The ratio of boys to girls in a group is 5:3. If there are 18 more boys than girls, work out how
many people there are in total.

Answer:

<ABC= 86 degrees

Step-by-step explanation:

The inverse of the given matrix does not exist. To determine if the inverse of a matrix exists, we need to check if the matrix is invertible, which is equivalent to checking if the matrix has a nonzero determinant.

The given matrix is a 2x2 matrix with elements 4, 5, 7, and 9. To calculate the determinant, we multiply the diagonal elements and subtract the product of the off-diagonal elements. In this case, the determinant is (4 * 9) - (5 * 7) = 36 - 35 = 1. Since the determinant is nonzero, we conclude that the matrix is invertible. However, to find the inverse of the matrix, we need to calculate the matrix of cofactors, transpose it, and divide by the determinant.

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The area of each isosceles triangle is \(120cm^{2}\). Some of these triangles are used to make a larger triangle.

To solve the problem, we need to know more information about how the smaller triangles are arranged to form the larger triangle. However, we can make some observations based on the given information.

Since the isosceles triangle has a base of 16cm and a height of 15cm, we can use the formula for the area of a triangle:

Area \(= (1/2)\)x base x height

Area\(= (1/2)\) x \(16cm\) x \(15cm\)

Area \(= 120cm^{2}\)

So the area of each isosceles triangle is \(120cm^{2}\).

If we know the number of isosceles triangles used to make the larger triangle and how they are arranged, we could find the dimensions and area of the larger triangle using geometric properties and formulas.

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Tom’ mot recent book earned 10*4 time a much money a hi firt book. then The amount that Tom’s most recent book earn is 10^7.

How to illustrate the exponent?

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Since Tom’s most recent book earned 10*4 times as much money as his first book which was 10³.

The total amount of the recent book will be:

= 10⁴ × 10³

= 10^(4 + 3)

= 10^7

The amount is 10^7.

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The oil mixture that will have the stronger vanilla smell is Mora oil.

The mixture with the stronger vanilla smell will be the mixture that has a lesser percentage of lavender as a percentage of vanilla in the oil.

Elfa's lavender  percentage :

= 8 / 12 x 100 %

= 67 %

Mora's lavender percentage :

= 6 / 10 x 100 %

= 60 %

This shows that Mora's mixture will have a stronger vanilla smell because the lavender is less.

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To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.

The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.

The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.

Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.

Solving for b, we find b = 30.

Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.

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Answer:

5

Step-by-step explanation:

Since y equals 200 + 10x and y also equals 5x, then

200 + 10x = 50x

Subtract 10x from both sides.

200 = 40x

Divide both sides by 40.

5 = x

Answer: He must sell 5 sculptures.

Answers:

========================================================

Explanation:

If the original slope is a/b, then the perpendicular slope is -b/a

We flip the fraction and we flip the sign from positive to negative, or vice versa.

As an example, the slope 1/3 flips its fraction to 3/1 or just 3. Then we flip the sign to -3. So if the original slope is 1/3, then its perpendicular counterpart is -3.

Notice how the two slopes multiply to -1

(1/3)*(-3) = -1

This applies to any pair of perpendicular lines such that neither line is horizontal and neither line is vertical either.

------------------------

If the original slope is some whole number, then rewrite it as a fraction over 1

Example: 2 becomes 2/1

That way we can flip the fraction and the sign

-------------------------

If we had an original slope of 0, then it's the same as 0/1

Flipping the fraction leads to 1/0, but that's undefined. We cannot divide by zero. So that explains the answer to part e).

Going in reverse of this process, any line with undefined slope will be perpendicular to lines of slope 0.

horizontal lines have slope of 0

vertical lines have undefined slopes

-------------------------

For part g), you'll need to convert from a mixed number to an improper fraction

Use this formula

a & b/c = (a*c + b)/c

So this means,

1 & 1/2 = (1*2 + 1)/2 = 3/2

which leads to

-1 & 1/2 = -3/2

Then applying the rule "flip the fraction flip the sign" gets us from -3/2 to 2/3.

Answer:

52 marbles i think

Step-by-step explanation:

There is a probability of 22% that exactly 4 defective parts will be found in a sample of 100.

Probability of a machine producing a defective part is 0.05,

p = 0.05

q  = 1 - p = 1 - 0.05 = 0.95

n = 100

P(x)  = ⁿCₓ pˣqⁿ⁻ˣ

x = 4  

P(4) = ¹⁰⁰C₄(0.05)⁴(0.95)⁹⁶

P(4) = 0.215569

=  0.2156

0.2156 is the probability of finding exactly 4 defective parts from a sample of 100.

The probability of defective parts is the likelihood that a part will be defective. This can be due to a variety of factors, such as poor quality control, incorrect manufacturing process, or use of sub-standard materials. A high probability of defective parts can lead to serious problems, such as faulty products, safety hazards, and financial losses.

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The order of the steps for the bisection of line segment AB will be D, E, B, C, and A.

The first thing we do for bisecting any line segment is to take up a distance of more than the approximate half of the line segment and place the compass on either point of the line.

Hence the first point will be D. Place the compass on point A and open it wider than half the distance of the segment.

Since an arc on both sides of the segment has to be drawn, the next point will be E. Swing an arc above and below the segment.

Since the same thing has to be repeated for the other point, the next point will be B. Keeping the compass the same width, place the compass on point B, and swing an arc above and below the segment.

Now we have got 2 points above and below the line segment, the next point has to be C. Place points C and D on the intersection of the arcs created above and below segment AB.

The line intersecting these points and AB has to be the point that divides AB in half, and the last point will be A. Draw a line from point C to point D.

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Complete Question

What is the correct order of steps for bisecting segment AB?

A. Draw a line from point C to point D.

B. Keeping the compass the same width, place the compass on point B, and swing an arc above and below the segment.

C. Place points C and D on the intersection of the arcs created above and below segment AB.

D. Place the compass on point A, and open it wider than half the distance of the segment.

E. Swing an arc above and below the segment.

Therefore, the area of the triangle is 2√5 square units, expressed in simplest radical form.

To find the area of a triangle, we can use Heron's formula, which states that the area (A) of a triangle with side lengths a, b, and c is given by:

A = √(s(s - a)(s - b)(s - c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

Given the side lengths of the triangle as 4, 3, and 3 units, we can calculate the semi-perimeter:

s = (4 + 3 + 3) / 2

= 5

Now, substituting the values into Heron's formula, we have:

A = √(5(5 - 4)(5 - 3)(5 - 3))

= √(5 * 1 * 2 * 2)

= √(20)

= 2√5

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answer:

\(x - y =4\)

steps shown below:

The value of g(4) in the function is -5 which is option b

To find the value of g(4) in the composite function, we need to evaluate the function when x = 4

In the first equation, since x is greater than 4 already, we can't use ot.

Let's proceed to the second equation;

g(x) = -2x + 3, x ≤ 4

Let's put the value x = 4 into the equation;

g(4) = -2(4) + 3

g(4) = -8 + 3

g(4) = -5

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════════ ∘◦❁◦∘ ════════

════════════════════

x1 = (-4)

y1 = (-3)

x2 = (-5)

y2 = (-6)

════════════════════

slope = gradient (m)

════════════════════

\(m = \frac{y2 - y1}{x2 - x1} = \frac{( - 6) - ( - 4)}{( - 5) - ( - 3)} = \frac{( - 2)}{( - 2)} = 1 \)

════════════════════

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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Answer:

b

Step-by-step explanation:

The correct value of p(x<8) is 1.875.

To determine how probable something is gonna occur, use probability. It is a number between 0 and 1, where 0 denotes the absence of a possibility and 1 denotes the existence of one. By dividing the number of favorable outcomes by the entire number of potential possibilities, the probability of an occurrence is determined.

To find the probability that is greater than 8, we need to integrate this probability density function from 5.5 to 20.5:

P(X < 8) = ∫[5.5,20.5] f(x) dx

= ∫[5.5,20.5] (1/8) dx

= [x/8] from 5.5 to 20.5

= (20.5/8) - (5.5/8)

= 15/8

= 1.875.

Therefore, the correct probability is 1.875.

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The value of z-stat is -0.6721.

What is z stat?

The relationship between a value and the mean of a group of values is quantified by a Z-stat. The Z-stat is calculated using standard deviations from the mean. When a data point's Z-stat is 0, it means that it has the same score as the mean.

One standard deviation from the mean would be indicated by a Z-stat of 1.0. Z-stats can be positive or negative; a positive value means the score is above the mean, while a negative value means it is below the mean.

Solution Explained:

We use the formula,

\(z = \frac{P - \pi }{\sqrt{\frac{\pi (1-\pi )}{200} }}\), where P is the observed proportion, π is the hypothesized proportion

Therefore, P = 42/200 = 0.21 & π = 23/100 = 0.23

Putting the values in

\(z = \frac{0.21 - 0.23 }{\sqrt{\frac{0.23 (1-0.23)}{200} }}\)

After calculating, z-stat is therefore equal to -0.6721

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Answer:

  7

Step-by-step explanation:

You want the tangent lengths from point D for ∆DEF circumscribing a circle, given DE=15, DF=12, DF=13.

The lengths of the tangent segments from vertex D are ...

  d = (DE +DF -EF)/2 = (15 +12 -13)/2 = 7

The tangent segments with end point D are 7 units long.

__

Additional comment

The tangents from each point are the same length, so we have ...

  d + e = DE . . . . where d, e, f are the lengths of the tangents from D, E, F

  e + f = EF

  d + f = DF

Forming the sum shown above, we have ...

  DE +DF -EF = (d +e) +(d +f) -(e +f) = 2d

  d = (DE +DF -EF)/2 . . . . as above

The other tangents are e = 8, f = 5.

1. The equation of the line in slope-intercept form is:

y = -5x - 16

2. The equation of the line in standard form is: -x - 3y = -7

(a) To write the equation of the line passing through (-4,4) with a slope of -5 in slope-intercept form (y = mx + b), we can substitute the given values into the equation and solve for the y-intercept (b).

The slope-intercept form is:

y = mx + b

Given:

m = -5

x = -4

y = 4

Substituting the values into the equation:

4 = -5(-4) + b

Simplifying:

4 = 20 + b

b = 4 - 20

b = -16

Therefore, the equation of the line in slope-intercept form is:

y = -5x - 16

(b) To write the equation of the line passing through (-1,4) and parallel to the line x + 3y = 7, we need to determine the slope and use the point-slope form or standard form.

Given:

Point: (-1,4)

Parallel line: x + 3y = 7

To find the slope, we can rearrange the equation x + 3y = 7 to solve for y in terms of x:

3y = -x + 7

y = (-1/3)x + 7/3

The slope of the parallel line is -1/3.

(a) Slope-intercept form:

Using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) = (-1, 4), and m = -1/3, we have:

y - 4 = (-1/3)(x + 1)

y - 4 = (-1/3)x - 1/3

y = (-1/3)x + 11/3

Therefore, the equation of the line in slope-intercept form is:

y = (-1/3)x + 11/3

(b) Standard form:

To convert the equation to standard form (Ax + By = C), we can multiply both sides of the equation by 3 to eliminate the fraction:

3y = -x + 7

-x - 3y = -7

Therefore, the equation of the line in standard form is:

-x - 3y = -7

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The slope of the line which is perpendicular to the given line 3x+18y=108 is (6).

We already know the equation of a line in slope intercept form y = mx + b and we also know that perpendicular lines that have slopes which are negative reciprocals of each other.

Given a line 13x + 18y=108, this slope intercept form can be written as,

3x + 18y = 108

18y = 108 - 3x

y = (108 /18) - (3/18)x.

y = (6) - 1x/6.

y = -(1/6)x + 6.

Hence the slope of the given line is (-1/6), thus the slope of the line which is perpendicular is (6).

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Answer:

complementary angle

Step-by-step explanation:

hope this helps u

The nurse should dispose of the mask. This exists because the safety mechanisms of the mask may be compromised and therefore pose a risk to the patient that exists undergoing surgery.

A surgical mask exists primarily utilized to protect patients and healthcare employees from people who may contain a respiratory infection or to protect sterilized or disinfected medical devices and supplies. The nurse should dispose of the mask. This exists because the safety mechanisms of the mask may be compromised and therefore pose a risk to the patient that exists undergoing surgery. It exists still suggested that medical personnel err on the side of warning when it arrives to the managing of equipment, whether it be a significant piece of equipment or even a small one like a surgical mask.

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Answer:

3.14

Step-by-step explanation:

-8 - 92.5 = -100.5, and then -100.5/(-32) = 3.14

Alternatively, type in (-8 -92.5)/(-32)

Answer:

x = 70

Step-by-step explanation:

0.04 + 0.015x = 1.09 ( subtract 0.04 from both sides )

0.015x = 1.05 ( divide both sides by 0.015 )

x = 70

In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable, which is manipulated in order to observe its effect on the dependent variable.

In the analysis of variance procedure (ANOVA), factor refers to:
b. the independent variable

In ANOVA, a factor is an independent variable that is manipulated or controlled to investigate its effect on the dependent variable. Different levels of a factor represent the variations in the independent variable being tested. The different levels of a treatment are often created by manipulating the factor.
In contrast, independent variables are not considered dependent on other variables in various experiments. [a] In this sense, some of the independent variables are time, area, density, size, flows, and some results before the affinity analysis (such as population size) to predict future outcomes (dependent variables).

In both cases it is always a variable whose variable is examined through a different input, statistically also called a regressor. Any variable in an experiment that can be assigned a value without assigning a value to another variable is called an independent variable.

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Answer:

c 1:3

Step-by-step explanation:

2/6 divide it by 1/3 and u get 1:3

Answer:

≈ 3.9 miles

Step-by-step explanation:

The third angle in the triangle is

180° - (53 + 78)° = 180° - 131° = 49°

Using the Sine rule in the triangle with distance from 2 being x, then

\(\frac{3}{sin49}\) = \(\frac{x}{sin78}\) ( cross- multiply )

x × sin49° = 3 × sin78° ( divide both sides by sin49° )

x = \(\frac{3sin78}{sin49}\) ≈ 3.9 ( to the nearest tenth )