explanation:

1.) Put the numbers in their correct lineup. 18 * x - 9

2. Add parentheses around 18 * x, secluding them away from the -9.
(18 * x) -9

3.) Remind yourself of PEMDAS (Parentheses, Exponents, Multiplication, Division, Add, and Subtract). In this equation, 18 * x are in parentheses().
(18 * x)

4.) Multiply 18 * x... Which equals 18x.

5. Equation should now look like : 18x - 9

6. You can't combine those two numbers because the coefficiant (The coefficiant is 18.) and the regular number (-9) are not equal.

8. Answer : 18x-9

The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

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Answer:

z<95

Step-by-step explanation:

z/5<19

5×7/5<5×19

z<95

Answer:

use sine or cosine rule

Step-by-step explanation:

that's the answer by using the sine rule

Answer:

Step-by-step explanation:

Answer:

-5/12

Step-by-step explanation:

you need to simplify both sides of the equasion, then isolate the variable

Answer:

y=2x

Step-by-step explanation: