A child grew 3 1/4 inches one year and 4 3/4 inches the next year. How many inches did the child grow over two years

a)The x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.

b)The co-ordinates of P and Q are (-5, -1) and Q = (1, 5).

The given equation of the circle is;

x² + y² = 26.

Th circle satisfies the line y = x + 4.

Thus, Put the value of y in the main equation.

x² + (x + 4)² = 26.

Simplify the equation;

x² + x² + 16 + 8x = 26

2x² + 8x - 10  = 0

Divide the equation by 2.

x² + 4x - 5  = 0  

Part a: This shows that x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.

Part b: Now, do the factorization of x² + 4x - 5  = 0.

(x + 5)(x - 1) = 0

x = -5 and 1.

For x = -5; y = -1

Point P = (-5, -1)

For x = 1; y = 5

Point Q = (1, 5)

Thus, the requires points P and Q are obtained.

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The total time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.

What is the concept of time and work?

Time and work defines the way how the particular work is done in the given time. It gives an exact relationship between the work and the number of days required to complete it.

Calculation of the total time taken by the machines A and B working together

Given that Machine A completes the entire job in 12 minutes.

So, machine A completes 1/12 of the job in one minute.

Machine B takes 18 minutes to complete the entire job.

So, machine B completes 1/18 of the job in one minute

When we combine their work, they will complete (1 / 12 + 1 / 18) job in one minute i.e.  (3 + 2) / 36 = 5/36 job in one minute     —---- 1

To find the time taketaken by them to produce x amount of peanut butter, we will reciprocate the result obtained in equation 1

i.e. 36 / 5 minutes to complete the entire job

i.e. 7.2 minutes

Hence, the time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.

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Answer:

[-3,∞)

Step-by-step explanation:

Since x is on the left side and is greater than -3, we will use a bracket in front of the -3. Since we do not know when the interval ends, we finish it with a positive infinity because we know that x is GREATER than (or equal) to -3. If it were less than -3, it would be negative infinity. Similarly, we use a rounded bracket because infinity is a positive value greater than -3.

The domain and range of trigonometric functions are as follows;

Function Domain Range

sin(x). All real numbers [-1, 1]

cos(x). All real numbers [-1, 1]

tan(x). {x| x ≠ -3•π/2, -π/2, π/2, } R

The domain and range of the inverse sine, cosine, and tangent are;

Function Domain Range

arcsin(x). (-1, 1) [-π/2, π/2]

arccos(x). (-1, 1) [0, π]

arctan(x) (-∞, ∞). [-π/2, π/2]

sin(x)

The domain of sin(x) is the set of possible values for x, for which sin(x) is defined, which is;

The range of sin(x) is the set of possible values output values of sin(x) is, which is; -1 ≤ sin(x) ≤ 1

cos(x)

Similarly;

tan(x)

tan(x) = sin(x)/cos(x), however, cos(x) = 0, when x = -3•π/2, -π/2, π/2, 3•π/2...

The domain of tan(x) is therefore;

sin(x) increases as cos(x) decreases, therefore;

The range of tan(x) = sin(x)/cos(x) is therefore;

arcsin(x)

The input of arcsin(x) is sin(x)

sin(x) = opposite/hypotenuse

Given that the magnitude of hypotenuse > opposite, the ratio, opposite/hypotenuse is < 1 in magnitude

The domain of arcsin(x) is therefore;

The range is the set of possible outputs, which is [-π/2, π/2], given that sin(x) is positive and negative from -π/2, π/2

arccos(x)

Similarly;

arctan(x)

The input of arctan(x) is tan(x)

tan(x) = sin(x)/cos(x)

The domain of arctan(x) is therefore;

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On simplifying  the given expression the no. that goes in green box is -7

The rule of addition of two numbers

adding two positive integers result in positive integer.

adding two negative integers results in the sum with a negative sign.

addition of two different signed Integer will result in subtraction only and the sign of the result is same as the larger number sign.

so

2 + 16x - 9 - 10x

6x + [-7]                   HERE [ 2 + (-9) = -7 ]

On simplifying  the given expression the no. that goes in green box is -7

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Answer:

The set of all whole numbers

Step-by-step explanation:

Real numbers, integers, and rational numbers can all contain negative numbers. Whole numbers include numbers from 0 and up.

Hope this helps!

Have a nice day

The pan that comes closest in area is the 8-inch square pan.

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

π = pi = 22/7

R = radius = diameter / 2 = 9/2 = 4.5 inches

22/7 x 4.5² = 63.64 in²

A square is a quadrilateral with four equal sides.

Area of a square = length²

8² = 64 in²

9² = 81 in²

10² = 100 in²

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Answer:

let y=0

3x+6(0)=18

3x=18

x=6

(6;0)

Answer: 3

Step-by-step explanation: If you solve the equation, like I did in the attached image, you will see that the x-intercept is 3.

Answer:

b=8

Step-by-step explanation:

-4b + 5 = -27

Move the 5 to the right side by subtraction, subtract five from the right side as well.

Now you should have:
-4b = -32

Now divide by -4 to get ‘b’ isolated, do this on both sides.

You should be left with:
b=8

10 combinations of two parts can be selected.

Combination is defined as the number of arrangements in a collection of items where the order of selection does not matter.

denoted by C(n,x)= ⁿcₓ=[tex]\frac{n!}{(x!)(n-x)!}[/tex]  ,

where n is the total number of elements in the set.

x is the number of selected objects.

According to the Question

Total number of elements = 5 = n

Number of objects to be selected = 2 = x

Substituting the values in the above formula

C(5,2)=[tex]\frac{5!}{2!*3!}[/tex]

[tex]=\frac{5*4*3!}{2*3!} \\ \\ =\frac{20}{2} \\ \\ =10[/tex]

Therefore , 10 combinations of two parts can be selected.

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The measure of the angle the minute hand traces in 36 minutes is 3.77 radians

From the question, we are to determine the measure of the angle the minute hand traces in 36 minutes

The minute hand makes a complete rotation after 60 minutes.

Thus,

The angle the minute hand would have traced in 36 minutes is

36/60 × 360°

= 12960/60

= 216°

Now, convert to radians

216° = 216 × π/180 rad

= 3.77 rad

Hence, the measure of the angle the minute hand traces in 36 minutes is 3.77 radians

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Answer:

The product is rational.

Step-by-step explanation:

A large polymeric molecule that is nonpolar over most of its structure but very polar at one end DNA and Phospholipid.

DNA and phospholipid were two examples of huge polymeric molecules that would be polar solely on a single end although nonpolar on the majority of their structure, as opposed to the other alternatives, which would be all monomeric compounds. Nucleotides are used to help DNA create its polymeric structure. Phosphodiester linkage aids in the arrangement of the nucleotides.

The polar molecule would only be found in one area of the vast strand-like polymeric structure. At one extremity of the strand, there is a polar phosphate link; with its assistance, some other monomeric units were joined, generating the phosphodiester bonds. Two fatty acids and the first molecule of glycerol work together to generate the structure known as the phosphodiester.

The phosphate group is present in the polar head region of the phosphate group. This help in the polarity of the phospholipid structure making the head region of the polymeric molecule hydrophilic.  

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The rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.

We know that the rate is nothing but the ratio of two different quantities which have different units.

In this question, we have been given two pounds of grapes cost $5

First we find the rate in pounds per dollar.

2 pounds of grapes = $5

As rate is the ratio of two different quantities, we find the ratio (pounds per dollar).

= 2 pounds /5 dollars

= (2/5) pounds per dollar

= 0.4 pounds per dollar              .......(1)

This means the rate of grapes is 0.4 pounds per dollar.

In this question, we have been given  Jordan says that's 2.5 pounds per dollar and Emika says it's 0.4 pounds per dollar.

From (1), we can clearly say that Emika is correct.

Therefore, the rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.

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If there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use

Given,

The conditions

We know

In multiple regression method the dependent variables are predicted by using the known independent variables. This method is usually used to analyze the relationship between multiple independent variables and one independent variables,

So here multiple regression method is using.

Hence, if there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use

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Option D is the correct answer (We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%)

Since the confidence interval is calculated for population proportion (parameter) based on sample data.

Because the figure is based on a sample of the population you are investigating; there is always uncertainty when you generate an estimate in statistics, whether it be a summary statistic or a test statistic. The confidence interval is the range of values. If you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time. The alpha value determines the confidence level, the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.

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Answer: your answer would be unimodal skewed. This graph only has one maxima, thus it can't be bimodal. However, it's not symmetric, meaning that it is skewed

Hope this helps you

Step-by-step explanation:

The histogram is solved and it is uni-modal skewed

A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable.

A histogram displays the frequency distribution of a set of continuous data. It is useful for visualizing the shape of the data distribution, such as whether it is symmetrical or skewed, and identifying any outliers or gaps in the data.

Given data ,

Let the histogram be represented as A

Now , the value of A is plotted on the graph

A. Unimodal skewed: This distribution has one peak (mode) and the tail of the distribution extends to one side. Depending on which side the tail is longer, it can be either positively skewed (tail extends to the right) or negatively skewed (tail extends to the left).

B. Bimodal symmetric: This distribution has two distinct peaks (modes) and is symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.

C. Unimodal symmetric: This distribution has one peak (mode) and is roughly symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.

D. Bimodal skewed: This distribution has two distinct peaks (modes) and the tail of the distribution extends to one side for each peak. Depending on which side each tail is longer, it can be either positively skewed (tail of one peak extends to the right and the other to the left) or negatively skewed (tail of one peak extends to the left and the other to the right).

E. Uniform: This distribution is flat and has roughly equal frequency for all values in the range of the dataset.

Hence , the histogram is unimodal skewed

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It can be seen that the mistake that was made by Marvin was on line 1.

2x² - 8x + 5.... move the 5 to the other side

2x² - 8x = -5

Now divide by 2

x² - 4x = -5/2

x² - 4x + 4 = -5/2 + 4

(x - 2)² = -5/2 + 8/2

(x - 2)² = 3/2

x - 2 = (+-)sqrt 3/2

x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2

Therefore, he made his mistake on line 1.

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Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27

debt-equity ratio is 0.92.

A firm's total liabilities and shareholder equity are compared using the debt-to-equity (D/E) ratio, which may be used to determine how heavily reliant a company is on debt. D/E ratios vary by sector and are most useful for comparing a firm to its closest rivals or tracking changes in its reliance on debt over time. When comparing similar organizations, a larger D/E ratio denotes greater risk, whereas a very low one can signify that a company is not utilizing debt funding to grow. Since long-term debt entails greater risk than short-term commitments, investors frequently change the D/E ratio to simply take it into account.

Debt-equity ratio is computed as follows:

= total debt ratio / (1 - total debt ratio)

= 0.48 / (1 - 0.48)

= 0.48 / 0.52

= 0.92

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Answer:

π/2 and ³√4

also -4.8237 and π/2

Step-by-step explanation:

number 2 and 4 are automatically out since every integer is a rational number.

√25 = 5 and 5 + 4 = 9, 9 can be expressed as 9/1 which falls under rational numbers.

π/2 on the other hand is not rational same goes for -4.8237 and ³√4 because these numbers cannot be written as a fraction with integers.

for the above numbers π/4 and ³√9 are irrational.

The value not in the solution is x = -10.2

The inequality expression is given as:

-4x - 6.8<34

Add 6.8 to both sides of the inequality

So, we have:

-4x < 40.8

Divide both sides by -4

x > -10.2

This means that only values greater than -10.2 are in the solution set

Hence, the value not in the solution is x = -10.2

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Answer:

989

Step-by-step explanation:

Answer:

986

The image after a dilation with a scale factor of 3 is A(-6, -3), B(0, 3), and C(3, -9) of triangle ABC.

Here, the coordinates are,

D = (-2, -1)

E = (0 , 1)

F = (1, -3)

After dilating triangle DEF using a scale factor of 3 and a center of dilation at the origin to form triangle ABC.

A = (-2 x 3, -1 x 3) = (-6, -3)

B = (0 x 3, 1 x 3) = (0, 3)

C = (1 x 3, -3 x 3) = (3, -9)

Line segments,

AB = 8.48

BC = 12.36

CD = 10.81

Therefore, after dilation by using a scale factor of 3 is  A(-6, -3), B(0, 3), and C(3, -9).

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Answer:

yes

Step-by-step explanation:

if (a,b) is on the graph of f(x) then (-a,-b) is on the graph of f^-1(x)

The answer of 18 is y = 0.5x + 0

The answer of 22 is y =  -0.4x + 0

Step-by-step explanation:

c is constant, m is gradient

18. m = 1/2

     m = 0.5

     1 = 0.5(2) + c

     1 = 1 + c

     c = 0

     y = 0.5x + 0

22. m = 2/-5

      m = -0.4

      2 = -0.4(-5) + c

      2 = 2 + c

      c = 0

      y = -0.4x + 0

The following can be used to rewrite the provided expression:            6(24) = 6(20 + 4).

The distributive Property states in that it is necessary to multiply every one of the two numbers by the factor before performing the addition operation when a factor is multiplied by that of the sum or addition of two terms. The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive principle of binary operations.

The following generic form can be used to specify the distribution property:

a(b+c) = ab + bc

the following expression:

6(24)

We can observe the following by contrasting this to the general form:

a = 6

b + c = 24

Consequently, we must identify two integers from the options whose sum is 24.

These numbers, out of the options provided, are 20 and 4.

The following can be used to rewrite the provided expression:            6(24) = 6(20 + 4).

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Jarome can make 6 whole pizzas with the leftover cheese.

Given that Jarome uses 2 1/2 cups of cheese for every 2 3/4 pizzas. He has 6 1/4 cups of cheese left in the bag.

We need to determine the number of pizza pies can he make with the leftover cheese.

To find out how many pizza pies Jarome can make with the leftover cheese, we need to determine how many sets of 2 3/4 pizzas can be made using 6 1/4 cups of cheese.

Let's start by finding the number of sets of 2 3/4 pizzas that can be made from 6 1/4 cups of cheese:

Number of sets = Total cheese available / Cheese per set

Number of sets = 6 1/4 cups / 2 1/2 cups per set

To make the calculation easier, let's convert all the mixed numbers to improper fractions:

6 1/4 cups = (4 x 6 + 1) / 4 = 25/4 cups

2 1/2 cups = (2 x 2 + 1) / 2 = 5/2 cups

Number of sets = (25/4) / (5/2)

Now, to divide fractions, we invert the divisor (5/2) and multiply:

Number of sets = (25/4) x (2/5)

= (25 x 2) / (4 x 5)

= 50/20

= 5/2

So, Jarome can make 5/2 sets of 2 3/4 pizzas with 6 1/4 cups of cheese.

Now, let's see how many pizzas he can make with the leftover cheese:

To calculate the number of pizzas in 5/2 sets, we multiply it by the number of pizzas per set (2 3/4 pizzas):

Number of pizzas = (5/2) x (2 3/4)

Again, let's convert all the mixed numbers to improper fractions:

2 3/4 pizzas = (4 x 2 + 3) / 4 = 11/4 pizzas

Number of pizzas = (5/2) x (11/4)

Now, when multiplying fractions, we simply multiply the numerators together and the denominators together:

Number of pizzas = (5 x 11) / (2 x 4) = 55/8

So, Jarome can make 55/8 pizzas with the leftover 6 1/4 cups of cheese.

Now, let's simplify the fraction:

55/8 = 6 7/8

Therefore, Jarome can make 6 7/8 pizzas with the leftover 6 1/4 cups of cheese.

Since we can't make a fraction of a pizza, he can make 6 whole pizzas with some cheese left over.

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A) Variance = 10.24

B) Standard Deviation = 3.2

One of the measurements of dispersion is the standard deviation, which is exclusively used for quantitative data. It aids in determining if the data's mean is a suitable measurement to reflect the core value.

TIME         FREQUENCY(f)  MIDPOINT(x)    d    d²     fd              fd²

0 - 0.9         43                          0.45             -3     9     -129            387

1.0 - 1.9         17                           1.45              -2    4     -34                68

2.0 - 2.9       19                            2.45             -1     1       -19               19

3.0 - 3.9        18                            3.45             0     0       0                  0

4.0 - 4.9        14                            4.45              1      1        14               14

5.0 -5.9         16                            5.45              2     4        32             64                            

∑f = 127                                                              

∑fd = -136  

∑fd² = 552

[tex]d = \frac{x - 3.45}{1}[/tex]

Standard Deviation = [tex]\sqrt \frac{fd^{2} }{N} - \sqrt \frac{(fd)^{2} }{N} * i[/tex]

[tex]\sqrt \frac{552}{127} -\sqrt (\frac{-136}{127})^{2} * 1[/tex]

√4.35 - √1.15

Standard Deviation = 3.2

(SD)² = (3.2)² = 10.24

Variance = 10.24

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