#9.
The table represents some points on the graph of linear function f.
Which function represents f ?
f(x)=32(3 x-1)
f(x)=-32(x-3)
f(x)=-2(32 x-3)
f(x)=16(2 x-1)

No, I don't agree with Sundeep. The mixture wont simply add up

When two liquids are mixed together, their volumes don't simply add up to equal the total volume of the mixture.

When sugar is mixed with water, the total volume of the mixture is usually slightly greater than the volume of the water alone, because the sugar particles take up space between the water molecules.

The volume of the mixture will be equal to the sum of the individual volumes only if the two liquids are completely immiscible, meaning they don't mix together at all. In this case, the total volume of the mixture will be equal to the sum of the volumes of water and sugar, which is 400 mL.

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Answer:

86

Step-by-step explanation:

=> \(7+(10-4)^2 /4 (\frac{1}{2} )^3\)

=> \(7+(6)^2 / 4(\frac{1}{8})\)

=> \(7+36 / \frac{1}{2}\)

=> \(43 * 2\)

=> 86

Answer:

When we dilate a figure with a scale factor between 0 and 1, the size of the figure shrinks but maintains the same orientation as the original figure. Therefore the correct option is B.

The area of the figure in this problem is given as follows:

131 cm².

The figure is a composite figure, hence the total area of the figure is given by the sum of the areas of each part that compose the figure.

The figure is composed as follows:

Hence the area of the figure is given as follows:

A = 0.5 x 16 x 7 + 4 x 11 + 4 x 1 + 3 x 9

A = 131 cm².

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Answer:

  745

Step-by-step explanation:

You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.

We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...

  (2x +298)/(5x +298) = 4//7

Cross multiplying gives ...

  7(2x +298) = 4(5x +298)

  3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))

  149 = x

  745 = 5x . . . . . . the original number of books in the library

There were 745 books in the library at first.

__

Additional comment

If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...

  2/5x +298 = 4/7(x +298)

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Answer:

x = 20

y = 10

Step-by-step explanation:

Rewrite the 2nd equation to make x the subject:

x + y = 30  ⇒  x = 30 - y

Substitute  x = 30 - y  into the first equation and solve for y:

20(30 - y) + 25y = 650

600 - 20y + 25y = 650

           600 + 5y = 650

                      5y = 50

                        y = 10

Substitute found value of y into  x = 30 - y to find x:

x = 30 - 10 = 20

So x = 20 and y = 10

Solution

We can find the individual parts of the area and we got:

And the total area would be:

then the final answer would be 64 ft^2

Answer:

Your second answer, otherwise know as 1 in. : 4ft. is the answer.

Step-by-step explanation:

The new map is 3 times bigger than the old map, therefore your given scale for the first map will shrink by 3 to compensate for the new map being bigger. Divide 12ft by 3 and you get 4 ft., so your answer is 1in. : 4ft.

The volume of the rectangular prism is 208cm³

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a rectangular a prism is expressed as base area × height. The base area is a rectangle and the area of a rectangle is Length × width

length = 2cm

width = 13 cm

height = 8cm

base area = 13× 2 = 26cm²

Volume of the prism = 26× 8 = 208cm³

Therefore the volume of the rectangular prism is 208cm³.

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Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

There are different types of triangulation, such as investigator triangulation, data triangulation, and interdisciplinary triangulation.

Let's dive deeper into each of these types:

This type of triangulation involves using multiple investigators or researchers to collect and analyze data. By involving more than one person, the likelihood of errors, biases, or individual perspectives influencing the results is reduced.

This type of triangulation involves using different methods, sources, or types of data to cross-check and confirm findings.

This type of triangulation involves using perspectives or methods from different disciplines to analyze data or solve a research question. By using different perspectives, the researcher can gain a more holistic understanding of the topic.

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Answer:

Verified

Explanation:

Given the identity:

We apply the following identity:

Therefore:

Thus, the identity is verified since both sides of the identity are equal.

Answer:

x>_-1

Step-by-step explanation:

x is such that x is greater or equal to -1

The best measure of variability to use for the distribution of dolphins sighted by the tour boat over 30 days is the interquartile range.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.

The interquartile range is the range of values that lie between the 25th and 75th percentile of the data set. This measure of variability is particularly useful when dealing with skewed distributions. It allows us to better understand the spread of values within the data set, in this case, the number of dolphins sighted. This measure is preferable to the mean and median because it is more resistant to outliers and is more representative of the data set. The mean absolute deviation can also be used to measure the variability of the data set, but it is less robust than the interquartile range.

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Find: the graph of -7i

Explanation:

Final answer: option d is correct option.

Answer:

29+3374=32483 that is the solution for the question

Answer:

4-1

Step-by-step explanation:

i think thats right

Answer: 8 bags.

Step-by-step explanation:

It is given that, a make-your-own ice pop kit says to pour 4 fluid ounces of juice into each bag.

We need to find the number of ice pop bags we can fill with 1 quart of juice.

We know that,

1 quart = 32 ounces

We have  32 ounces of juice and each bag contains 4 fluid ounces.

\(\text{Number of ice pop bags}=\dfrac{\text{Total juice}}{\text{Juice contained in each bag}}\)

\(\text{Number of ice pop bags}=\dfrac{32}{4}\)

\(\text{Number of ice pop bags}=8\)

Therefore, 8 ice pop bags we can  fill with 1 quart of juice.

Answer:

8 bags

Step-by-step explanation:

Answer:

B. because 6×1000 = 6000

Answer:

Its 25

Step-by-step explanation:

It is 25 as 4x5 is 20 so u have the denominator so u do the same for 5 , 5x5 is 25 so 4/5=20/25

The perimeter οf Shape is 286.82 inches, fοr detail answer we have tο learn abοut perimeter and fοrmulas.

Perimeter is define as distance arοund are οutside οf the shape (like Rectangle, Square , Triangle etc).

Perimeter οf Equilateral Triangle = \(\frac{\sqrt{3} }{4}\) side²

Here Side = 24 inch

Sο, Perimeter οf Equilateral Triangle = \(\frac{\sqrt{3} }{4}\) × 24²

=  \(\frac{\sqrt{3} }{4}\) × 24 × 24

= √3 × 24 × 6

= 249.41 inches

Perimeter οr Circumference οf Semi-Circle = πr + 2r

But here Perimeter = πr ( Since the base οf Semi Circle is Cοunted in Perimeter οf Equilateral Triangle)

3.14 × 12

= 37.68 inches

Sο, the perimeter οf Shape

= 249.41 + 37.68

= 286.82 inches

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\({\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}\)

Let \(\alpha\) and \(\beta\) be the two zeroes of P(x) = \(\sf {a}^{2} + bx + c\)

• A polynomial is always equal to it's factors, also the constant "k" is not equal to zero

\( \tt \sf {a}^{2} + bx + c = k(x - \alpha )(x - \beta )\)

• Using distributive property

\(\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} - \beta x - \alpha x + \alpha \beta \bigg)\)

\(\tt \sf {a}^{2} + bx + c = k {x}^{2} -k (\beta x )- k(\alpha x )+k( \alpha \beta )\)

• Taking common

\(\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)\)

• Equating coefficients of like terms

\( \sf \: a = k - - (2)\)

\( \sf b = - k( \alpha + \beta ) - - (3)\)

\( \sf c = k \alpha \beta - - (4)\)

★ From 3

\( \sf b = - k( \alpha + \beta ) - - (3)\)

★ From 2 we have a = k so we have -

\( \sf b = - a( \alpha + \beta ) \)

\(\sf - \dfrac{b}{a} = ( \alpha + \beta ) \)

\(\sf \therefore \boxed {{ \red{( \alpha + \beta ) = - \dfrac{b}{a} } }}\)

• Sum of zeros = \(- \dfrac{b}{a}\)

★ From 4

\( \sf c = k \alpha \beta - - (4)\)

★ From 2 we have a = k so we have -

\( \sf c = a \: \alpha \: \beta\)

\(\sf \dfrac{c}{a} = \alpha \beta\)

\(\sf \therefore \boxed {{ \red{( \alpha \beta ) = \dfrac{c}{a} } }}\)

• Product of zeros = \( \dfrac{c}{a}\)

Also,

★ From 1

\(\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)\)

\(\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( \alpha + \beta ) + ( \alpha \beta \bigg) \)

• Now just put S instead of sum of zeroes and P instead of product of zeroes

\( \tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( S ) + ( P \bigg) \)

\(\tt \sf{a}^{2} + bx + c = \boxed{ \red{ \sf \tt k \bigg( {x}^{2} - Sx + ( P \bigg ) }}\)

\(\rule{280pt}{2pt}\)

The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.

Please find attached the graph of the residual plot for the data created with MS Excel

A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.

The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158

The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;

Area (in²)    \({}\)              Residuals

x-value

5 \({}\)                             -1.0178

10 \({}\)                           -0.2718

24 \({}\)                           0.605

46 \({}\)                           0.7874

53 \({}\)                           0.7018

78 \({}\)                           0.0758

84 \({}\)                           -0.129

100 \({}\)                         -0.7538

The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option

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The three consecutive multiples of 3 are 15, 18 and 21

First, let's determine three successive multiples of 3:

The subsequent two would be "x+3" and "x+6" if we call the initial number "x".

Since we are aware that the third number (x+6) is one more than the first two numbers (x + x+3), we can write the following equation:

2/3(x + x+3) = (x+6) + 1

Simplifying this equation, we get:

2/3(2x+3) = x+7

Multiplying both sides by 3, we get:

2(2x+3) = 3(x+7)

Expanding and simplifying, we get:

4x + 6 = 3x + 21

Subtracting 3x and 6 from both sides, we get:

x = 15

Therefore, the three consecutive multiples of 3 are 15, 18 and 21

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We can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

To determine the interval within which 95 percent of the sample means will fall, we need to calculate the margin of error using the standard deviation and the desired level of confidence.

The formula to calculate the margin of error is given by:

Margin of Error = Z * (Standard Deviation / √n)

Where:

Z is the critical value corresponding to the desired level of confidence

Standard Deviation is the standard deviation of the population

n is the sample size

Since the sample size is 41 and we want to find the interval at a 95 percent confidence level, we need to find the critical value corresponding to a 95 percent confidence level.

The critical value can be found using a standard normal distribution table or a calculator. For a 95 percent confidence level, the critical value is approximately 1.96.

Now we can calculate the margin of error:

Margin of Error = 1.96 * (0.0050 / √41)

Calculating this, we find:

Margin of Error ≈ 0.001624

To find the interval within which 95 percent of the sample means will fall, we need to subtract and add the margin of error to the true mean:

Interval = True Mean ± Margin of Error

Interval = 0.9550 ± 0.001624

Calculating this, we find:

Interval ≈ (0.9534, 0.9566)

Therefore, we can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

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To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.